# Leetcode – Find a Corresponding Node of a Binary Tree in a Clone of That Tree Solution

The problem titled “Find a Corresponding Node of a Binary Tree in a Clone of That Tree” is a fascinating challenge frequently seen on Leetcode. This problem involves binary tree traversal and testing your understanding of Python’s object-oriented features. In this comprehensive guide, we’ll discuss the problem in detail, explore multiple solutions, and provide tips to achieve optimal performance.

1. Understanding the Problem Statement
2. Introducing the Binary Tree Data Structure
3. Initial Thoughts and Pseudocode
4. Solving Using Depth-First Search (DFS)
5. Solving Using Breadth-First Search (BFS)
6. Time and Space Complexity Analysis
7. Testing and Edge Cases
8. Conclusion

## 1. Understanding the Problem Statement

In this problem, you are given two binary trees, original and cloned, and a reference to a node target in the original tree. The cloned tree is a copy of the original tree. Your task is to return a reference to the same node in the cloned tree.

### Constraints and Assumptions

• The number of nodes in the tree is in the range [1, 10^4].
• The values of the nodes of the original tree are unique.
• target node is a reference to a node in the original tree.
• cloned is a copy of original.

## 2. Introducing the Binary Tree Data Structure

Before diving into the problem, let’s define the TreeNode class, which we will use to represent the nodes in the tree.

class TreeNode:
def __init__(self, value=0, left=None, right=None):
self.val = value
self.left = left
self.right = right

## 3. Initial Thoughts and Pseudocode

We can solve this problem by traversing both trees simultaneously until we find the node in the original tree that matches the target. Once we do, we’ll return the corresponding node in the cloned tree.

Pseudocode for DFS approach:

1. Start DFS traversal from the root of the original and cloned trees.
2. If you find target in original, return the corresponding node in cloned.
3. Otherwise, traverse the left and right subtrees.

## 4. Solving Using Depth-First Search (DFS)

The following Python code solves the problem using DFS.

def getTargetCopy(self, original: TreeNode, cloned: TreeNode, target: TreeNode) -> TreeNode:
if not original:
return None

if original == target:
return cloned

left = self.getTargetCopy(original.left, cloned.left, target)
if left:
return left

right = self.getTargetCopy(original.right, cloned.right, target)
if right:
return right

## 5. Solving Using Breadth-First Search (BFS)

You can also solve this problem using BFS, where you’d use a queue to traverse the tree level by level.

from collections import deque

def getTargetCopy(self, original: TreeNode, cloned: TreeNode, target: TreeNode) -> TreeNode:
queue = deque([(original, cloned)])
while queue:
ori, clo = queue.popleft()
if ori == target:
return clo
if ori.left:
queue.append((ori.left, clo.left))
if ori.right:
queue.append((ori.right, clo.right))

## 6. Time and Space Complexity Analysis

• DFS and BFS both have a time complexity of O(n), where n is the number of nodes in the tree.
• The space complexity is also O(n) for both methods due to the maximum recursion depth for DFS and the maximum queue size for BFS.

## 7. Testing and Edge Cases

Test your solution on multiple test cases to make sure it handles all scenarios, including edge cases like a single-node tree or a completely unbalanced tree.

## 8. Conclusion

The problem “Find a Corresponding Node of a Binary Tree in a Clone of That Tree” is an excellent test of your understanding of tree traversal algorithms and object-oriented programming in Python. Both DFS and BFS are viable solutions, with comparable time and space complexity.