Explain and implement inorder, preorder, and postorder traversals of a binary tree.
Binary tree traversal is foundational to understanding tree-based data structures. Interviewers use this question to assess your grasp of recursion, stack-based iteration, and your ability to reason about the order of operations on hierarchical data.
Define each traversal order: inorder (left-root-right), preorder (root-left-right), postorder (left-right-root).
Implement each recursively first — it is the simplest and most readable approach.
Show iterative versions using an explicit stack to demonstrate deeper understanding.
Discuss use cases: inorder for BST sorted output, preorder for tree serialization, postorder for deletion or expression evaluation.
In inorder traversal we visit left subtree, then root, then right subtree — for a BST this gives nodes in sorted order. Preorder visits root first, then left, then right — useful for serializing or copying a tree. Postorder visits left, right, then root — ideal for deleting a tree or evaluating postfix expressions. Recursively, each is a simple three-line function that changes only the order of the recursive calls and the visit step. Iteratively, inorder uses a stack: push all left children, pop and visit, then move to the right child. Preorder pushes root, pops and visits, then pushes right before left. Postorder can be done with two stacks or by reversing a modified preorder. All three run in O(n) time and O(h) space where h is the tree height. I always mention the iterative versions because they show you can convert recursion into explicit state management, which matters for very deep trees.
Know the iterative version of at least inorder — interviewers often ask for it as a follow-up.
Mention Morris traversal for O(1) space if you want to impress.
Relate traversal orders to real problems: inorder for validation, preorder for cloning.
O(n) for all three traversals since every node is visited exactly once.
Preorder is useful for creating a copy of the tree or serializing it to a flat structure for storage.
Level-order (BFS) visits nodes level by level using a queue. It is different from the three depth-first traversals.
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