- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# XOR of the path between any two nodes in a Binary Tree in C++

In this problem, we are given a binary tree and two nodes of the binary tree. Our task is to print the XOR of all nodes that come in the path between the two nodes.

Let’s take an example to understand the problem,

We need to find the xor of all nodes between 2 and 3.

The path from 2 to 3, 2 → 6 → 1 → 3.

We will find 2^3^1^3.

**Output** −

To solve this problem, we need to find the paths from one to another node. For this, we will find the XOR of all nodes in the path from the root to both nodes. On doing this there is two cases while traversing from the root node, either the source and destination node both lie on the same side of the root node or they lie on different sides of the root node. In the first case, all nodes that do not come in the path will be traversed twice and will be canceled out. And in the former case whole path from the root to nodes is needs to be considered. At each step we will find the XOR of the node with the previous found XOR result, this will save space.

## Example

Program to show the implementation of our solution,

#include <bits/stdc++.h> using namespace std; struct Node { int data; Node *left, *right; }; struct Node* getNode(int data){ struct Node* newNode = new Node; newNode->data = data; newNode->left = newNode->right = NULL; return newNode; } void pathStoD(Node* root, unordered_map<int, int>& path, int XOR){ if (!root) return; path.insert(make_pair(root->data, XOR ^ root->data)); XOR ^= root->data; if (root->left) pathStoD(root->left, path, XOR); if (root->right) pathStoD(root->right, path, XOR); } int findPathXOR(unordered_map<int, int> path, int node1, int node2){ return path[node1] ^ path[node2]; } int main(){ struct Node* root = getNode(1); root->left = getNode(6); root->left->left = getNode(2); root->left->right = getNode(4); root->right = getNode(3); root->right->left = getNode(7); root->right->right = getNode(5); int XOR = 0; unordered_map<int, int> mp; int source = 2; int destination = 3; pathStoD(root, mp, XOR); cout<<"The XOR of all node from "<<source<<" to "<<destination<<" of the tree is : "; cout<<findPathXOR(mp, source, destination); return 0; }

## Output

The XOR of all node from 2 to 3 of the tree is : 7

- Related Questions & Answers
- Print path between any two nodes in a Binary Tree in C++ Programming.
- Program to find the largest sum of the path between two nodes in a binary tree in Python
- Find distance between two nodes of a Binary Tree in C++
- Program to find longest path between two nodes of a tree in Python
- Find distance between two nodes of a Binary Tree in C++ Program
- Print all nodes between two given levels in Binary Tree in C++
- Program to find largest sum of any path of a binary tree in Python
- Program to find out distance between two nodes in a binary tree in Python
- Program to print nodes between two given level numbers of a binary tree using C++
- C++ Program to Find Path Between Two Nodes in a Graph
- Queries to find distance between two nodes of a Binary tree – O(logn) method in C++
- Validate Binary Tree Nodes in C++
- Product of all nodes in a Binary Tree in C++
- XOR of all the nodes in the sub-tree of the given node in C++
- Minimum sum path between two leaves of a binary trees in C++