<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 {
public:
    void FindStart(TreeNode* root, int startValue, unordered_map<TreeNode*,TreeNode*> &parent, TreeNode* &startNode) {
        if (root == nullptr) return;
        if (root->val == startValue) {
            startNode = root;
        }
        
        bool ans = false;
        if (root->left) {
            parent[root->left] = root;
            FindStart(root->left, startValue, parent, startNode);
        }
        if (root->right) {
            parent[root->right] = root;
            FindStart(root->right, startValue, parent, startNode);
        }
        return;
    }
    string BackTrackPath(TreeNode* node, unordered_map<TreeNode*,pair<TreeNode*,string>> &GoThrough) {
        string s;
        while (GoThrough.count(node)) {
            s += GoThrough[node].second;
            node = GoThrough[node].first;
        }
        reverse(s.begin(), s.end());
        return s;
    }
    string getDirections(TreeNode* root, int startValue, int destValue) {
        unordered_map<TreeNode*,TreeNode*> parent;
        TreeNode* startNode;
        int num = 0;
        FindStart(root, startValue, parent, startNode);
        
        unordered_map<TreeNode*,bool> visited;
        unordered_map<TreeNode*,pair<TreeNode*,string>> GoThrough;  // <next_node, <cur_node,operation>>
        queue<TreeNode*> q;
        q.push(startNode);
        visited[startNode] = true;
        
        while (!q.empty()) {
            int n = q.size();
            
            for (int i = 0; i < n; i++) {
                auto node = q.front();
                q.pop();
                if (node->val == destValue) {
                    return BackTrackPath(node, GoThrough);
                }
                
                if (node->left && !visited.count(node->left)) {
                    q.push(node->left);
                    GoThrough[node->left] = {node,"L"};
                    visited[node->left] = true;
                }
                if (node->right && !visited.count(node->right)) {
                    q.push(node->right);
                    GoThrough[node->right] = {node,"R"};
                    visited[node->right] = true;
                }
                if (parent.count(node) && !visited.count(parent[node])) {
                    q.push(parent[node]);
                    GoThrough[parent[node]] = {node,"U"};
                    visited[parent[node]] = true;
                }
            }
        }
        return "";
    }
};
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