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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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 [tabbyending]

Output:

1


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Improved By : SURENDRA_GANGWAR



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