Implementing the three fundamental depth-first traversal methods for binary trees.
Depth-First Search (DFS) for a binary tree involves exploring as far as possible down each branch before backtracking. There are three common ways to traverse a tree using DFS, and the difference lies in the order in which the root node is visited relative to its left and right subtrees. All are naturally implemented using recursion. **Inorder Traversal**: The sequence is (1) traverse the left subtree, (2) visit the root, (3) traverse the right subtree. For a Binary Search Tree, an inorder traversal visits the nodes in ascending order, which is a very useful property. **Preorder Traversal**: The sequence is (1) visit the root, (2) traverse the left subtree, (3) traverse the right subtree. A preorder traversal is often used to create a copy of the tree or to get a prefix expression representation of an expression tree. **Postorder Traversal**: The sequence is (1) traverse the left subtree, (2) traverse the right subtree, (3) visit the root. Postorder traversal is used in processes where children must be processed before their parent, such as deleting nodes in a tree (to avoid creating dangling pointers) or getting a postfix expression from an expression tree. Mastering these three traversals is absolutely fundamental to solving tree-based problems.