# Maximum XOR with given value in the path from root to given node in the tree

Given a tree with N distinct nodes from the range [1, n] and two integers x and val. The task is to find the maximum value of any node when XORed with x on the path from the root to val.

Examples:

```Input: val = 6, x = 4
1
/ \
2   3
/     \
4       5
/
6
Output: 7
the path is 1 -> 3 -> 5 -> 6
1 ^ 4 = 5
3 ^ 4 = 7
5 ^ 4 = 1
6 ^ 4 = 2
Maximum is 7

Input: val = 4, x = 1
1
/ \
2   3
/
4
Output: 5
```

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

Approach:

• An optimized solution to the problem is to create a parent array to store the parent of each of the node.
• Start from the given node and keep on going up in the tree using the parent array (this will be helpful when answering a number of queries as only the nodes on the path will be traversed). Take the xor with x of all the nodes in the path till root.
• The maximum xor calculated for the path is the answer.

Below is the implementation of the above approach:

## C++

 `// CPP implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Tree node ` `class` `Node ` `{ ` `public``: ` `    ``int` `data; ` `    ``Node *left, *right; ` ` `  `    ``Node(``int` `data) ` `    ``{ ` `        ``this``->data = data; ` `        ``this``->left = NULL; ` `        ``this``->right = NULL; ` `    ``} ` `}; ` ` `  `// Recursive function to update ` `// the parent array such that parent[i] ` `// stores the parent of i ` `void` `updateParent(``int` `*parent, Node *node) ` `{ ` `    ``// If node is null then return ` `    ``if` `(node == NULL) ` `        ``return``; ` ` `  `    ``// If left child of the node is not ` `    ``// null then set node as the parent ` `    ``// of its left child ` `    ``if` `(node->left != NULL) ` `        ``parent[node->left->data] = node->data; ` ` `  `    ``// If right child of the node is not ` `    ``// null then set node as the parent ` `    ``// of its right child ` `    ``if` `(node->right != NULL) ` `        ``parent[node->right->data] = node->data; ` ` `  `    ``// Recursive call for the ` `    ``// children of current node ` `    ``updateParent(parent, node->left); ` `    ``updateParent(parent, node->right); ` `} ` ` `  `// Function to return the maximum value ` `// of a node on the path from root to val ` `// when Xored with x ` `int` `getMaxXor(Node *root, ``int` `n, ``int` `val, ``int` `x) ` `{ ` `    ``// Create the parent array ` `    ``int` `*parent = ``new` `int``[n + 1]; ` `    ``updateParent(parent, root); ` ` `  `    ``// Initialze max with x XOR val ` `    ``int` `maximum = x ^ val; ` ` `  `    ``// Get to the parent of val ` `    ``val = parent[val]; ` ` `  `    ``// 0 is the parent of the root ` `    ``while` `(val != 0) ` `    ``{ ` `        ``// Update maximum ` `        ``maximum = max(maximum, x ^ val); ` ` `  `        ``// Get one level up the tree ` `        ``val = parent[val]; ` `    ``} ` `    ``return` `maximum; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `n = 6; ` `    ``Node *root; ` `    ``root = ``new` `Node(1); ` `    ``root->left = ``new` `Node(2); ` `    ``root->right = ``new` `Node(3); ` `    ``root->left->left = ``new` `Node(4); ` `    ``root->right->right = ``new` `Node(5); ` `    ``root->right->right->left = ``new` `Node(6); ` ` `  `    ``int` `val = 6, x = 4; ` `    ``cout << getMaxXor(root, n, val, x) << endl; ` ` `  `    ``return` `0; ` `} ` ` `  `// This code is contributed by ` `// sanjeev2552 `

