Implementing the fundamental operations of a Binary Search Tree.
The core functionality of a Binary Search Tree revolves around three main operations: search, insert, and delete. The 'search' operation is the most straightforward. Starting from the root, we compare the target value with the current node's value. If the target is smaller, we move to the left child; if it's larger, we move to the right child. This process continues until we find the value or reach a null pointer, indicating the value isn't in the tree. The 'insert' operation follows a similar logic. We search for the position where the new value should be, and once we find a null spot, we create a new node and attach it. The 'delete' operation is the most complex. If the node to be deleted is a leaf, we can simply remove it. If it has one child, we replace the node with its child. The tricky case is when the node has two children. Here, we must replace it with its in-order successor (the smallest value in its right subtree) or in-order predecessor (the largest value in its left subtree) to maintain the BST property. We then recursively delete the successor/predecessor from its original position. Understanding these operations is crucial, as they form the basis for all tree-based data structures and algorithms.