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Imbalance of a Binary Search Tree: Understanding Depth and Complexity

This document explores the concept of imbalance in a Binary Search Tree (BST), defined as the absolute difference between the depths of its left and right subtrees. The provided Java methods calculate this imbalance by assessing the depth of each node recursively. The algorithm's complexity is analyzed, revealing that it visits every node exactly once, resulting in a time complexity of O(n). A deeper understanding of BST structure is crucial for optimizing search operations and maintaining balance for enhanced performance.

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Imbalance of a Binary Search Tree: Understanding Depth and Complexity

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  2. // Imbalance of a BST defined to be the absolute difference// between depth of its left and right subtrees public static int imbalance(BSTnodebn) {return Math.abs(Depth(bn.left)-Depth(bn.right)); } public static int Depth(BSTnodebn) {if(bn == null) return 0;return Math.Max(Depth(bn.left), Depth(bn.right))+1; } What is the complexity of this algorithm? This algorithm visits every node once, so complexity is O(n)

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