Given a binary tree with value on each node representing a lowercase letter, find the lexicographically smallest string starting from the leaf to root node

Intuition

We use DFS to find all strings from the root node to the leaf nodes, then reverse the string and compare it withe the largest string.

Approach

We use current to represent the string starting from the root node to the current node and we use result to store the currently best result. When we reach the leaf node, we compare the current with result and update result.

Complexity

$$O(n)$$
$$O(\log n)$$

Code

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/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution {
public:
    void dfs(TreeNode* root, string &current, string &result) {
        current.push_back('a' + root->val);
        // leaf node
        if (!root->left && !root->right) {
            // update result
            reverse(current.begin(), current.end());
            if (current < result)   result = current;
            reverse(current.begin(), current.end());
        } else {
            if (root->left) dfs(root->left, current, result);
            if (root->right) dfs(root->right, current, result);
        }
        current.pop_back();
    }

    string smallestFromLeaf(TreeNode* root) {
        string result(8501, 'z');
        string current;
        dfs(root, current, result);
        return result;
    }
};