<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:
        parent = {root.val: [-1, 'U']}

        q = [root]
        foundStartValue, foundDestValue = False, False

        while foundStartValue == False or foundDestValue == False:
            curNode = q.pop(0)

            if curNode.val == startValue:
                foundStartValue = True
            if curNode.val == destValue:
                foundDestValue = True

            if foundStartValue and foundDestValue:
                break

            if curNode.left != None:
                parent[curNode.left.val] = [curNode.val, 'L']
                q.append(curNode.left)

            if curNode.right != None:
                parent[curNode.right.val] = [curNode.val, 'R']
                q.append(curNode.right)
                
        temp = startValue
        startVal_history = []
        while temp in parent:
            startVal_history.append([temp, parent[temp][1]])
            temp = parent[temp][0]

        temp = destValue
        destVal_history = []
        while temp in parent:
            destVal_history.append([temp, parent[temp][1]])
            temp = parent[temp][0]

        #print(startVal_history, destVal_history)

        # Check for same node as that is the shared highest level parent
        '''
        if len(destVal_history) < len(startVal_history):
            shortestPath = destVal_history
            longerPath = startVal_history
        else:
            shortestPath = startVal_history
            longerPath = destVal_history

        s_idx = -1
        l_idx = -1
        print(shortestPath, longerPath)
        for i in range(len(shortestPath)):
            if shortestPath[i] in longerPath:
                s_idx = i
                l_idx = longerPath.index(shortestPath[i])
                break
        '''
        s_idx = -1
        d_idx = -1
        for i in range(len(startVal_history)):
            if startVal_history[i] in destVal_history:
                s_idx = i
                d_idx = destVal_history.index(startVal_history[i])
                break

        startVal_history = startVal_history[:s_idx]
        destVal_history = destVal_history[:d_idx]
        #print(s_idx, l_idx, startVal_history, destVal_history)
        res = ""
        for _ in range(len(startVal_history)):
            res += "U"
        for i in range(len(destVal_history)-1, -1, -1):
            res += destVal_history[i][1]
        
        return res

57193