Implement inorder, preorder, postorder, and level-order traversals iteratively and recursively.
Published March 9, 2025
Tree traversal defines the order in which nodes are visited. Mastering all four traversal orders — both recursive and iterative — is essential for tree-based interview problems.
public class TreeNode {
int val;
TreeNode left, right;
TreeNode(int val) { this.val = val; }
}
For BSTs, inorder traversal produces sorted output.
// Recursive
public List<Integer> inorder(TreeNode root) {
List<Integer> result = new ArrayList<>();
dfs(root, result);
return result;
}
void dfs(TreeNode node, List<Integer> result) {
if (node == null) return;
dfs(node.left, result);
result.add(node.val);
dfs(node.right, result);
}
// Iterative
public List<Integer> inorderIterative(TreeNode root) {
List<Integer> result = new ArrayList<>();
Deque<TreeNode> stack = new ArrayDeque<>();
TreeNode curr = root;
while (curr != null || !stack.isEmpty()) {
while (curr != null) { stack.push(curr); curr = curr.left; }
curr = stack.pop();
result.add(curr.val);
curr = curr.right;
}
return result;
}
Useful for: copying a tree, serialization.
// Iterative
public List<Integer> preorder(TreeNode root) {
List<Integer> result = new ArrayList<>();
if (root == null) return result;
Deque<TreeNode> stack = new ArrayDeque<>();
stack.push(root);
while (!stack.isEmpty()) {
TreeNode node = stack.pop();
result.add(node.val);
if (node.right != null) stack.push(node.right); // right first (LIFO)
if (node.left != null) stack.push(node.left);
}
return result;
}
Useful for: deleting a tree, evaluating expression trees.
// Iterative (reverse preorder trick)
public List<Integer> postorder(TreeNode root) {
LinkedList<Integer> result = new LinkedList<>();
if (root == null) return result;
Deque<TreeNode> stack = new ArrayDeque<>();
stack.push(root);
while (!stack.isEmpty()) {
TreeNode node = stack.pop();
result.addFirst(node.val); // prepend
if (node.left != null) stack.push(node.left);
if (node.right != null) stack.push(node.right);
}
return result;
}
public List<List<Integer>> levelOrder(TreeNode root) {
List<List<Integer>> result = new ArrayList<>();
if (root == null) return result;
Queue<TreeNode> queue = new LinkedList<>();
queue.offer(root);
while (!queue.isEmpty()) {
int size = queue.size(); // snapshot this level's size
List<Integer> level = new ArrayList<>();
for (int i = 0; i < size; i++) {
TreeNode node = queue.poll();
level.add(node.val);
if (node.left != null) queue.offer(node.left);
if (node.right != null) queue.offer(node.right);
}
result.add(level);
}
return result;
}
public List<List<Integer>> zigzagLevelOrder(TreeNode root) {
List<List<Integer>> result = new ArrayList<>();
if (root == null) return result;
Queue<TreeNode> queue = new LinkedList<>();
queue.offer(root);
boolean leftToRight = true;
while (!queue.isEmpty()) {
int size = queue.size();
LinkedList<Integer> level = new LinkedList<>();
for (int i = 0; i < size; i++) {
TreeNode node = queue.poll();
if (leftToRight) level.addLast(node.val);
else level.addFirst(node.val);
if (node.left != null) queue.offer(node.left);
if (node.right != null) queue.offer(node.right);
}
result.add(level);
leftToRight = !leftToRight;
}
return result;
}