# Find the node whose xor with x gives maximum value

Given a tree, and the weights of all the nodes and an integer **x**, the task is to find a node **i** such that **weight[i] xor x** is maximum.

**Examples:**

Input:

x = 15

Output:1

Node 1: 5 xor 15 = 10

Node 2: 10 xor 15 = 5

Node 3: 11 xor 15 = 4

Node 4: 8 xor 15 = 7

Node 5: 6 xor 15 = 9

**Approach:** Perform dfs on the tree and keep track of the node whose weighted xor with **x** gives the maximum value.

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `maximum = INT_MIN, x, ans; ` ` ` `vector<` `int` `> graph[100]; ` `vector<` `int` `> weight(100); ` ` ` `// Function to perform dfs to find ` `// the maximum xored value ` `void` `dfs(` `int` `node, ` `int` `parent) ` `{ ` ` ` `// If current value is less than ` ` ` `// the current maximum ` ` ` `if` `(maximum < (weight[node] ^ x)) { ` ` ` `maximum = weight[node] ^ x; ` ` ` `ans = node; ` ` ` `} ` ` ` `for` `(` `int` `to : graph[node]) { ` ` ` `if` `(to == parent) ` ` ` `continue` `; ` ` ` `dfs(to, node); ` ` ` `} ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `x = 15; ` ` ` ` ` `// Weights of the node ` ` ` `weight[1] = 5; ` ` ` `weight[2] = 10; ` ` ` `weight[3] = 11; ` ` ` `weight[4] = 8; ` ` ` `weight[5] = 6; ` ` ` ` ` `// Edges of the tree ` ` ` `graph[1].push_back(2); ` ` ` `graph[2].push_back(3); ` ` ` `graph[2].push_back(4); ` ` ` `graph[1].push_back(5); ` ` ` ` ` `dfs(1, 1); ` ` ` ` ` `cout << ans; ` ` ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 implementation of the approach ` `import` `sys ` `maximum ` `=` `-` `sys.maxsize ` `-` `1` `graph ` `=` `[[` `0` `for` `i ` `in` `range` `(` `100` `)] ` ` ` `for` `j ` `in` `range` `(` `100` `)] ` `weight ` `=` `[` `0` `for` `i ` `in` `range` `(` `100` `)] ` `ans ` `=` `[] ` ` ` `# Function to perform dfs to find ` `# the maximum xored value ` `def` `dfs(node, parent): ` ` ` `global` `maximum ` ` ` ` ` `# If current value is less than ` ` ` `# the current maximum ` ` ` `if` `(maximum < (weight[node] ^ x)): ` ` ` `maximum ` `=` `weight[node] ^ x ` ` ` `ans.append(node) ` ` ` ` ` `for` `to ` `in` `graph[node]: ` ` ` `if` `(to ` `=` `=` `parent): ` ` ` `continue` ` ` `dfs(to, node) ` ` ` `# Driver code ` `if` `__name__ ` `=` `=` `'__main__'` `: ` ` ` `x ` `=` `15` ` ` ` ` `# Weights of the node ` ` ` `weight[` `1` `] ` `=` `5` ` ` `weight[` `2` `] ` `=` `10` ` ` `weight[` `3` `] ` `=` `11` ` ` `weight[` `4` `] ` `=` `8` ` ` `weight[` `5` `] ` `=` `6` ` ` ` ` `# Edges of the tree ` ` ` `graph[` `1` `].append(` `2` `) ` ` ` `graph[` `2` `].append(` `3` `) ` ` ` `graph[` `2` `].append(` `4` `) ` ` ` `graph[` `1` `].append(` `5` `) ` ` ` ` ` `dfs(` `1` `, ` `1` `) ` ` ` ` ` `print` `(ans[` `0` `]) ` ` ` `# This code is contributed by ` `# Surendra_Gangwar ` |

*chevron_right*

*filter_none*

**Output:**

1

## Recommended Posts:

- Find the node whose sum with X has maximum set bits
- Find the node whose absolute difference with X gives maximum value
- Find the node with maximum value in a Binary Search Tree
- Find the maximum node at a given level in a binary tree
- Find the node with maximum value in a Binary Search Tree using recursion
- Node having maximum sum of immediate children and itself in n-ary tree
- Sum of the distances from every node to all other nodes is maximum
- Get maximum left node in binary tree
- Maximum XOR with given value in the path from root to given node in the tree
- Maximum difference between node and its ancestor in Binary Tree
- Maximum number of nodes which can be reached from each node in a graph.
- Print the node with the maximum degree in the prufer sequence
- Iterative Segment Tree (Range Maximum Query with Node Update)
- Minimum and maximum node that lies in the path connecting two nodes in a Binary Tree
- Implementing a BST where every node stores the maximum number of nodes in the path till any leaf

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.