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Inserting an element into a highly unbalanced binary search tree containing N nodes will take time _______.

Question

Inserting an element into a highly unbalanced binary search tree containing N nodes will take time _______.

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Solution

Inserting an element into a highly unbalanced binary search tree (BST) will take time proportional to the height of the tree. In the worst-case scenario, where the tree is entirely unbalanced (like a linked list), the height of the tree can be N, where N is the number of nodes.

  1. Time Complexity: The time complexity of insertion in a binary search tree is O(h), where h is the height of the tree.

  2. Unbalanced Tree Case: In a highly unbalanced binary search tree, the height can reach N (inserting elements in sequential order without balancing), leading to:

    O(N) O(N)

Thus, inserting an element into a highly unbalanced binary search tree containing N nodes will take time O(N) in the worst-case scenario.

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