Rất nhiều sinh viên bối rối khi hiểu khái niệm về độ phức tạp của thời gian, nhưng trong bài viết này, chúng tôi sẽ giải thích nó bằng một ví dụ rất đơn giản
Q. Hãy tưởng tượng một lớp học có 100 sinh viên, trong đó bạn đưa bút cho một người. Bạn phải tìm cây bút đó mà không biết bạn đã cho ai.
Dưới đây là một số cách để tìm bút và thứ tự O là gì
- O[n2]. Bạn đi và hỏi người đầu tiên trong lớp nếu anh ta có bút. Ngoài ra, bạn hỏi người này về 99 người khác trong lớp xem họ có chiếc bút đó hay không, v.v.
Đây là cái mà chúng tôi gọi là O[n2]. - Trên]. Đi và hỏi riêng từng học sinh là O[N].
- O[logn]. Bây giờ tôi chia lớp thành hai nhóm, sau đó hỏi. “Nó ở bên trái hay bên phải của lớp học?” . Lặp lại quy trình cho đến khi bạn chỉ còn lại một học sinh cầm bút của bạn. Đây là ý của bạn bởi O[log n].
tôi có thể cần phải làm
- O[n2] tìm kiếm nếu chỉ một học sinh biết học sinh nào giấu bút.
- O[n] nếu một học sinh có bút và chỉ họ biết điều đó.
- Phép tìm O[log n] nếu tất cả học sinh đều biết, nhưng chỉ cho tôi biết nếu tôi đoán đúng vế.
O -> ở trên được gọi là Big – Oh là một ký hiệu tiệm cận. Có các ký hiệu tiệm cận khác như theta và Omega
GHI CHÚ. Chúng tôi quan tâm đến tốc độ tăng trưởng theo thời gian đối với các yếu tố đầu vào được thực hiện trong quá trình thực hiện chương trình
Độ phức tạp về thời gian của Thuật toán/Mã có giống với Thời gian chạy/thực thi của mã không?
Độ phức tạp về thời gian của một thuật toán/mã không bằng thời gian thực tế cần thiết để thực thi một mã cụ thể, mà là số lần một câu lệnh thực thi. Chúng ta có thể chứng minh điều này bằng cách sử dụng lệnh time.
Ví dụ. Viết mã bằng C/C++ hoặc bất kỳ ngôn ngữ nào khác để tìm giá trị lớn nhất giữa N số, trong đó N thay đổi từ 10, 100, 1000 và 10000. Đối với hệ điều hành dựa trên Linux [Fedora hoặc Ubuntu], hãy sử dụng các lệnh bên dưới.
Để biên dịch chương trình. chương trình gcc. chương trình c – o
Để thực hiện chương trình. thời gian. /chương trình
Bạn sẽ nhận được kết quả đáng ngạc nhiên tôi. e
- Với N = 10. bạn có thể nhận được 0. thời gian 5 ms,
- Với N = 10.000. bạn có thể nhận được 0. thời gian 2 mili giây.
- Ngoài ra, bạn sẽ nhận được thời gian khác nhau trên các máy khác nhau. Ngay cả khi bạn không nhận được cùng thời gian trên cùng một máy cho cùng một mã, thì lý do đằng sau đó là tải mạng hiện tại
Vì vậy, chúng ta có thể nói rằng thời gian thực tế cần thiết để thực thi mã phụ thuộc vào máy [cho dù bạn đang sử dụng Pentium 1 hay Pentium 5] và nó cũng xem xét tải mạng nếu máy của bạn ở trong mạng LAN/WAN.
Độ phức tạp thời gian của một thuật toán có nghĩa là gì?
Bây giờ, câu hỏi đặt ra là nếu độ phức tạp của thời gian không phải là thời gian thực tế cần thiết để thực thi mã, thì nó là gì?
Câu trả lời là.
