<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 {
private:
    // [Node, Parent]
    using Parents = std::unordered_map<TreeNode*, TreeNode*>;
    using Directions = std::string;
    struct TrackerEntry {
        int parent;
        char direction;
    };
    // [Node, {Parent, Direction}] - use values
    using PathTracker = std::unordered_map<int, TrackerEntry>;
    using Visited = std::unordered_set<TreeNode*>;
public:
    Directions getDirections(TreeNode* root, int startValue, int destValue) {
        auto parents = buildParents(root);
        PathTracker tracker;
        std::queue<TreeNode*> queue;
        auto* start = findNode(root, startValue);
        queue.push(start);
        Visited visited;
        while (!queue.empty() && queue.front()->val != destValue) {
            auto* current = queue.front();
            queue.pop();
            visited.insert(current);
            if (current->left && !visited.count(current->left)) {
                tracker[current->left->val] = {current->val, 'L'};
                queue.push(current->left);
            }
            if (current->right && !visited.count(current->right)) {
                tracker[current->right->val] = {current->val, 'R'};
                queue.push(current->right);
            }
            auto* parent = parents[current];
            if (parent && !visited.count(parent)) {
                tracker[parent->val] = {current->val, 'U'};
                queue.push(parent);
            }
        }
        Directions directions;
        while (destValue != startValue) {
            auto& [parent, direction] = tracker[destValue];
            directions += direction;
            destValue = parent;
        }
        std::reverse(directions.begin(), directions.end());
        return directions;
    }
private:
    Parents buildParents(TreeNode* root) {
        Parents parents;
        parents[root] = nullptr;
        std::queue<TreeNode*> queue;
        queue.push(root);
        while (!queue.empty()) {
            auto* current = queue.front();
            queue.pop();
            if (current->left) {
                parents[current->left] = current;
                queue.push(current->left);
            }
            if (current->right) {
                parents[current->right] = current;
                queue.push(current->right);
            }
        }
        return parents;
    }
    TreeNode* findNode(TreeNode* node, int value) {
        if (!node) return nullptr;
        if (node->val == value) return node;
        auto* lhs = findNode(node->left, value);
        auto* rhs = findNode(node->right, value);
        return lhs ? lhs : rhs;
    }
};
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