The problem asks for the lowest common ancestor (LCA) of the deepest leaves in a binary tree. A postorder traversal can help track the depth of leaves while identifying the LCA. This approach ensures an efficient and clear solution through DFS and state management.
Problem Statement
Given the root of a binary tree, return the lowest common ancestor of its deepest leaves. In a binary tree, the deepest leaves are those with the greatest depth. The lowest common ancestor is the shared ancestor of two or more nodes that is located furthest from the root.
For example, in a tree with root = [3,5,1,6,2,0,8,null,null,7,4], the LCA of the deepest leaves, nodes 7 and 4, is node 2. Similarly, for simpler cases like root = [1], the only node is the LCA by default.
Examples
Example 1
Input: root = [3,5,1,6,2,0,8,null,null,7,4]
Output: [2,7,4]
We return the node with value 2, colored in yellow in the diagram. The nodes coloured in blue are the deepest leaf-nodes of the tree. Note that nodes 6, 0, and 8 are also leaf nodes, but the depth of them is 2, but the depth of nodes 7 and 4 is 3.
Example 2
Input: root = [1]
Output: [1]
The root is the deepest node in the tree, and it's the lca of itself.
Example 3
Input: root = [0,1,3,null,2]
Output: [2]
The deepest leaf node in the tree is 2, the lca of one node is itself.
Constraints
- The number of nodes in the tree will be in the range [1, 1000].
- 0 <= Node.val <= 1000
- The values of the nodes in the tree are unique.
Solution Approach
Postorder Traversal with State Tracking
Start by performing a postorder traversal of the tree. This helps process nodes from the bottom to the top. As you traverse, track the deepest leaf's depth and check for the lowest common ancestor of all nodes at the deepest level.
Depth Comparison During Traversal
As the traversal progresses, compare the depths of encountered leaf nodes. For each leaf node, determine if its depth is the deepest encountered so far. If multiple nodes share the deepest level, determine the LCA from those nodes.
Efficient DFS Approach
Depth-First Search (DFS) allows an optimal exploration of the tree with minimal space complexity. Using recursion, return both the depth and the LCA during traversal to ensure efficiency in reaching the solution.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n) |
| Space | O(n) |
The time complexity is O(n) because each node is visited once during the traversal. The space complexity is O(n) due to the recursion stack and auxiliary data structures used to track the depths and ancestors of nodes.
What Interviewers Usually Probe
- The candidate demonstrates understanding of binary tree traversal techniques.
- The candidate uses an optimal approach, focusing on DFS and state tracking.
- The candidate explains how to compare depths and find the LCA efficiently.
Common Pitfalls or Variants
Common pitfalls
- Failing to correctly identify the deepest leaves before determining the LCA.
- Misunderstanding that the LCA must be common to the deepest nodes only.
- Overcomplicating the solution with unnecessary space or traversal steps.
Follow-up variants
- Handling different tree structures, such as skewed trees or trees with only one node.
- Optimizing for larger input sizes with stricter time/space constraints.
- Adapting the solution to find the LCA for multiple nodes at varying depths.
How GhostInterview Helps
- GhostInterview provides a direct walkthrough for mastering binary tree traversal techniques, ensuring optimal solutions.
- It helps practice efficient DFS approaches, preventing common pitfalls in space complexity and traversal depth tracking.
- The solver provides examples and hints to focus on the key concept of depth comparison and ancestor tracking, aiding in problem-solving clarity.
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 pattern for solving the Lowest Common Ancestor of Deepest Leaves problem?
The pattern involves using a postorder DFS traversal with state tracking for depth and ancestor identification. This ensures efficient tracking of the deepest leaves and their common ancestor.
How do I identify the deepest leaves in a binary tree?
By performing a traversal and comparing node depths, the deepest leaves are identified as those with the greatest depth in the tree.
What is the time complexity of the solution?
The time complexity is O(n), where n is the number of nodes in the tree, as each node is visited once.
Can this solution handle very large trees?
Yes, the solution is efficient enough to handle large trees within the problem's constraints, with a time complexity of O(n) and space complexity of O(n).
What are common mistakes when solving this problem?
Common mistakes include failing to correctly track the depth of leaf nodes and not properly identifying the LCA of multiple deepest leaves.
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