<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.
# class TreeNode:
#     def __init__(self, val=0, left=None, right=None):
#         self.val = val
#         self.left = left
#         self.right = right
class Solution:
    def getDirections(self, root: Optional[TreeNode], startValue: int, destValue: int) -> str:
        if not root:
            return ""

        self.nodes = {}

        def traverse(root, parent):
            if not root:
                return
            if root.val not in self.nodes:
                self.nodes[root.val] = []
            if parent != -1:
                self.nodes[root.val].append((parent, 'U'))
            if root.left:
                self.nodes[root.val].append((root.left.val, 'L'))
            if root.right:
                self.nodes[root.val].append((root.right.val, 'R'))

            traverse(root.left, root.val)
            traverse(root.right, root.val)

        traverse(root, -1)

        def bfs(start, end):
            queue = deque([(start, '')])
            visited = set([start])
            
            while queue:
                node, path = queue.popleft()
                if node == end:
                    return path
                for neighbor, direction in self.nodes[node]:
                    if neighbor not in visited:
                        visited.add(neighbor)
                        queue.append((neighbor, path + direction))
            return ""

        return bfs(startValue, destValue)


        # self.visited = set()
        # self.visited.add(startValue)
        # self.path_l = []

        # def dfs(cur, dest, path):
            
        #     if cur not in self.nodes:
        #         return

        #     if cur == dest:
        #         self. path_l.append(path.copy())
                

        #     for neighbor in self.nodes[cur]:
        #         if neighbor[0] not in self.visited:
        #             self.visited.add(neighbor[0])
        #             path.append(neighbor[1])
        #             dfs(neighbor[0], dest, path)
        #             path.pop()

        # dfs(startValue, destValue, [])

        # return "".join(self.path_l[0])

        # for i in range(len(self.path_l)):
        #     length = len(self.path_l[i])
        #     self.path_l[i] = (length, "".join(self.path_l[i]))

        # if len(self.path_l) == 1:
        #     return self.path_l[0][1]

        # self.path_l.sort()
        # return self.path_l[0][1]


  

        



            



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