Use depth-first search to traverse each path from leaves to the root while building the corresponding string. Track the current string in reverse order to efficiently compare lexicographical order. Backtracking ensures all paths are explored without overwriting previous state, capturing the globally smallest leaf-to-root string.
Problem Statement
Given the root of a binary tree where each node's value is an integer from 0 to 25 representing letters 'a' to 'z', construct strings by following paths from any leaf node up to the root. Return the lexicographically smallest string among all leaf-to-root paths.
A string is considered lexicographically smaller if it would appear first in dictionary order. For example, shorter prefixes take precedence over longer strings with the same starting sequence. The binary-tree traversal must correctly handle all branches and leaf paths to determine the minimal string.
Examples
Example 1
Input: root = [0,1,2,3,4,3,4]
Output: "dba"
Example details omitted.
Example 2
Input: root = [25,1,3,1,3,0,2]
Output: "adz"
Example details omitted.
Example 3
Input: root = [2,2,1,null,1,0,null,0]
Output: "abc"
Example details omitted.
Constraints
- The number of nodes in the tree is in the range [1, 8500].
- 0 <= Node.val <= 25
Solution Approach
DFS Traversal with Path Accumulation
Perform a depth-first search starting from the root, appending the current node's character to a path string. When a leaf node is reached, reverse the accumulated path to get the leaf-to-root string and compare it with the current minimum.
Backtracking to Explore All Paths
After visiting each child node, backtrack by removing the last character added to the path string. This ensures that sibling paths are evaluated independently without corrupting the accumulated string.
Lexicographical Comparison at Leaves
At each leaf node, compare the reversed path string with the current smallest string. Update the result if the new string is smaller. This guarantees that the final answer represents the globally smallest string across all leaf-to-root paths.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n \cdot n) |
| Space | O(n \cdot n) |
The algorithm visits each node once, building a string of length up to the tree height n along each path. Each leaf comparison involves a string of size up to n, resulting in O(n * n) time complexity. Space complexity is also O(n * n) due to storing path strings during DFS traversal.
What Interviewers Usually Probe
- Check if the candidate correctly reverses paths from leaf to root before comparison.
- Observe if the candidate uses backtracking to manage path state efficiently.
- Notice whether the solution handles lexicographical comparison accurately at each leaf.
Common Pitfalls or Variants
Common pitfalls
- Failing to reverse the path string before comparing leaf-to-root strings, yielding incorrect lexicographical order.
- Modifying a shared path string without proper backtracking, causing sibling path evaluation errors.
- Comparing incomplete paths or intermediate nodes instead of strictly leaf-to-root paths.
Follow-up variants
- Compute the largest string from leaf to root using the same DFS and backtracking framework.
- Return the smallest string starting from a specific leaf instead of all leaves, requiring targeted path tracking.
- Handle n-ary trees instead of binary trees, adapting DFS and path management to multiple children.
How GhostInterview Helps
- Provides a clear DFS-based path-tracking template tailored to leaf-to-root string comparison.
- Highlights subtle lexicographical pitfalls and ensures backtracking is applied correctly across branches.
- Guides the candidate through exploring all leaf paths without overcomplicating state management or comparisons.
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 main idea behind Smallest String Starting From Leaf?
Use DFS to traverse all leaf-to-root paths, reverse the path strings, and compare lexicographically to find the smallest.
Why is backtracking necessary in this problem?
Backtracking prevents the current path string from contaminating sibling paths, ensuring accurate leaf-to-root comparisons.
How do we handle lexicographical comparisons efficiently?
Reverse the accumulated path at each leaf and compare strings directly to maintain the smallest result found so far.
What is the time and space complexity?
Both time and space complexity are O(n * n), with n being the number of nodes, due to path accumulation and comparisons.
Can this approach be adapted to n-ary trees?
Yes, the DFS and backtracking framework works for n-ary trees by iterating through all children at each node.
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Find all root-to-leaf paths in a binary tree using DFS and backtracking, constructing strings for each complete path efficiently.
Open problem page#1028 Recover a Tree From Preorder TraversalRecover a binary tree from its preorder traversal string by tracking node depth and reconstructing child relationships efficiently.
Open problem page#606 Construct String from Binary TreeGiven a binary tree, construct a string representation based on preorder traversal while adhering to specific formatting rules.
Open problem page