Hướng dẫn pascal triangle using recursion in c++ - tam giác pascal sử dụng đệ quy trong c++

Question

Có một số vấn đề với mã của bạn như điều kiện chấm dứt đệ quy:

Nội dung chính Show

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 31 1 1 1 2 1 1 3 3 1 1 4 6 4 1 5 for8
#include long paskal(int, int); int main() { int n = 0; int m = 0; int k = 0; int s = 0; printf ("Enter number of rows:\n"); scanf("%d", &n); for(k = 0; n >= k; k++) { for(s = 0; s < n-k; s++) //Add spaces before each row printf(" "); for(m = 0; k >= m; m++) { long f = paskal(k, m); printf("%ld ", f); } printf("\n"); } return 0; } long paskal(int n, int i) { if(n == i || i == 0) return 1; else return paskal(n-1, i) + paskal(n-1, i-1); } 82 #include long paskal(int, int); int main() { int n = 0; int m = 0; int k = 0; int s = 0; printf ("Enter number of rows:\n"); scanf("%d", &n); for(k = 0; n >= k; k++) { for(s = 0; s < n-k; s++) //Add spaces before each row printf(" "); for(m = 0; k >= m; m++) { long f = paskal(k, m); printf("%ld ", f); } printf("\n"); } return 0; } long paskal(int n, int i) { if(n == i || i == 0) return 1; else return paskal(n-1, i) + paskal(n-1, i-1); } 83
Công thức đệ quy cho tam giác của Pascal là gì?
Tam giác của Pascal trong C là gì?
Tam giác Pascal giải thích với một ví dụ là gì?
Pascal có hỗ trợ đệ quy không?

if(n == 1 && i == 1 )

Điều này không đúng và dẫn đến việc tái sử dụng chức năng mãi mãi và cuối cùng chương trình sẽ chấm dứt bất thường.

Hơn nữa, nếu bạn sửa chữa điều kiện này, bạn sẽ không lấy hình tam giác Pascal làm đầu ra vì cả hai vòng ____99 trong

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0 đều khởi tạo biến vòng lặp với

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1 sẽ ăn hết cột đầu tiên của mỗi hàng hình tam giác Pascal.

Đối với điều kiện chấm dứt của chức năng đệ quy

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

2 -

Trong hàm

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

3,

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

4 đại diện cho hàng trong khi

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

5 biểu thị cột trong hàng cụ thể đó và hàm

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

6 được cho là để tính toán phần tử tại một vị trí cụ thể.

Một vài điểm, trong Tam giác Pascal:

Phần tử ngoài cùng bên trái và ngoài cùng bên phải của mỗi hàng là
```
if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;
```
1.
Mỗi hàng chứa số lượng cột giống như số hàng.

Vì vậy, tôi có thể nói -

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

có thể là điều kiện chấm dứt của chức năng đệ quy.

Chung, chương trình của bạn sẽ là một cái gì đó như thế này:

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

Hi vọng điêu nay co ich.

Tam giác Pascal là một mảng hình tam giác gồm các hệ số nhị thức. Viết một hàm lấy giá trị số nguyên n làm đầu vào và in đầu tiên n của tam giác pascal. Sau đây là 6 hàng đầu tiên của hình tam giác Pascal.

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

Phương pháp 1 (O (N^3) Độ phức tạp thời gian) & NBSP; Số lượng mục nhập trong mỗi dòng bằng số dòng. Ví dụ, dòng đầu tiên có 1 1, dòng thứ hai có 1 1 1, dòng thứ ba có dòng 1 1 1 1, .. v.v. Mỗi mục trong một dòng là giá trị của một hệ số nhị thức. Giá trị của mục nhập ith trong dòng dòng là c (dòng, i). Giá trị có thể được tính bằng cách sử dụng công thức sau. & Nbsp;
The number of entries in every line is equal to line number. For example, the first line has “1”, the second line has “1 1”, the third line has “1 2 1”,.. and so on. Every entry in a line is value of a Binomial Coefficient. The value of ith entry in line number line is C(line, i). The value can be calculated using following formula.

