<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:

        valuesFound = {"START","DEST"}
        def isStartOrDestinationOrNone(startValue:int, destValue:int, currValue:int) -> str:
            nonlocal valuesFound
            if currValue == startValue:
                return "START"
            elif currValue == destValue:
                return "DEST"
            else:
                return "NONE"        
        
        def getDirectionsRecursive(node,left,right):
            nonlocal valuesFound
            if node is None:
                return ("NONE",[])
            print(node.val)
            

            left,leftArray = getDirectionsRecursive(node.left,left,right)
            right,rightArray = getDirectionsRecursive(node.right,left,right)
            print("both")
            
            print(node.val,"Exit")
            if left == "BOTH":
                return ("BOTH",leftArray)

            if right == "BOTH":
                return ("BOTH",rightArray)
            new_res = []
            res = isStartOrDestinationOrNone(startValue,destValue,node.val)

            
            if res is "START" and left is "DEST":
                startArray = leftArray
                startArray.append("L")
                startArray.reverse()
                for i in startArray:
                    if i == "L" or i == "R":
                        new_res.append(i)
                return("BOTH",new_res)
            elif res is "START" and right is "DEST":
                startArray = rightArray
                startArray.append("R")
                startArray.reverse()
                for i in startArray:
                    if i == "L" or i == "R":
                        new_res.append(i)
                return("BOTH",new_res)
            elif res is "START" and left is "NONE" and right is "NONE":
                return ("START",[])
            elif res is "DEST" and left is "START":
                startArray = leftArray
                startArray.append("L")
                for i in startArray:
                    if i == "L" or i == "R":
                        new_res.append("U")
                return("BOTH",new_res)
            elif res is "DEST" and right is "START":
                startArray = rightArray
                startArray.append("R")
                for i in startArray:
                    if i == "L" or i == "R":
                        new_res.append("U")
                return("BOTH",new_res)
            elif res is "DEST" and left is "NONE" and right is "NONE":
                return ("DEST",[])


            if(left in valuesFound and right in valuesFound):
                if left == "START":
                    startArray = leftArray
                    startArray.append("L")
                elif right == "START":
                    startArray = rightArray
                    startArray.append("R")
                
                if left == "DEST":
                    endArray = leftArray
                    endArray.append("L")
                elif right == "DEST":
                    endArray = rightArray
                    endArray.append("R")

                
                for i in startArray:
                    if i == "L" or i == "R":
                        new_res.append("U")
                endArray.reverse()
                for i in endArray:
                    if i =="L":
                        new_res.append("L")
                    else:
                        new_res.append("R")
        
                return ("BOTH",new_res)
                
            if left == "NONE" and right == "NONE":
                return("NONE",[])
            
            if left == "NONE":
                rightArray.append("R")
                return(right,rightArray)
            
            if right == "NONE":
                leftArray.append("L")
                return(left,leftArray)

                
        
        _,res = getDirectionsRecursive(root,startValue,destValue)
        result = "".join(res)
        return result
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