How to Traverse a Binary Tree (All Four Ways)

Different traversal orders visit nodes in different sequences and are useful for different purposes. Inorder traversal of a BST gives sorted output. Preorder is used to copy or serialize a tree. Postorder is used to delete a tree or evaluate expressions. Level Order gives a breadth-first view of the tree.

Inorder visits nodes in Left, Root, Right order. Recursively traverse the left subtree first. Then process the current node. Then recursively traverse the right subtree. For a Binary Search Tree, this produces all values in ascending sorted order.

Preorder visits nodes in Root, Left, Right order. Process the current node first. Then recursively traverse the left subtree. Then recursively traverse the right subtree. The root is always the first element in a preorder sequence, which makes it useful for reconstructing trees.

Postorder visits nodes in Left, Right, Root order. Recursively traverse the left subtree first. Then recursively traverse the right subtree. Then process the current node last. Children are always processed before their parent, making this useful for safe deletion or for evaluating expression trees from leaves up.

For Inorder, Preorder, and Postorder, the base case is identical. If the current node is NULL, simply return. This handles leaf nodes naturally because their left and right children are both NULL and the recursion stops without any extra checks.

Level Order traversal uses a Queue instead of recursion. Add the root to the queue. Then enter a loop where you dequeue a node, process it, and enqueue its left and right children if they exist. Repeat until the queue is empty. This visits nodes level by level from top to bottom and left to right.

To store results grouped by level, check the queue size at the start of each level. That size tells you exactly how many nodes belong to the current level. Process that many nodes in an inner loop, adding their children to the queue. After the inner loop, one complete level has been processed and stored.