<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:
        q: list[TreeNode] = [root]
        while q:
            cur_node: TreeNode = q.pop()
            if cur_node.val == startValue:
                start_node = cur_node  # here we're setting up the start node
                break

            if cur_node.left:
                q.append(cur_node.left)
            if cur_node.right:
                q.append(cur_node.right)

        # child node value -> TreeNode object which is parent to node with this value
        nodes_parents: dict[int, TreeNode] = {}
        q = [root]
        while q:
            cur_node = q.pop()
            if cur_node.left:
                nodes_parents[cur_node.left.val] = cur_node
                q.append(cur_node.left)
            if cur_node.right:
                nodes_parents[cur_node.right.val] = cur_node
                q.append(cur_node.right)

        visited = set()
        q = [start_node]
        # key is the destination node to which we travel - value is a tuple with 2 elements - (source_node, direction)
        tracked_path: dict[TreeNode, tuple(TreeNode, str)] = {}

        while q:
            cur_node = q.pop()
            visited.add(cur_node)

            if cur_node.val == destValue:
                destination_node = cur_node
                break  # we've reached the target node

            if cur_node.val in nodes_parents and nodes_parents[cur_node.val] not in visited:
                parent = nodes_parents[cur_node.val]
                q.append(parent)
                tracked_path[parent] = (cur_node, "U")  # this is parent node, we go up

            if cur_node.left and cur_node.left not in visited:
                q.append(cur_node.left)
                tracked_path[cur_node.left] = (cur_node, "L")

            if cur_node.right and cur_node.right not in visited:
                q.append(cur_node.right)
                tracked_path[cur_node.right] = (cur_node, "R")

        # Now we need to construct path in a string from tracked_path we have
        result_path: list[str] = []
        cur_node = destination_node

        while cur_node != start_node:
            source_node, direction = tracked_path[cur_node]
            result_path.append(direction)  # directions will be in reversed order
            cur_node = source_node

        result_path.reverse()
        return "".join(result_path)
399