C(line, i)   = line! / ( (line-i)! * i! )

Hướng dẫn pascal triangle using recursion in c++ - tam giác pascal sử dụng đệ quy trong c++

Một phương pháp đơn giản là chạy hai vòng và tính giá trị của hệ số nhị thức trong vòng lặp bên trong. & NBSP;

C++

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

8

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

1

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

7

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

C(line, i)   = line! / ( (line-i)! * i! )

5

C(line, i)   = line! / ( (line-i)! * i! )

6

C(line, i)   = line! / ( (line-i)! * i! )

7

C(line, i)   = line! / ( (line-i)! * i! )

8

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )

6

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

8

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

9

C(line, i)   = line! / ( (line-i)! * i! )

0

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5

6

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2 for3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

7

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

C(line, i)   = line! / ( (line-i)! * i! )

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

27

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

28

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

29

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

30

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

8

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

9

C(line, i)   = line! / ( (line-i)! * i! )

0

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5

6

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2 for3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

Java

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

83

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

84

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

86

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

99

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

01

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

10

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

12

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

13

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

14

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

18

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

35

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

7

8

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

0

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

49

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

5

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

9

C(line, i)   = line! / ( (line-i)! * i! )

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

55

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

5

6

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

69

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

74

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

75

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

Python3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

82

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

83

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

86

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

88

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

91

C(line, i)   = line! / ( (line-i)! * i! )

0for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

94

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

C(line, i)   = line! / ( (line-i)! * i! )

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

05

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

06

C(line, i)   = line! / ( (line-i)! * i! )

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

08

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

10

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

13

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

82

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

15

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

222

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

23

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

24

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

26

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

28

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

23

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

30

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

94

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

43

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

44

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

23

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

46

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

51

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

51

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

53

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

00

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

59

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

28

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

75

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

63

C#

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

65

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

86

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

99

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

01

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

10

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

89

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

13

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

14

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

95

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

35

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

7

8

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

0

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

49

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

5

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

9

C(line, i)   = line! / ( (line-i)! * i! )

5

1

C(line, i)   = line! / ( (line-i)! * i! )

0

5

6

C(line, i)   = line! / ( (line-i)! * i! )

0

5

6

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

69

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2 for3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 31 1 1 1 2 1 1 3 3 1 1 4 6 4 1 5 for8

C(line, i)   = line! / ( (line-i)! * i! )

51

Java

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

83

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

84

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

86

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

99

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

01

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

10

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

35

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

7

8

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

49

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

5

6

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

69

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

74

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

75

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

54

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

56

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

C(line, i)   = line! / ( (line-i)! * i! )

54

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

60

#include long paskal(int, int); int main() { int n = 0; int m = 0; int k = 0; int s = 0; printf ("Enter number of rows:\n"); scanf("%d", &n); for(k = 0; n >= k; k++) { for(s = 0; s < n-k; s++) //Add spaces before each row printf(" "); for(m = 0; k >= m; m++) { long f = paskal(k, m); printf("%ld ", f); } printf("\n"); } return 0; } long paskal(int n, int i) { if(n == i || i == 0) return 1; else return paskal(n-1, i) + paskal(n-1, i-1); } 82 #include long paskal(int, int); int main() { int n = 0; int m = 0; int k = 0; int s = 0; printf ("Enter number of rows:\n"); scanf("%d", &n); for(k = 0; n >= k; k++) { for(s = 0; s < n-k; s++) //Add spaces before each row printf(" "); for(m = 0; k >= m; m++) { long f = paskal(k, m); printf("%ld ", f); } printf("\n"); } return 0; } long paskal(int n, int i) { if(n == i || i == 0) return 1; else return paskal(n-1, i) + paskal(n-1, i-1); } 83

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

61

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

C(line, i)   = line! / ( (line-i)! * i! )

52

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

63

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

69

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

74

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

76

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

13

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

14

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

82

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

83

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

C(line, i)   = line! / ( (line-i)! * i! )

