<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:
    // pair<int,>
    bool find_depth(TreeNode* root,TreeNode* p, TreeNode* q,TreeNode* &ans)
    {
        if(root==NULL)
            return 0;
        else
        {
            bool l=find_depth(root->left,p,q,ans);
            bool r=find_depth(root->right,p,q,ans);
            if(l==true && r==true)
            {
                if(ans==NULL)
                    ans=root;
                return true;
            }
            else if(l==false && r==true)
            {
                if(ans==NULL && (root==p || root==q))
                {
                    ans=root;
                    return true;
                }
                return true;
            }
            else if(l==true && r==false)
            {
                if(ans==NULL && (root==p || root==q))
                {
                    ans=root;
                    return true;
                }
                return true;
            }
            else
            {
                if(ans==NULL && (root==p || root==q))
                {
                    return true;
                }
                return false;
            }
        }
    }
    TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) 
    {
        TreeNode* ans=NULL;
        bool b=find_depth(root,p,q,ans);
        return ans;
    }
    bool to_dest(TreeNode* root,TreeNode* dest,string &rans)
    {
        if(root==NULL)
        {
            return false;
        }
        else
        {
            bool l=to_dest(root->left,dest,rans);
            bool r=to_dest(root->right,dest,rans);
            if(root==dest)
            {
                return true;
            }
            if(l)
            {
                rans.push_back('L');
                return true;
            }
            else if(r)
            {
                rans.push_back('R');
                return true;
            }
            else
            {
                return false;
            }
        }
    }
    TreeNode* find(TreeNode* root,int k)
    {
        if(root==NULL)
            return NULL;
        else if(root->val==k)
        {
            return root;
        }
        else
        {
            TreeNode* l=find(root->left,k);
            TreeNode* r=find(root->right,k);
            if(l==NULL && r==NULL)
                return NULL;
            else if(l!=NULL && r==NULL)
                return l;
            else
                return r;
        }
    }
    int depth(TreeNode* root,TreeNode* st)
    {
        if(root==NULL)
            return 1000000;
        else
        {
            int l=depth(root->left,st);
            int r=depth(root->right,st);
            if(root==st)
                return 0;
            else
                return 1+min(l,r);
        }
    }
    string getDirections(TreeNode* root, int startValue, int destValue) 
    {
        // cout<<"k";
        TreeNode* stn=find(root,startValue);
        // cout<<"k";
        TreeNode* destn=find(root,destValue);
        // cout<<"k";
        TreeNode* lca=lowestCommonAncestor(root,stn,destn) ;
        // cout<<"k";
        int d=depth(lca,stn);
        // cout<<"k";
        string ans="";
        while(d>0)
        {
            ans=ans+'U';
            d--;
        }
        // cout<<"k";
        string rans;
        bool b=to_dest(lca,destn,rans);
        reverse(rans.begin(),rans.end());
        // cout<<"k";
        for(auto it:rans)
            ans.push_back(it);
        // ans=ans+rans;
        return ans;
    }
};
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