<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:
    string getDirections(TreeNode* root, int startValue, int destValue) {
        if (!root) return "";
        unordered_map<TreeNode*,TreeNode*> m;
        unordered_map<TreeNode*, char> p;
        unordered_map<int,TreeNode*> a;
        unordered_map<TreeNode*,int> l;
        queue<TreeNode*> q;
        q.push(root);
        m[root]=NULL;
        l[root]=0;
        TreeNode *x,*y;
        while(!q.empty()){
            x=q.front();
            q.pop();
            a[x->val]=x;
            if(x->left){
                q.push(x->left);
                m[x->left]=x;
                p[x->left]='L';
                l[x->left]=l[x]+1;
            }
            if(x->right){
                q.push(x->right);
                m[x->right]=x;
                p[x->right]='R';
                l[x->right]=l[x]+1;
            }
        }
        stack<TreeNode*> sp,sq;
        x=a[startValue];
        while(x){
            sp.push(x);
            x=m[x];
        }
        x=a[destValue];
        while(x){
            sq.push(x);
            x=m[x];
        }
        x=a[startValue];
        y=a[destValue];
        string ret="";


        TreeNode *prev=NULL;
        while(sp.top()==sq.top()){
            if (sp.top()==x || sp.top()==y) break;
            prev=sp.top();
            sp.pop();
            sq.pop();
        }

        if (sp.top()==x && sq.top()==y){
            while(!sp.empty()){
                ret+='U';
                sp.pop();
            }
            while(!sq.empty()){
                x=sq.top();
                ret+=p[x];
                sq.pop();
            }
            return ret;
        }
        if (sp.top()==x && sq.top()==x){
            sq.pop();
            while(!sq.empty()){
                x=sq.top();
                ret+=p[x];
                sq.pop();
            }
            return ret;
        } 
        if (sp.top()==y && sq.top()==y){
            sp.pop();
            while(!sp.empty()){
                x=sp.top();
                ret+='U';
                sp.pop();
            }
            return ret;
        }
        while(!sp.empty()){
            ret+='U';
            sp.pop();
        }
        while(!sq.empty()){
            ret+=p[sq.top()];
            sq.pop();
        }
        return ret;
    }
};
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