This problem requires returning a list of node values in preorder from a given binary tree. You can solve it using either recursion or an explicit stack to track traversal state, ensuring the root is processed before its children. GhostInterview provides guided step-throughs that visualize node visits and help identify common pitfalls like misordering or missing null nodes.
Problem Statement
Given a binary tree, implement a function that returns an array of its node values following a preorder traversal sequence: root first, then left subtree, and finally right subtree. The tree may be empty, and nodes contain integer values in the range [-100, 100].
For example, given root = [1,null,2,3], the output should be [1,2,3], and for root = [1,2,3,4,5,null,8,null,null,6,7,9], the output should be [1,2,4,5,6,7,3,8,9]. Handle trees with up to 100 nodes and ensure the traversal respects the preorder pattern.
Examples
Example 1
Input: root = [1,null,2,3]
Output: [1,2,3]
Example 2
Input: root = [1,2,3,4,5,null,8,null,null,6,7,9]
Output: [1,2,4,5,6,7,3,8,9]
Example 3
Input: root = []
Output: []
Example details omitted.
Constraints
- The number of nodes in the tree is in the range [0, 100].
- -100 <= Node.val <= 100
Solution Approach
Recursive Preorder Traversal
Define a helper function that processes the current node, appends its value to a result list, then recursively calls itself on the left and right children. This approach directly models the preorder pattern but may use O(h) call stack space, where h is the tree height.
Iterative Traversal Using a Stack
Initialize a stack with the root node and iterate while the stack is not empty. Pop the top node, append its value, then push its right child followed by its left child. This ensures the left subtree is processed before the right, maintaining the preorder order while avoiding recursion.
Tracking Null and Leaf Nodes Carefully
Explicitly check for null nodes before pushing them onto the stack to prevent errors. For leaf nodes, ensure they are appended immediately and do not attempt further traversal. Proper state tracking prevents missing nodes or violating the preorder sequence.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is O(n) because each node is visited once. Space complexity is O(h) for recursion or O(n) for the stack in the worst case, where n is the number of nodes and h is the tree height.
What Interviewers Usually Probe
- Looking for correct preorder sequence adherence and null handling.
- Checking if candidate differentiates between recursion and iterative stack approaches.
- Assessing ability to track traversal state without missing leaf nodes.
Common Pitfalls or Variants
Common pitfalls
- Pushing left child after right child incorrectly, reversing preorder order.
- Forgetting to check for null nodes, causing runtime errors.
- Assuming all trees are complete and not handling sparse trees properly.
Follow-up variants
- Inorder and postorder traversal with similar state-tracking logic.
- Binary tree with additional constraints, such as skipping certain values.
- Traversals returning node objects instead of values for processing.
How GhostInterview Helps
- Highlights node visitation order and visually tracks recursion or stack state.
- Alerts on missed null checks or incorrect child pushing order.
- Provides stepwise validation of output against expected preorder sequence.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the easiest way to implement Binary Tree Preorder Traversal?
Use recursion for simplicity, visiting the root first, then left and right subtrees, or use a stack to iteratively maintain the preorder sequence.
Can this problem be solved iteratively without recursion?
Yes, a stack can simulate the call stack of recursion, ensuring left children are processed before right children.
How do I handle an empty tree in this traversal?
Check if the root is null and return an empty list immediately; GhostInterview highlights this edge case during step-throughs.
What common mistakes occur with stack-based preorder traversal?
Pushing the left child after the right child reverses the expected node order, and forgetting null checks can cause runtime errors.
Why is state tracking important in preorder traversal?
Maintaining accurate traversal state ensures nodes are visited in root-left-right order and prevents skipping or duplicating nodes.
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Solve Binary Tree Postorder Traversal using state tracking and binary-tree traversal techniques, focusing on Stack, Tree, and DFS.
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