# Maximum XOR path of a Binary Tree

Given a Binary Tree, the task is to find the maximum of all the XOR value of all the nodes in the path from the root to leaf.

Examples:

```Input:
2
/ \
1   4
/ \
10  8
Output: 11
Explanation:
All the paths are:
2-1-10 XOR-VALUE = 9
2-1-8 XOR-VALUE = 11
2-4 XOR-VALUE = 6

Input:
2
/   \
1     4
/ \   / \
10  8 5  10
Output: 12
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

1. To solve the question mentioned above we have to traverse the tree recursively using pre-order traversal. For each node keep calculating the XOR of the path from root till the current node.

XOR of current node’s path = (XOR of the path till the parent) ^ (current node value)

2. If the node is a leaf node that is left and the right child for the current nodes are NULL then we compute the max-Xor, as

max-Xor = max(max-Xor, cur-Xor).

Below is the implementation of the above approach:

## C++

 `// C++ program to compute the ` `// Max-Xor value of path from ` `// the root to leaf of a Binary tree ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Binary tree node ` `struct` `Node { ` `    ``int` `data; ` ` `  `    ``struct` `Node *left, *right; ` `}; ` ` `  `// Function to create a new node ` `struct` `Node* newNode(``int` `data) ` `{ ` `    ``struct` `Node* newNode = ``new` `Node; ` ` `  `    ``newNode->data = data; ` ` `  `    ``newNode->left ` `        ``= newNode->right = NULL; ` ` `  `    ``return` `(newNode); ` `} ` ` `  `// Function calculate the ` `// value of max-xor ` `void` `Solve(Node* root, ``int` `xr, ` `           ``int``& max_xor) ` `{ ` ` `  `    ``// Updating the xor value ` `    ``// with the xor of the ` `    ``// path from root to ` `    ``// the node ` `    ``xr = xr ^ root->data; ` ` `  `    ``// Check if node is leaf node ` `    ``if` `(root->left == NULL ` `        ``&& root->right == NULL) { ` ` `  `        ``max_xor = max(max_xor, xr); ` `        ``return``; ` `    ``} ` ` `  `    ``// Check if the left ` `    ``// node exist in the tree ` `    ``if` `(root->left != NULL) { ` `        ``Solve(root->left, xr, ` `              ``max_xor); ` `    ``} ` ` `  `    ``// Check if the right node ` `    ``// exist in the tree ` `    ``if` `(root->right != NULL) { ` `        ``Solve(root->right, xr, ` `              ``max_xor); ` `    ``} ` ` `  `    ``return``; ` `} ` ` `  `// Function to find the ` `// required count ` `int` `findMaxXor(Node* root) ` `{ ` ` `  `    ``int` `xr = 0, max_xor = 0; ` ` `  `    ``// Recursively traverse ` `    ``// the tree and compute ` `    ``// the max_xor ` `    ``Solve(root, xr, max_xor); ` ` `  `    ``// Return the result ` `    ``return` `max_xor; ` `} ` ` `  `// Driver code ` `int` `main(``void``) ` `{ ` `    ``// Create the binary tree ` `    ``struct` `Node* root = newNode(2); ` `    ``root->left = newNode(1); ` `    ``root->right = newNode(4); ` `    ``root->left->left = newNode(10); ` `    ``root->left->right = newNode(8); ` `    ``root->right->left = newNode(5); ` `    ``root->right->right = newNode(10); ` ` `  `    ``cout << findMaxXor(root); ` ` `  `    ``return` `0; ` `} `

## Python3

 `# Python3 program to compute the  ` `# Max-Xor value of path from  ` `# the root to leaf of a Binary tree  ` ` `  `# Binary tree node ` `class` `Node: ` `     `  `    ``# Function to create a new node ` `    ``def` `__init__(``self``, data): ` `         `  `        ``self``.data ``=` `data ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` ` `  `# Function calculate the  ` `# value of max-xor ` `def` `Solve(root, xr, max_xor): ` `     `  `    ``# Updating the xor value  ` `    ``# with the xor of the  ` `    ``# path from root to  ` `    ``# the node ` `    ``xr ``=` `xr ^ root.data ` `     `  `    ``# Check if node is leaf node ` `    ``if` `(root.left ``=``=` `None` `and`  `        ``root.right ``=``=` `None``): ` `        ``max_xor[``0``] ``=` `max``(max_xor[``0``], xr) ` `     `  `    ``# Check if the left  ` `    ``# node exist in the tree ` `    ``if` `root.left !``=` `None``: ` `        ``Solve(root.left, xr, max_xor) ` `     `  `    ``# Check if the right node  ` `    ``# exist in the tree  ` `    ``if` `root.right !``=` `None``: ` `        ``Solve(root.right, xr, max_xor) ` `         `  `    ``return` ` `  `# Function to find the  ` `# required count  ` `def` `findMaxXor(root): ` `     `  `    ``xr, max_xor ``=` `0``, [``0``] ` `     `  `    ``# Recursively traverse  ` `    ``# the tree and compute  ` `    ``# the max_xor  ` `    ``Solve(root, xr, max_xor) ` `     `  `    ``# Return the result ` `    ``return` `max_xor[``0``] ` ` `  `# Driver code ` ` `  `# Create the binary tree ` `root ``=` `Node(``2``) ` `root.left ``=` `Node(``1``) ` `root.right ``=` `Node(``4``)  ` `root.left.left ``=` `Node(``10``)  ` `root.left.right ``=` `Node(``8``)  ` `root.right.left ``=` `Node(``5``)  ` `root.right.right ``=` `Node(``10``)  ` ` `  `print``(findMaxXor(root)) ` ` `  `# This code is contributed by Shivam Singh `

Output:

```12
```

Time Complexity: We are iterating over each node only once, therefore it will take O(N) time where N is the number of nodes in the Binary tree.
Auxiliary Space Complexity: The Auxiliary Space complexity will be O(1), as there is no extra space used My Personal Notes arrow_drop_up Check out this Author's contributed articles.

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