<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 {
    int TreeDepth[100001];
    int TreeParent[100001];
    TreeNode* TreePtr[1000001];
public:
#if 0
    void searchDepth(TreeNode* node, int depth, int parent)
    {
        if (node->left != nullptr)
            searchDepth(node->left, depth + 1, node->val);
        TreeDepth[node->val] = depth;
        TreeParent[node->val] = parent;
        TreePtr[node->val] = node;
        if (node->right != nullptr)
            searchDepth(node->right, depth + 1, node->val);
    }
#else
    void searchDepth(TreeNode* root, int depth, int parent)
    {
        queue<tuple<TreeNode*, int, int>> q;

        q.push(make_tuple(root, depth, -1));
        while (q.empty() != true) {
            TreeNode* node = get<0>(q.front());
            depth = get<1>(q.front());
            parent = get<2>(q.front());
            q.pop();
            TreeDepth[node->val] = depth;
            TreeParent[node->val] = parent;
            TreePtr[node->val] = node;
            if (node->left != nullptr)
                q.push(make_tuple(node->left, depth + 1, node->val));
            if (node->right != nullptr)
                q.push(make_tuple(node->right, depth + 1, node->val));
        }
    }
#endif
    string getDirections(TreeNode* root, int startValue, int destValue) {

        searchDepth(root, 0, root->val);

        int strDepth = TreeDepth[startValue];
        int dstDepth = TreeDepth[destValue];
        int lca;
        int sValue = startValue;
        int dValue = destValue;

        if (strDepth < dstDepth) {
            while (strDepth < dstDepth) {
                dValue = TreeParent[dValue];
                dstDepth = TreeDepth[dValue];
            }
        }
        else {
            while (strDepth > dstDepth) {
                sValue = TreeParent[sValue];
                strDepth = TreeDepth[sValue];
            }
        }

        while (sValue != dValue) {
            sValue = TreeParent[sValue];
            dValue = TreeParent[dValue];
        }

        lca = sValue;
        //cout << lca << endl;
        string str;

        int rPathLen = TreeDepth[startValue] - TreeDepth[lca];
        str.resize(rPathLen, 'U');
        dValue = destValue;

        //cout << TreeDepth[dValue] << " " << TreeDepth[lca] << endl;
        rPathLen = TreeDepth[dValue] - TreeDepth[lca];
        string rPath;
        rPath.resize(rPathLen);

        while (dValue != lca)
        {
            int tmp = TreeParent[dValue];
            if (TreePtr[tmp]->left != nullptr && TreePtr[tmp]->left->val == dValue) {
                //cout << "L";
                rPath[rPathLen - 1] = 'L';
            }
            else {
                //cout << "R";
                rPath[rPathLen - 1] = 'R';
            }
            rPathLen--;
            dValue = tmp;
        }
        //cout << str << rPath << endl;

        return  str + rPath;
    }
};
128803