<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>

class Solution:
    def getDirections(
        self, root: TreeNode, startValue: int, destValue: int
    ) -> str:
        # Map to store parent nodes
        parent_map = {}

        # Find the start node and populate parent map
        start_node = self._find_start_node(root, startValue)
        self._populate_parent_map(root, parent_map)

        # Perform BFS to find the path
        q = deque([start_node])
        visited_nodes = set()
        # Key: next node, Value: <current node, direction>
        path_tracker = {}
        visited_nodes.add(start_node)

        while q:
            current_element = q.popleft()

            # If destination is reached, return the path
            if current_element.val == destValue:
                return self._backtrack_path(current_element, path_tracker)

            # Check and add parent node
            if current_element.val in parent_map:
                parent_node = parent_map[current_element.val]
                if parent_node not in visited_nodes:
                    q.append(parent_node)
                    path_tracker[parent_node] = (current_element, "U")
                    visited_nodes.add(parent_node)

            # Check and add left child
            if (
                current_element.left
                and current_element.left not in visited_nodes
            ):
                q.append(current_element.left)
                path_tracker[current_element.left] = (current_element, "L")
                visited_nodes.add(current_element.left)

            # Check and add right child
            if (
                current_element.right
                and current_element.right not in visited_nodes
            ):
                q.append(current_element.right)
                path_tracker[current_element.right] = (current_element, "R")
                visited_nodes.add(current_element.right)

        # This line should never be reached if the tree is valid
        return ""

    def _backtrack_path(self, node, path_tracker):
        path = []
        # Construct the path
        while node in path_tracker:
            # Add the directions in reverse order and move on to the previous node
            path.append(path_tracker[node][1])
            node = path_tracker[node][0]
        path.reverse()
        return "".join(path)

    def _populate_parent_map(self, node, parent_map):
        if not node:
            return

        # Add children to the map and recurse further
        if node.left:
            parent_map[node.left.val] = node
            self._populate_parent_map(node.left, parent_map)

        if node.right:
            parent_map[node.right.val] = node
            self._populate_parent_map(node.right, parent_map)

    def _find_start_node(self, node, start_value):
        if not node:
            return None

        if node.val == start_value:
            return node

        left_result = self._find_start_node(node.left, start_value)

        # If left subtree returns a node, it must be StartNode. Return it
        # Otherwise, return whatever is returned by right subtree.
        if left_result:
            return left_result
        return self._find_start_node(node.right, start_value)
408