## Java

 `// Java implementation of the approach ` `public` `class` `GFG { ` ` `  `    ``// Tree node ` `    ``static` `class` `Node { ` `        ``int` `data; ` `        ``Node left, right; ` `        ``Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `            ``left = ``null``; ` `            ``right = ``null``; ` `        ``} ` `    ``} ` ` `  `    ``// Recursive function to update ` `    ``// the parent array such that parent[i] ` `    ``// stores the parent of i ` `    ``static` `void` `updateParent(``int` `parent[], ` `                             ``Node node) ` `    ``{ ` ` `  `        ``// If node is null then return ` `        ``if` `(node == ``null``) ` `            ``return``; ` ` `  `        ``// If left child of the node is not ` `        ``// null then set node as the parent ` `        ``// of its left child ` `        ``if` `(node.left != ``null``) ` `            ``parent[node.left.data] = node.data; ` ` `  `        ``// If right child of the node is not ` `        ``// null then set node as the parent ` `        ``// of its right child ` `        ``if` `(node.right != ``null``) ` `            ``parent[node.right.data] = node.data; ` ` `  `        ``// Recursive call for the ` `        ``// children of current node ` `        ``updateParent(parent, node.left); ` `        ``updateParent(parent, node.right); ` `    ``} ` ` `  `    ``// Function to return the maximum value ` `    ``// of a node on the path from root to val ` `    ``// when Xored with x ` `    ``static` `int` `getMaxXor(Node root, ` `                         ``int` `n, ``int` `val, ``int` `x) ` `    ``{ ` ` `  `        ``// Create the parent array ` `        ``int` `parent[] = ``new` `int``[n + ``1``]; ` `        ``updateParent(parent, root); ` ` `  `        ``// Initialze max with x XOR val ` `        ``int` `max = x ^ val; ` ` `  `        ``// Get to the parent of val ` `        ``val = parent[val]; ` ` `  `        ``// 0 is the parent of the root ` `        ``while` `(val != ``0``) { ` ` `  `            ``// Update maximum ` `            ``max = Math.max(max, x ^ val); ` ` `  `            ``// Get one level up the tree ` `            ``val = parent[val]; ` `        ``} ` `        ``return` `max; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``int` `n = ``6``; ` `        ``Node root = ``new` `Node(``1``); ` `        ``root.left = ``new` `Node(``2``); ` `        ``root.right = ``new` `Node(``3``); ` `        ``root.left.left = ``new` `Node(``4``); ` `        ``root.right.right = ``new` `Node(``5``); ` `        ``root.right.right.left = ``new` `Node(``6``); ` ` `  `        ``int` `val = ``6``, x = ``4``; ` `        ``System.out.println(getMaxXor(root, n, val, x)); ` `    ``} ` `} `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Tree node ` `class` `Node: ` `    ``def` `__init__(``self``, data): ` `        ``self``.data ``=` `data ` `        ``self``.left ``=` `None` `        ``self``.right ``=` `None` `     `  `# Recursive function to update ` `# the parent array such that parent[i] ` `# stores the parent of i ` `def` `updateParent(parent, node): ` ` `  `    ``# If node is None then return ` `    ``if` `(node ``=``=` `None``): ` `        ``return` `parent ` ` `  `    ``# If left child of the node is not ` `    ``# None then set node as the parent ` `    ``# of its left child ` `    ``if` `(node.left !``=` `None``): ` `        ``parent[node.left.data] ``=` `node.data ` ` `  `    ``# If right child of the node is not ` `    ``# None then set node as the parent ` `    ``# of its right child ` `    ``if` `(node.right !``=` `None``): ` `        ``parent[node.right.data] ``=` `node.data ` ` `  `    ``# Recursive call for the ` `    ``# children of current node ` `    ``parent ``=` `updateParent(parent, node.left) ` `    ``parent ``=` `updateParent(parent, node.right) ` `    ``return` `parent ` ` `  `# Function to return the maximum value ` `# of a node on the path from root to val ` `# when Xored with x ` `def` `getMaxXor(root, n, val, x): ` ` `  `    ``# Create the parent array ` `    ``parent ``=` `[``0``]``*``(n ``+` `1``) ` `    ``parent``=``updateParent(parent, root) ` ` `  `    ``# Initialze max with x XOR val ` `    ``maximum ``=` `x ^ val ` ` `  `    ``# Get to the parent of val ` `    ``val ``=` `parent[val] ` ` `  `    ``# 0 is the parent of the root ` `    ``while` `(val !``=` `0``): ` `     `  `        ``# Update maximum ` `        ``maximum ``=` `max``(maximum, x ^ val) ` ` `  `        ``# Get one level up the tree ` `        ``val ``=` `parent[val] ` `     `  `    ``return` `maximum ` ` `  `# Driver Code ` `n ``=` `6` ` `  `root ``=` `Node(``1``) ` `root.left ``=` `Node(``2``) ` `root.right ``=` `Node(``3``) ` `root.left.left ``=` `Node(``4``) ` `root.right.right ``=` `Node(``5``) ` `root.right.right.left ``=` `Node(``6``) ` ` `  `val ``=` `6` `x ``=` `4` `print``( getMaxXor(root, n, val, x) ) ` ` `  `# This code is contributed by Arnab Kundu ` ` `  ` `