Thay vì đo thời gian thực tế cần thiết để thực thi từng câu lệnh trong mã, Độ phức tạp về thời gian xem xét mỗi câu lệnh thực thi bao nhiêu lần.
ví dụ 1. Xem xét mã đơn giản dưới đây để in Hello World
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Đầu ra
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Độ phức tạp về thời gian. Trong đoạn mã trên, Hello Hello World chỉ được in một lần trên màn hình.
Vì vậy, độ phức tạp thời gian là hằng số. Ô[1] tôi. e. mỗi lần cần một lượng thời gian không đổi để thực thi mã, bất kể bạn đang sử dụng hệ điều hành nào hoặc cấu hình máy nào.
Không gian phụ. Ô[1]
ví dụ 2
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Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!!68
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Đầu ra
Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!!
Độ phức tạp về thời gian. Trong đoạn mã trên “Xin chào thế giới. ” chỉ được in ra màn hình n lần vì giá trị của n có thể thay đổi.
Vì vậy, độ phức tạp thời gian là tuyến tính. O[n] tôi. e. mỗi lần, một lượng thời gian tuyến tính được yêu cầu để thực thi mã.
Không gian phụ. Ô[1]
ví dụ 3
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Đầu ra
Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!! Hello World !!!0
Độ phức tạp về thời gian. O[log2[n]]
Không gian phụ. Ô[1]
Ví dụ 4
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Đầu ra
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Độ phức tạp về thời gian. O[log[log n]]
Không gian phụ. Ô[1]
Làm thế nào để tìm độ phức tạp thời gian của một thuật toán?
Bây giờ chúng ta hãy xem một số ví dụ khác và quy trình tìm độ phức tạp thời gian của một thuật toán
Ví dụ. Chúng ta hãy xem xét một mô hình máy có các thông số kỹ thuật sau.
- Bộ xử lý đơn
- 32 bit
- Thực hiện tuần tự
- 1 đơn vị thời gian cho các phép toán số học và logic
- 1 đơn vị thời gian cho câu lệnh gán và trả về
Q1. Tìm Tổng của 2 số ở máy trên
Đối với bất kỳ máy nào, mã giả để cộng hai số sẽ giống như thế này
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Thời gian phức tạp.
- Đoạn mã trên sẽ mất 2 đơn vị thời gian [không đổi].
- một cho các hoạt động số học và
- một cho trở lại. [theo quy ước trên].
- Do đó tổng chi phí để thực hiện phép tính tổng [Tsum] = 1 + 1 = 2
- Độ phức tạp thời gian = O[2] = O[1], vì 2 là hằng số
Không gian phụ trợ. Ô[1]
quý 2. Tìm tổng tất cả các phần tử của một danh sách/mảng
Mã giả để làm như vậy có thể được đưa ra như
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Để hiểu độ phức tạp về thời gian của đoạn mã trên, hãy xem mỗi câu lệnh sẽ mất bao nhiêu thời gian
Độ phức tạp về thời gian của câu lệnh in là gì?
độ phức tạp Thời gian của mã này là O[N*N] bởi vì đó là một vòng lặp N lần in ra.
Có sự phức tạp về thời gian trong Python không?
Độ phức tạp về thời gian cho chúng tôi biết thời gian thực thi của một thuật toán, so với kích thước đầu vào của nó . Đó là một cách nhanh chóng để hiểu hiệu suất tương đối của một thuật toán.
Làm cách nào để tìm thời gian thực hiện trong Python?
Để tính thời gian thực thi mã, mô-đun thời gian có thể được sử dụng. .
Lưu dấu thời gian ở đầu mã bắt đầu sử dụng time[]
Lưu dấu thời gian ở cuối mã
Tìm sự khác biệt giữa kết thúc và bắt đầu, cho biết thời gian thực hiện
Làm cách nào để tìm độ phức tạp về thời gian của một chương trình trong Python trực tuyến?
Để tính độ phức tạp của thời gian, bạn chỉ cần nhập tên thuật toán rồi xác định hàm cho thuật toán cụ thể này như chúng tôi đã làm với . Sau đó ta test thuật toán bằng hàm test[] của BigO là ra kết quả luôn.