Binary search tree insert recursive python
The problem is that a Let's have a look:
In order to fix it we need to "go one level up" and if One way to do it would be:
Two comments:
What is Binary Search Tree?
The above properties of Binary Search Tree provides an ordering among keys so that the operations like search, minimum and maximum can be done fast. If there is no ordering, then we may have to compare every key to search for a given key. How to search a key in given Binary Tree?For searching a value, if we had a sorted array we could have performed a binary search. Let’s say we want to search a number in the array, in binary search, we first define the complete list as our search space, the number can exist only within the search space. Now we compare the number to be searched or the element to be searched with the middle element (median) of the search space and if the record being searched is less than the middle element, we go searching in the left half, else we go searching in the right half, in case of equality we have found the element. In binary search, we start with ‘n’ elements in search space and if the mid element is not the element that we are looking for, we reduce the search space to ‘n/2’ we keep reducing the search space until we either find the record that we are looking for or we get to only one element in search space and be done with this whole reduction. Search operations in binary search trees will be very similar. Let’s say we want to search for the number, we start at the root, and then we compare the value to be searched with the value of the root, if it’s equal we are done with the search if it’s smaller we know that we need to go to the left subtree because in a binary search tree all the elements in the left subtree are smaller and all the elements in the right subtree are larger. Searching an element in the binary search tree is basically this traversal, at each step we go either left or right and at each step we discard one of the sub-trees. If the tree is balanced (we call a tree balanced if for all nodes the difference between the heights of left and right subtrees is not greater than one) we start with a search space of ‘n’ nodes and as we discard one of the sub-trees, we discard ‘n/2’ nodes so our search space gets reduced to ‘n/2’. In the next step, we reduce the search space to ‘n/4’ and we repeat until we find the element or our search space is reduced to only one node. The search here is also a binary search hence the name; Binary Search Tree. Implementation: C++
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Illustration to search 6 in below tree:
Insertion of a key : A new key is always inserted at the leaf. We start searching for a key from the root until we hit a leaf node. Once a leaf node is found, the new node is added as a child of the leaf node. 100 100 / \ Insert 40 / \ 20 500 ———> 20 500 / \ / \ 10 30 10 30 \ 40 Implementation: C++
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Output 20 30 40 50 60 70 80 Illustration to insert 2 in below tree:
Time Complexity: The worst-case time complexity of search and insert operations is O(h) where h is the height of the Binary Search Tree. In the worst case, we may have to travel from root to the deepest leaf node. The height of a skewed tree may become n and the time complexity of search and insert operation may become O(n). Implementation: Insertion using loop. C++
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Output 10 15 20 30 40 50 60 Some Interesting Facts:
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