<p>You are given the <code>root</code> of a binary tree where each node has a value in the range <code>[0, 25]</code> representing the letters <code>&#39;a&#39;</code> to <code>&#39;z&#39;</code>.</p>

<p>Return <em>the <strong>lexicographically smallest</strong> string that starts at a leaf of this tree and ends at the root</em>.</p>

<p>As a reminder, any shorter prefix of a string is <strong>lexicographically smaller</strong>.</p>

<ul>
	<li>For example, <code>&quot;ab&quot;</code> is lexicographically smaller than <code>&quot;aba&quot;</code>.</li>
</ul>

<p>A leaf of a node is a node that has no children.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/01/30/tree1.png" style="width: 534px; height: 358px;" />
<pre>
<strong>Input:</strong> root = [0,1,2,3,4,3,4]
<strong>Output:</strong> &quot;dba&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/01/30/tree2.png" style="width: 534px; height: 358px;" />
<pre>
<strong>Input:</strong> root = [25,1,3,1,3,0,2]
<strong>Output:</strong> &quot;adz&quot;
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/02/01/tree3.png" style="height: 490px; width: 468px;" />
<pre>
<strong>Input:</strong> root = [2,2,1,null,1,0,null,0]
<strong>Output:</strong> &quot;abc&quot;
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 8500]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 25</code></li>
</ul>

class Solution {
public:
    string smallestFromLeaf(TreeNode* root) {
        string result = "";

        string path = "";
        backtrack(root, path, result);

        reverse(result.begin(), result.end());

        return result;
    }

private:
    void backtrack(TreeNode* current, string& path, string& result) {
        if (current == nullptr) return;

        path.push_back(static_cast<char>(current->val + 'a'));

        if (current->left == nullptr && current->right == nullptr) {
            if (result == "" || smaller(path, result)) {
                result = path;
            }

        } else {
            backtrack(current->left, path, result);
            backtrack(current->right, path, result);
        }

        path.pop_back();
    }
    bool smaller(const std::string& s1, const std::string& s2) {
        auto it1 = s1.rbegin();
        auto it2 = s2.rbegin();

        while (it1 != s1.rend() && it2 != s2.rend()) {
            if (*it1 != *it2) {
                return *it1 < *it2;
            }
            ++it1;
            ++it2;
        }

        return s1.length() < s2.length();
    }
};
19500