<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) {}
 * };
 */

#define um unordered_map

class Solution {
public:
        string getDirections(TreeNode* root, int startValue, int destValue) {
        um<int, int> left_ancestors; // idx to level
        um<int, int> right_ancestors;
        string left = "";
        string right = "";
        recur_start(root, 0, startValue, left_ancestors, left);
        recur_dest(root, 0, destValue, right_ancestors, right);
        int common_largest = 0;
        int left_max = 0;
        int right_max = 0;
        for (auto& [k, v] : left_ancestors){
            left_max = max(left_max, v);
            if (right_ancestors.count(k)){
                common_largest = max(common_largest, v);
            }
        }
        for (auto& [k, v] : right_ancestors){
            right_max = max(right_max, v);
        }
        if (right_ancestors.count(startValue)) {
            left = "";
            right = right.substr(0, right_max - right_ancestors[startValue]+1);
        } else if (left_ancestors.count(destValue)){
            left = left.substr(0, left_max - left_ancestors[destValue]+1);
            right = "";
        } else{
            left = left.substr(0, left_max-common_largest+1);
            right = right.substr(0, right_max - common_largest+1);
        }
        reverse(right.begin(), right.end());
        return left + right;
    }

    bool recur_start(TreeNode* root, int level, int target, um<int, int>& aTol, string& str){
        if (root == nullptr){
            return false;
        }
        if (root->val == target){
            return true;
        }
        // find it
        if (recur_start(root->left, level+1, target, aTol, str) || recur_start(root->right, level+1, target, aTol, str)){
            aTol[root->val] = level;
            str.push_back('U');
            return true;
        }
        return false;
    }

    
    bool recur_dest(TreeNode* root, int level, int target, um<int, int>& aTol, string& str){
        if (root == nullptr){
            return false;
        }
        if (root->val == target){
            return true;
        }
        // find it
        if (recur_dest(root->left, level+1, target, aTol, str)){
            aTol[root->val] = level;
            str.push_back('L');
            return true;
        } else if (recur_dest(root->right, level+1, target, aTol, str)) {
            aTol[root->val] = level;
            str.push_back('R');
            return true;
        }
        return false;
    }
};
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