<p>You are given the <code>root</code> of a <strong>binary tree</strong> with <code>n</code> nodes. Each node is uniquely assigned a value from <code>1</code> to <code>n</code>. You are also given an integer <code>startValue</code> representing the value of the start node <code>s</code>, and a different integer <code>destValue</code> representing the value of the destination node <code>t</code>.</p>

<p>Find the <strong>shortest path</strong> starting from node <code>s</code> and ending at node <code>t</code>. Generate step-by-step directions of such path as a string consisting of only the <strong>uppercase</strong> letters <code>&#39;L&#39;</code>, <code>&#39;R&#39;</code>, and <code>&#39;U&#39;</code>. Each letter indicates a specific direction:</p>

<ul>
	<li><code>&#39;L&#39;</code> means to go from a node to its <strong>left child</strong> node.</li>
	<li><code>&#39;R&#39;</code> means to go from a node to its <strong>right child</strong> node.</li>
	<li><code>&#39;U&#39;</code> means to go from a node to its <strong>parent</strong> node.</li>
</ul>

<p>Return <em>the step-by-step directions of the <strong>shortest path</strong> from node </em><code>s</code><em> to node</em> <code>t</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/15/eg1.png" style="width: 214px; height: 163px;" />
<pre>
<strong>Input:</strong> root = [5,1,2,3,null,6,4], startValue = 3, destValue = 6
<strong>Output:</strong> &quot;UURL&quot;
<strong>Explanation:</strong> The shortest path is: 3 &rarr; 1 &rarr; 5 &rarr; 2 &rarr; 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/15/eg2.png" style="width: 74px; height: 102px;" />
<pre>
<strong>Input:</strong> root = [2,1], startValue = 2, destValue = 1
<strong>Output:</strong> &quot;L&quot;
<strong>Explanation:</strong> The shortest path is: 2 &rarr; 1.
</pre>

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

<ul>
	<li>The number of nodes in the tree is <code>n</code>.</li>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= Node.val &lt;= n</code></li>
	<li>All the values in the tree are <strong>unique</strong>.</li>
	<li><code>1 &lt;= startValue, destValue &lt;= n</code></li>
	<li><code>startValue != destValue</code></li>
</ul>

/**
 * 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 {
private:
    string root_to_start;
    string root_to_dest;
    bool start_flag;
    bool dest_flag;

    void dfs(TreeNode* node, int& start, int& dest) {
        // terminate
        if (start_flag && dest_flag) { return; }
        if (node->val == start) { start_flag = true; }
        if (node->val == dest) { dest_flag = true; }
        // explore + backtrack
        if (node->left) {
            if (!start_flag) { root_to_start += "L"; }
            if (!dest_flag) { root_to_dest += "L"; }
            dfs(node->left, start, dest);
            if (!start_flag) { root_to_start.pop_back(); }
            if (!dest_flag) { root_to_dest.pop_back(); }
        }

        if (node->right) {
            if (!start_flag) { root_to_start += "R"; }
            if (!dest_flag) { root_to_dest += "R"; }
            dfs(node->right, start, dest);
            if (!start_flag) { root_to_start.pop_back(); }
            if (!dest_flag) { root_to_dest.pop_back(); }
        }
    }

    string merge(string& to_start, string& to_dest) {
        // // debug
        // cout << "start: " << to_start << ", dest: " << to_dest << endl;
        //
        int n1 = to_start.size();
        int n2 = to_dest.size();
        int pre = -1;
        while (pre + 1 < min(n1, n2)) {
            if (to_start[pre+1] == to_dest[pre+1]) {
                pre++;
            } else {
                break;
            }
        }
        // ans: "U"x(n1 - (pre+1)) --- "C" ([pre+1, n2-1])
        string u_str = string(n1 - (pre+1), 'U');
        // string f_str = to_dest.substr(pre+1, n2);
        string f_str = to_dest.substr(pre+1);
        // // debug
        // cout << "u_str: " << u_str << ", f_str: " << f_str << endl;
        return u_str + f_str;
    }

public:
    string getDirections(TreeNode* root, int startValue, int destValue) {
        root_to_start = "";
        root_to_dest = "";
        start_flag = false;
        dest_flag = false;
        // 1. complete both strings in 1-pass DFS
        dfs(root, startValue, destValue);
        // 2. merge into one path string
        string ans = merge(root_to_start, root_to_dest);
        return ans;
    }
};
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