Binary Search Trees: How to Implement Efficient Search Using Binary Search Trees?

A Binary Search Tree (BST) is an efficient data structure designed to solve the problem of "quickly locating targets" in daily data retrieval. It is a special type of binary tree where each node satisfies the following condition: all values in the left subtree are less than the current node's value, and all values in the right subtree are greater than the current node's value. The efficiency of BST stems from its "left smaller, right larger" rule. When searching, starting from the root node, we compare the target value with the current node's value at each step. If the target is smaller, we recursively search the left subtree; if it is larger, we recursively search the right subtree. This process eliminates half of the nodes with each comparison, resulting in a stable time complexity of O(log n), which outperforms unordered arrays (O(n)) and binary search on sorted arrays (which has low insertion efficiency). The core of the search process is "comparison - narrowing the range": starting from the root node, if the target value equals the current node's value, the target is found. If it is smaller, we move to the left subtree; if it is larger, we move to the right subtree, repeating this recursively. This can be implemented using either recursion or iteration. For example, the recursive method compares values level by level starting from the root, while the iterative method uses a loop to narrow down the search range. It is important to note that if a BST becomes unbalanced (e.g., degenerating into a linked list), its efficiency degrades to O(n). However, balanced trees such as Red-Black Trees and AVL Trees can maintain a stable O(log n) time complexity. BST achieves efficient ordered search by "navigating" to narrow down the range step by step.