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Binary Search Trees Explained: How They Balance Speed and Flexibility

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A Binary Search Tree (BST) is a data structure that organizes values so that every node's left subtree holds smaller values and its right subtree holds larger ones. This ordering rule allows search, insertion, and deletion operations to run in O(log n) time on a well-balanced tree, making BSTs more dynamic than sorted arrays. Unlike sorted arrays, BSTs avoid the costly element-shifting required during frequent insertions and deletions. However, a BST's efficiency depends heavily on its height — a skewed, unbalanced tree can degrade to O(n) performance, resembling a linked list. A key property of valid BSTs is that an in-order traversal always produces values in sorted ascending order.

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