<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 buildMaps(TreeNode* root, 
        std::unordered_map<TreeNode*, TreeNode*>& nodeToParent, 
        std::unordered_map<int, TreeNode*>& valueToNode)
    {
        if (!root)
        {
            return;        
        }        

        valueToNode[root->val] = root;
        
        if (root->left)
        {
            nodeToParent[root->left] = root;
        }

        if (root->right)
        {
            nodeToParent[root->right] = root;
        }

        buildMaps(root->left, nodeToParent, valueToNode);
        buildMaps(root->right, nodeToParent, valueToNode);
    }

    void walkUp(
        std::unordered_map<TreeNode*, TreeNode*>& nodeToParent, 
        TreeNode* start, 
        TreeNode* end, 
        std::string& path)
    {
        std::string tmp;
        while (start != end)
        {
            auto parent = nodeToParent[start];
            if (start == parent->left)
            {
                tmp += 'L';
            }
            else
            {
                tmp += 'R';
            }
            start = parent;
        }
        std::reverse(tmp.begin(), tmp.end());
        path += tmp;
    }

    string getDirections(TreeNode* root, int startValue, int destValue)
    {
        std::unordered_map<TreeNode*, TreeNode*> nodeToParent;
        std::unordered_map<int, TreeNode*> valueToNode;

        buildMaps(root, nodeToParent, valueToNode);

        TreeNode* start = valueToNode[startValue];
        TreeNode* dest = valueToNode[destValue];

        std::unordered_set<TreeNode*> startParents;
        TreeNode* cur = start;
        while (cur)
        {
            startParents.insert(cur);
            cur = nodeToParent[cur];
        }
        TreeNode* commonParent = dest;
        while (!startParents.contains(commonParent))
        {
            commonParent = nodeToParent[commonParent];
        }
        
        // s to parent
        std::string path;
        walkUp(nodeToParent, start, commonParent, path);
        std::string result(path.size(), 'U');

        // dest to parent
        walkUp(nodeToParent, dest, commonParent, result);
        
        return result;
    }
};
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