<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:
        # need to find where the start and dest nodes are
        # find the last common node between the start and dest nodes
        def dfs(node, target, history):
            if not node:
                return False
            if node.val == target:
                return True
            history.append((node.val, "L"))
            l_res = dfs(node.left, target, history)
            if l_res:
                return True
            history.pop()

            history.append((node.val, "R"))
            r_res = dfs(node.right, target, history)
            if r_res:
                return True
            history.pop()
            return False
        
        s_hist, d_hist = [], []
        dfs(root, startValue, s_hist)
        dfs(root, destValue, d_hist)
        common_ptr = 0
        for i in range(1, min(len(s_hist), len(d_hist))):
            if s_hist[i][0] == d_hist[i][0]:
                common_ptr = i
        
        # print(common_ptr)
        # print(s_hist)
        # print(d_hist)
        for i in range(common_ptr, len(s_hist)):
            if s_hist[i][0] == destValue:
                # print("end in path to start", common_ptr, len(s_hist), i)
                return "U"*(len(s_hist) - i)
        for i in range(common_ptr, len(d_hist)):
            if d_hist[i][0] == startValue:
                # print("start in path to end", common_ptr, len(d_hist), i)
                return "".join([i[1] for i in d_hist[i:]])
        
        path = ["U" for _ in range(len(s_hist[common_ptr:]))] + [i[1] for i in d_hist[common_ptr:]]
        return "".join(path)


        # def dfs(node, level, target, parents):
        #     print(node.val if node else "No Node", target)
        #     if not node or node.val == target:
        #         print("returning parents!", parents)
        #         return True
        #     parents.add((level, node.val))
        #     if dfs(node.left, level + 1, target, parents):
        #         return True
        #     if dfs(node.right, level + 1, target, parents):
        #         return True
        #     parents.remove((level, node.val))
        #     return False

        # s_parent_nodes = set()
        # dfs(root, 0, startValue, s_parent_nodes)
        # d_parent_nodes = set()
        # dfs(root, 0, destValue, d_parent_nodes)

        # print(s_parent_nodes, d_parent_nodes)

56106