52

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

91

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

95

C(line, i)   = line! / ( (line-i)! * i! )

0

7

8

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

0

C(line, i)   = line! / ( (line-i)! * i! )

0____9

03

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

5

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

9

C(line, i)   = line! / ( (line-i)! * i! )

5

1

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

5

6

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

18

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

21

Đầu ra

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

Độ phức tạp về thời gian: O (n^3) Không gian phụ trợ: O (1)O(n^3)
Auxiliary Space: O(1)

Phương pháp 2 (O (N^2) Thời gian và O (N^2) Không gian bổ sung) & nbsp; Nếu chúng ta tiến gần hơn ở tam giác, chúng ta quan sát thấy mọi mục nhập là tổng của hai giá trị trên nó. Vì vậy, chúng ta có thể tạo một mảng 2D lưu trữ các giá trị được tạo trước đó. Để tạo giá trị trong một dòng, chúng ta có thể sử dụng các giá trị được lưu trữ trước đó từ Array. & NBSP; & NBSP;
If we take a closer at the triangle, we observe that every entry is sum of the two values above it. So we can create a 2D array that stores previously generated values. To generate a value in a line, we can use the previously stored values from array.

C++

22

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

1

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

33

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

7

50

C(line, i)   = line! / ( (line-i)! * i! )

5

52

C(line, i)   = line! / ( (line-i)! * i! )

0

54

C(line, i)   = line! / ( (line-i)! * i! )

5

56

57

58

C(line, i)   = line! / ( (line-i)! * i! )

0

60

C(line, i)   = line! / ( (line-i)! * i! )

7

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

66

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

33

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

C(line, i)   = line! / ( (line-i)! * i! )

0

52

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

54

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

11

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

27

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

16

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

7

50

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

33

for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

50

C(line, i)   = line! / ( (line-i)! * i! )

0for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

Java

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

83

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

84

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

86

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

89

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

54

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

95

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

97

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

99

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

01

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

03

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

07

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

40

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

Python3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

45

C(line, i)   = line! / ( (line-i)! * i! )

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

74

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

49

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

63

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

64

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

66

for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

99

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

01

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

10

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

85

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

56

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

82

14

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2222

C(line, i)   = line! / ( (line-i)! * i! )

5

54

73

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

18

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

20

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00 for

23__

27for

29

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

88

26

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

86

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

88

C(line, i)   = line! / ( (line-i)! * i! )

0for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

94

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

88

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

00

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

99__

C(line, i)   = line! / ( (line-i)! * i! )

5

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

53

55

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

63

C#

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

06

62____

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

06

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

67

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

C(line, i)   = line! / ( (line-i)! * i! )

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

56

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0____9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

C(line, i)   = line! / ( (line-i)! * i! )

4

C(line, i)   = line! / ( (line-i)! * i! )

0for40

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

54

C(line, i)   = line! / ( (line-i)! * i! )

0for44

for45for46

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for48

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

for51

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

40

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8 for59

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

PHP

C(line, i)   = line! / ( (line-i)! * i! )

51

C(line, i)   = line! / ( (line-i)! * i! )

52

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

C(line, i)   = line! / ( (line-i)! * i! )

54

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

56

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

Các

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

C(line, i)   = line! / ( (line-i)! * i! )

82

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

C(line, i)   = line! / ( (line-i)! * i! )

81

C(line, i)   = line! / ( (line-i)! * i! )

82

C(line, i)   = line! / ( (line-i)! * i! )

81

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

5

7

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

011

C(line, i)   = line! / ( (line-i)! * i! )

81

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

06for75

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

018

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

020

C(line, i)   = line! / ( (line-i)! * i! )

81

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

022

C(line, i)   = line! / ( (line-i)! * i! )

5

54

Các

‘

C(line, i)   = line! / ( (line-i)! * i! )

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

39 for75

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

018

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

020

C(line, i)   = line! / ( (line-i)! * i! )

81

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0522.

