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;
} |
Java
// 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 |
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 |
C#
// 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 |
Javascript
<script> // Javascript implementation of the approach let maximum = Number.MIN_SAFE_INTEGER; let ans = []; let graph = new Array();
for (let i = 0; i < 100; i++){
graph.push( new Array().fill(0));
} let weight = new Array(100).fill(0);
// Function to perform dfs to find // the maximum xored value function dfs(node, parent) {
// If current value is less than
// the current maximum
if (maximum < (weight[node] ^ x)) {
maximum = weight[node] ^ x;
ans = node;
}
for (let to of graph[node]) {
if (to == parent)
continue ;
dfs(to, node);
}
} // Driver code let 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(2); graph[2].push(3); graph[2].push(4); graph[1].push(5); dfs(1, 1); document.write(ans); // This code is contributed by gfgking </script> |
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.