Tree Traversals

Overview

Tree traversal is the process of visiting each node in a tree exactly once. The order in which nodes are visited depends on the traversal method. There are three main depth-first traversal orders: in-order, pre-order, and post-order.

In-Order Traversal

In-order traversal visits the left subtree first, then the root, then the right subtree. For binary search trees, this produces nodes in sorted order, making it useful for displaying data in ascending order.

Pre-Order Traversal

Pre-order traversal visits the root first, then the left subtree, then the right subtree. This order is useful for creating a copy of the tree or getting a prefix expression from an expression tree.

Post-Order Traversal

Post-order traversal visits the left subtree, then the right subtree, then the root. This is useful for deleting a tree or getting a postfix expression, since you process children before the parent.

Level-Order Traversal

Level-order, or breadth-first, traversal visits nodes level by level from top to bottom, left to right. This uses a queue to process nodes at each level before moving to the next level.

Recursive Nature

Most tree traversals are naturally recursive. You process the current node, then recursively process its left and right subtrees. The order of these three operations determines which traversal method you're using.