## C#

 `// C# implementation of the approach  ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `    ``// Tree node ` `    ``public` `class` `Node  ` `    ``{ ` `        ``public` `int` `data; ` `        ``public` `Node left, right; ` `        ``public` `Node(``int` `data) ` `        ``{ ` `            ``this``.data = data; ` `            ``left = ``null``; ` `            ``right = ``null``; ` `        ``} ` `    ``} ` ` `  `    ``// Recursive function to update ` `    ``// the parent array such that parent[i] ` `    ``// stores the parent of i ` `    ``static` `void` `updateParent(``int` `[]parent, ` `                             ``Node node) ` `    ``{ ` ` `  `        ``// If node is null then return ` `        ``if` `(node == ``null``) ` `            ``return``; ` ` `  `        ``// If left child of the node is not ` `        ``// null then set node as the parent ` `        ``// of its left child ` `        ``if` `(node.left != ``null``) ` `            ``parent[node.left.data] = node.data; ` ` `  `        ``// If right child of the node is not ` `        ``// null then set node as the parent ` `        ``// of its right child ` `        ``if` `(node.right != ``null``) ` `            ``parent[node.right.data] = node.data; ` ` `  `        ``// Recursive call for the ` `        ``// children of current node ` `        ``updateParent(parent, node.left); ` `        ``updateParent(parent, node.right); ` `    ``} ` ` `  `    ``// Function to return the maximum value ` `    ``// of a node on the path from root to val ` `    ``// when Xored with x ` `    ``static` `int` `getMaxXor(Node root, ``int` `n,  ` `                         ``int` `val, ``int` `x) ` `    ``{ ` ` `  `        ``// Create the parent array ` `        ``int` `[]parent = ``new` `int``[n + 1]; ` `        ``updateParent(parent, root); ` ` `  `        ``// Initialze max with x XOR val ` `        ``int` `max = x ^ val; ` ` `  `        ``// Get to the parent of val ` `        ``val = parent[val]; ` ` `  `        ``// 0 is the parent of the root ` `        ``while` `(val != 0)  ` `        ``{ ` ` `  `            ``// Update maximum ` `            ``max = Math.Max(max, x ^ val); ` ` `  `            ``// Get one level up the tree ` `            ``val = parent[val]; ` `        ``} ` `        ``return` `max; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``int` `n = 6; ` `        ``Node root = ``new` `Node(1); ` `        ``root.left = ``new` `Node(2); ` `        ``root.right = ``new` `Node(3); ` `        ``root.left.left = ``new` `Node(4); ` `        ``root.right.right = ``new` `Node(5); ` `        ``root.right.right.left = ``new` `Node(6); ` ` `  `        ``int` `val = 6, x = 4; ` `        ``Console.WriteLine(getMaxXor(root, n, val, x)); ` `    ``} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```7
```

Time Complexity: O(N)

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