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

39

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

54

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

065

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

C(line, i)   = line! / ( (line-i)! * i! )

54

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

60

JavaScript

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

61

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

071

77

for5

C(line, i)   = line! / ( (line-i)! * i! )

52

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

63

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

077

for

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

079

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

083

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

7

50

C(line, i)   = line! / ( (line-i)! * i! )

0

52

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

54

C(line, i)   = line! / ( (line-i)! * i! )

0

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

11

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

096

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

82

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

101

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

21

Đầu ra

Phương pháp này có thể được tối ưu hóa để sử dụng không gian thêm O (n) vì chúng ta chỉ cần các giá trị từ hàng trước. Vì vậy, chúng ta có thể tạo một mảng phụ trợ có kích thước N và ghi đè lên các giá trị. Sau đây là một phương pháp khác chỉ sử dụng o (1) không gian thêm.Method 3 (o (n^2) thời gian và o (1) không gian thêm Dòng là hệ số nhị thức c (dòng, i) và tất cả các dòng bắt đầu bằng giá trị 1. Ý tưởng là tính toán c (dòng, i) sử dụng c (dòng, i-1). Nó có thể được tính theo thời gian O (1) bằng cách sử dụng các phần sau. & Nbsp; & nbsp;
Method 3 ( O(n^2) time and O(1) extra space )
This method is based on method 1. We know that ith entry in a line number line is Binomial Coefficient C(line, i) and all lines start with value 1. The idea is to calculate C(line, i) using C(line, i-1). It can be calculated in O(1) time using the following.

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

C++

22

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

0

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

1

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

118

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

122

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

127

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

131

C(line, i)   = line! / ( (line-i)! * i! )

7

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

135

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

139

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

118

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

122

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

127

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

27

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

180

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

135

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

25

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

5 for8

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

Java

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

83

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

84

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

86

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

99

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1____1220

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

238

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

135

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

225

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

18

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

08

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1____210

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

Python3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

45

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

74

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

49

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

82

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

264

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

86

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

277 ____309

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

1

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

22

C(line, i)   = line! / ( (line-i)! * i! )

0for

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

94

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

87

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

311

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

28

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

09

C(line, i)   = line! / ( (line-i)! * i! )
C(line, i-1) = line! / ( (line - i + 1)! * (i-1)! )
We can derive following expression from above two expressions.
C(line, i) = C(line, i-1) * (line - i + 1) / i

So C(line, i) can be calculated from C(line, i-1) in O(1) time

49

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

2

for5

C#

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

9

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

65

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

85 for10

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

1

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

333

C(line, i)   = line! / ( (line-i)! * i! )

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

335

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

340

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

127

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

349

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

135

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

357

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

359

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

66

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

88

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

8 for59

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

2

77

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

PHP

C(line, i)   = line! / ( (line-i)! * i! )

51

C(line, i)   = line! / ( (line-i)! * i! )

52

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

C(line, i)   = line! / ( (line-i)! * i! )

54

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

56

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

385______517

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

395

C(line, i)   = line! / ( (line-i)! * i! )

61

Các

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

5

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

395

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

414

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

5

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

395

C(line, i)   = line! / ( (line-i)! * i! )

73

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

395

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

421

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

17

C(line, i)   = line! / ( (line-i)! * i! )

0

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

0

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

04

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

5

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

1

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

C(line, i)   = line! / ( (line-i)! * i! )

54

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

065

#include 

long paskal(int, int);

int main() {
   int n = 0;
   int m = 0;
   int k = 0;
   int s = 0;
   printf ("Enter number of rows:\n");
   scanf("%d", &n);

   for(k = 0; n >= k; k++) {
            for(s = 0; s < n-k; s++) //Add spaces before each row
                    printf(" ");
            for(m = 0; k >= m; m++) {
                    long f = paskal(k, m);
                    printf("%ld ", f);
            }
            printf("\n");
    }
    return 0;
}

long paskal(int n, int i) {
        if(n == i || i == 0)
                return 1;
        else
                return paskal(n-1, i) + paskal(n-1, i-1);
}

9

C(line, i)   = line! / ( (line-i)! * i! )

