Smallest String Starting From Leaf

LeetCode 1030 | Difficulty: Medium

Medium

Problem Description

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`

Topics: String, Backtracking, Tree, Depth-First Search, Binary Tree

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Approach

Backtracking

Explore all candidates by building solutions incrementally. At each step, choose an option, explore further, then unchoose (backtrack) to try the next option. Prune branches that can't lead to valid solutions.

When to use

Generate all combinations/permutations, or find solutions that satisfy constraints.

Tree DFS

Traverse the tree recursively (or with a stack). At each node, decide: what information do I need from the left/right subtrees? Process: go left → go right → combine results. Consider preorder, inorder, or postorder traversal based on when you need to process the node.

When to use

Path problems, subtree properties, tree structure manipulation.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 237 ms)

Metric	Value
Runtime	237 ms
Memory	39.8 MB
Date	2022-01-12

Solution

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left;
 *     public TreeNode right;
 *     public TreeNode(int val=0, TreeNode left=null, TreeNode right=null) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
public class Solution {
    public string SmallestFromLeaf(TreeNode root) {
        if(root == null) return null;
    return SmallestHelper(root, "");
}

public string SmallestHelper(TreeNode root, string suffix)
{
    if(root == null) return suffix;
    suffix = (char)(root.val+'a') + suffix;
    if(root.left == null)
    return SmallestHelper(root.right, suffix);
    if(root.right == null)
    return SmallestHelper(root.left, suffix);
    
    string left = SmallestHelper(root.left, suffix);
    string right = SmallestHelper(root.right, suffix);
    if(left.CompareTo(right) < 0) return left;
    else return right;
}
}

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Complexity Analysis

Approach	Time	Space
Backtracking	$O(n! or 2^n)$	$O(n)$
Tree Traversal	$O(n)$	$O(h)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Consider: "What information do I need from each subtree?" — this defines your recursive return value.
• Identify pruning conditions early to avoid exploring invalid branches.