<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 {

    string makeString(TreeNode* node, unordered_map <TreeNode*, pair<TreeNode*, char>> &pathTrack, string &ans) {
        while(pathTrack[node].first){
            ans += pathTrack[node].second;
            node = pathTrack[node].first;
        }

        reverse(ans.begin(), ans.end());
        return ans;
    }

    void findPath(TreeNode* startNode, TreeNode* endNode, unordered_map<TreeNode*, TreeNode*> &parentTrack, string &str) {
        queue<TreeNode*> q;
        unordered_map <TreeNode*, bool> visited;
        unordered_map <TreeNode*, pair<TreeNode*, char>> pathTrack;

        q.push(startNode);
        visited[startNode] = true;
        pair<TreeNode*, char> p;
        p.first = NULL;
        p.second = 'x';
        pathTrack[startNode] = p;

        while(!q.empty()){
            int size = q.size();

            for(int i = 0; i < size; i++){
                TreeNode* frontNode = q.front();
                q.pop();

                if(frontNode == endNode) {
                    makeString(frontNode, pathTrack, str);
                    return;
                }

                if(frontNode -> left && !visited[frontNode -> left]){
                    q.push(frontNode -> left);
                    visited[frontNode -> left] = true;
                    pathTrack[frontNode -> left] = {frontNode, 'L'};
                }

                if(frontNode -> right && !visited[frontNode -> right]){
                    q.push(frontNode -> right);
                    visited[frontNode -> right] = true;
                    pathTrack[frontNode -> right] = {frontNode, 'R'};
                }

                if(parentTrack[frontNode] && !visited[parentTrack[frontNode]]){
                    q.push(parentTrack[frontNode]);
                    visited[parentTrack[frontNode]] = true;
                    pathTrack[parentTrack[frontNode]] = {frontNode, 'U'};
                }
            }
        }
    }

public:
    string getDirections(TreeNode* root, int startValue, int destValue) {
        unordered_map<TreeNode*, TreeNode*> parentTrack;
        queue<TreeNode*> q;
        q.push(root);
        TreeNode* startNode = NULL, *destNode = NULL;

        while(!q.empty()) {
            TreeNode* frontNode = q.front();
            q.pop();
            if(frontNode -> val == startValue) startNode = frontNode;
            if(frontNode -> val == destValue) destNode = frontNode; 
            if(frontNode -> left){
                q.push(frontNode -> left);
                parentTrack[frontNode -> left] = frontNode;
            }

            if(frontNode -> right) {
                q.push(frontNode -> right);
                parentTrack[frontNode -> right] = frontNode;
            }
        }
        
        if(!startNode || !destNode) {
            string ans = "";
            return ans;
        }

        string ans = "";
        findPath(startNode, destNode, parentTrack, ans);

        return ans;
    }
};
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