54

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

60

JavaScript

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

61

C(line, i)   = line! / ( (line-i)! * i! )

52

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

63

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

450

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

071

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

455

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3for

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

458

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

2

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

462

C(line, i)   = line! / ( (line-i)! * i! )

7

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

C(line, i)   = line! / ( (line-i)! * i! )

0

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

135

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

82

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

101

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

35

1  
1 1 
1 2 1 
1 3 3 1 
1 4 6 4 1 
1 5 10 10 5 1

3

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

 1
 1 1
 1 2 1
 1 3 3 1
 1 4 6 4 1
 1 5 10 10 5 1
 1 6 15 20 15 6 1

4

if(n == i || i == 0) //i.e. if ((row == col) || (col == 0)) return 1;
    return 1;

071

77

for5

21

Đầu ra

Độ phức tạp về thời gian: O (N2) Không gian phụ trợ: O (1)O(n2)
Auxiliary Space: O(1)

Vì vậy, phương pháp 3 là phương pháp tốt nhất trong số tất cả, nhưng nó có thể gây ra tràn số nguyên cho các giá trị lớn của N vì nó nhân hai số nguyên để thu được các giá trị. & NBSP;

Bài viết này được tổng hợp bởi Rahul và được xem xét bởi nhóm GeekSforGeeks. Vui lòng viết nhận xét nếu bạn tìm thấy bất cứ điều gì không chính xác, hoặc bạn muốn chia sẻ thêm thông tin về chủ đề được thảo luận ở trên. & NBSP;Rahul and reviewed by GeeksforGeeks team. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Công thức đệ quy cho tam giác của Pascal là gì?

Nói chung, tổng thứ n, s (n), được tìm thấy bằng cách thêm n vào tổng (n-1).Nghĩa là, s (n) = s (n -1) + n.Đây là một mối quan hệ tái phát để mô tả các tổng của các yếu tố trong cột đầu tiên của hình tam giác của Pascal.S(n) = S(n -1) + n. This is a recurrence relationship to describe the sums of the elements in the first column of Pascal's Triangle.

Tam giác của Pascal trong C là gì?

Tam giác của Pascal là một mảng hình tam giác gồm các hệ số nhị thức trong đó hàng thứ n chứa các hệ số nhị thức NC0, NC1, NC2,a triangular array of binomial coefficients in which the n^th row contains binomial coefficients ⁿC₀, ⁿC₁, ⁿC₂, ……. ⁿ.

Tam giác Pascal giải thích với một ví dụ là gì?

Tam giác của Pascal, trong đại số, một sự sắp xếp hình tam giác của các số cung cấp các hệ số trong việc mở rộng bất kỳ biểu thức nhị thức nào, chẳng hạn như (x + y) n.Nó được đặt theo tên của nhà toán học người Pháp thế kỷ 17, Blaise Pascal, nhưng nó già hơn rất nhiều.a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)ⁿ. It is named for the 17th-century French mathematician Blaise Pascal, but it is far older.

Pascal có hỗ trợ đệ quy không?

Trong Pascal, cả quy trình và chức năng có thể được đệ quy mà không cần phải khai báo theo bất kỳ cách đặc biệt nào.Vì vậy, rất dễ dàng để thực hiện một giải pháp đệ quy cho một vấn đề.both procedures and functions can be recursive without having to declare it in any special manner. Thus, it is very easy to implement a recursive solution to a problem.

programming pascal 118 Pascals triangle Pascal triangle questions

Hướng dẫn pascal triangle using recursion in c++ - tam giác pascal sử dụng đệ quy trong c++

C++

C

Java

Python3

C#

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 31 1 1 1 2 1 1 3 3 1 1 4 6 4 1 5 for8

C++

C

C

Python3

C#

PHP

JavaScript

C++

C

C

Python3

C#

PHP

JavaScript

Công thức đệ quy cho tam giác của Pascal là gì?

Tam giác của Pascal trong C là gì?

Tam giác Pascal giải thích với một ví dụ là gì?

Pascal có hỗ trợ đệ quy không?

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