LeetCode #988 — MEDIUM

Smallest String Starting From Leaf

Move from brute-force thinking to an efficient approach using backtracking strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given the root of a binary tree where each node has a value in the range [0, 25] representing the letters 'a' to 'z'.

Return the lexicographically smallest string that starts at a leaf of this tree and ends at the root.

As a reminder, any shorter prefix of a string is lexicographically smaller.

  • For example, "ab" is lexicographically smaller than "aba".

A leaf of a node is a node that has no children.

Example 1:

Input: root = [0,1,2,3,4,3,4]
Output: "dba"

Example 2:

Input: root = [25,1,3,1,3,0,2]
Output: "adz"

Example 3:

Input: root = [2,2,1,null,1,0,null,0]
Output: "abc"

Constraints:

  • The number of nodes in the tree is in the range [1, 8500].
  • 0 <= Node.val <= 25
Patterns Used

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: You are given the root of a binary tree where each node has a value in the range [0, 25] representing the letters 'a' to 'z'. Return the lexicographically smallest string that starts at a leaf of this tree and ends at the root. As a reminder, any shorter prefix of a string is lexicographically smaller. For example, "ab" is lexicographically smaller than "aba". A leaf of a node is a node that has no children.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Backtracking · Tree

Example 1

[0,1,2,3,4,3,4]

Example 2

[25,1,3,1,3,0,2]

Example 3

[2,2,1,null,1,0,null,0]

Related Problems

  • Sum Root to Leaf Numbers (sum-root-to-leaf-numbers)
  • Binary Tree Paths (binary-tree-paths)
Step 02

Core Insight

What unlocks the optimal approach

  • No official hints in dataset. Start from constraints and look for a monotonic or reusable state.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #988: Smallest String Starting From Leaf
/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    private StringBuilder path;
    private String ans;

    public String smallestFromLeaf(TreeNode root) {
        path = new StringBuilder();
        ans = String.valueOf((char) ('z' + 1));
        dfs(root, path);
        return ans;
    }

    private void dfs(TreeNode root, StringBuilder path) {
        if (root != null) {
            path.append((char) ('a' + root.val));
            if (root.left == null && root.right == null) {
                String t = path.reverse().toString();
                if (t.compareTo(ans) < 0) {
                    ans = t;
                }
                path.reverse();
            }
            dfs(root.left, path);
            dfs(root.right, path);
            path.deleteCharAt(path.length() - 1);
        }
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n!)
Space
O(n)

Approach Breakdown

EXHAUSTIVE
O(nⁿ) time
O(n) space

Generate every possible combination without any filtering. At each of n positions we choose from up to n options, giving nⁿ total candidates. Each candidate takes O(n) to validate. No pruning means we waste time on clearly invalid partial solutions.

BACKTRACKING + PRUNING
O(n!) time
O(n) space

Backtracking explores a decision tree, but prunes branches that violate constraints early. Worst case is still factorial or exponential, but pruning dramatically reduces the constant factor in practice. Space is the recursion depth (usually O(n) for n-level decisions).

Shortcut: Backtracking time = size of the pruned search tree. Focus on proving your pruning eliminates most branches.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Missing undo step on backtrack

Wrong move: Mutable state leaks between branches.

Usually fails on: Later branches inherit selections from earlier branches.

Fix: Always revert state changes immediately after recursive call.

Forgetting null/base-case handling

Wrong move: Recursive traversal assumes children always exist.

Usually fails on: Leaf nodes throw errors or create wrong depth/path values.

Fix: Handle null/base cases before recursive transitions.