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++



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// 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;
}

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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG 
{
  
    static int maximum = Integer.MIN_VALUE, x, ans;
  
    @SuppressWarnings("unchecked")
    static Vector<Integer>[] graph = new Vector[100];
    static int[] weight = new int[100];
  
    // This block is executed even before main() function
    // This is necessary otherwise this program will
    // throw "NullPointerException"
    static 
    {
        for (int i = 0; i < 100; i++)
            graph[i] = new Vector<>();
    }
  
    // Function to perform dfs to find
    // the maximum xored value
    static 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
    public static void main(String[] args) 
    {
        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].add(2);
        graph[2].add(3);
        graph[2].add(4);
        graph[1].add(5);
  
        dfs(1, 1);
  
        System.out.println(ans);
    }
}
  
// This code is contributed by
// sanjeev2552

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Python3

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# 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

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C#

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// C# implementation of the approach 
using System; 
using System.Collections.Generic; 
  
class GFG 
  
static int maximum = int.MinValue, x, 
ans = int.MaxValue; 
  
static List<List<int>> graph = new List<List<int>>(); 
static List<int> weight = new List<int>(); 
  
  
// Function to perform dfs to find 
// the maximum value 
static 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 i = 0; i < graph[node].Count; i++) 
    
        if (graph[node][i] == parent) 
            continue
        dfs(graph[node][i], node); 
    
  
// Driver code 
public static void Main() 
    x = 15; 
  
    // Weights of the node 
    weight.Add(0); 
    weight.Add(5); 
    weight.Add(10); 
    weight.Add(11);; 
    weight.Add(8); 
    weight.Add(6); 
      
    for(int i = 0; i < 100; i++) 
    graph.Add(new List<int>()); 
  
    // Edges of the tree 
    graph[1].Add(2); 
    graph[2].Add(3); 
    graph[2].Add(4); 
    graph[1].Add(5); 
  
    dfs(1, 1); 
    Console.Write( ans); 
  
// This code is contributed by SHUBHAMSINGH10 

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Output:

1

Complexity Analysis:

  • Time Complexity : O(N).
    In dfs, every node of the tree is processed once and hence the complexity due to the dfs is O(N) if there are total N nodes in the tree. Therefore, the time complexity is O(N).
  • Auxiliary Space : O(1).
    Any extra space is not required, so the space complexity is constant.

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