<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 Visited = std::unordered_set<TreeNode*>;
    // [Node, [From, Path]]
    using PathTracker = std::unordered_map<TreeNode*, std::pair<TreeNode*, char>>;
public:
    string getDirections(TreeNode* root, int startValue, int destValue) {
        Parents parents;
        populateParents(root, parents);

        auto* startNode = findNode(root, startValue);

        // BFS and populate path tracker
        std::queue<TreeNode*> queue;
        Visited visited;
        PathTracker pathTracker;

        queue.push(startNode);
        visited.insert(startNode);

        while (!queue.empty()) {
            auto* current = queue.front();
            queue.pop();

            if (current->val == destValue) {
                return reconstructPath(pathTracker, current);
            }

            if (parents.count(current) > 0) {
                auto* parent = parents[current];
                if (visited.count(parent) == 0) {
                    queue.push(parent);
                    pathTracker[parent] = {current, 'U'};
                    visited.insert(parent);
                }
            }
            if (current->left &&
                    visited.count(current->left) == 0) {
                queue.push(current->left);
                pathTracker[current->left] = {current, 'L'};
                visited.insert(current->left);
            }
            if (current->right &&
                    visited.count(current->right) == 0) {
                queue.push(current->right);
                pathTracker[current->right] = {current, 'R'};
                visited.insert(current->right);
            }
        }

        assert(false && "We should never get here");
        return "";
    }
private:
    std::string reconstructPath(PathTracker& pathTracker, TreeNode* node)  {
        std::string result;
        while (pathTracker.count(node) != 0) {
            auto [from, direction] = pathTracker[node];
            result += direction;
            node = from;
        }
        std::reverse(result.begin(), result.end());
        return result;
    }

    void populateParents(TreeNode* node, Parents& parents) {
        if (!node) return;
        if (node->left) {
            parents[node->left] = node;
            populateParents(node->left, parents);
        }
        if (node->right) {
            parents[node->right] = node;
            populateParents(node->right, parents);
        }
    }

    TreeNode* findNode(TreeNode* node, int value) {
        if (!node) return nullptr;
        if (node->val == value) return node;
        auto* lhs = findNode(node->left, value);
        if (lhs) return lhs;
        return findNode(node->right, value);
    }
};
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