<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>

class Solution {
public:
    string getDirections(TreeNode* root, int startValue, int destValue) {
        queue<TreeNode*>q;
        q.push(root);
        TreeNode* s=nullptr;    //starting
        unordered_map<int,TreeNode*>parents;
        // find the starting node and record the nodes' parents
        while(!q.empty()){
            TreeNode* cur=q.front();
            q.pop();
            if(cur->val == startValue){
                s=cur;
            }
            if(cur->left){
                parents[cur->left->val]=cur;
                q.push(cur->left);
            }
            if(cur->right){
                parents[cur->right->val]=cur;
                q.push(cur->right);
            }
        }

        unordered_set<TreeNode*>visited;
        unordered_map<TreeNode*,pair<TreeNode*,char>>track_path;
        TreeNode* t=nullptr; //destination
        q.push(s);
        while(!q.empty()){
            TreeNode* cur=q.front();
            q.pop();
            visited.insert(cur);

            if(cur->val==destValue){
                t=cur;
                break;
            }
            if(parents.find(cur->val)!=parents.end() && visited.find(parents[cur->val])==visited.end()){
                TreeNode* p=parents[cur->val];
                q.push(p);
                track_path[p]=make_pair(cur,'U');
            }
            if(cur->left && visited.find(cur->left)==visited.end()){
                q.push(cur->left);
                track_path[cur->left]=make_pair(cur,'L');
            }
            if(cur->right && visited.find(cur->right)==visited.end()){
                q.push(cur->right);
                track_path[cur->right]=make_pair(cur,'R');
            }

        }

        stack<char> result_path;
        TreeNode* cur_node = t;

        while (cur_node != s) {
            auto it = track_path.find(cur_node);
            if (it != track_path.end()) {
                result_path.push(it->second.second); 
                cur_node = it->second.first;
            }
        }

        string res;
        while (!result_path.empty()) {
            res += result_path.top();
            result_path.pop();
        }

        return res;
    }
};
218420