Count of pairs with bitwise XOR value greater than its bitwise AND value

Last Updated : 28 Oct, 2022

Given an array arr that contains N positive Integers. Find the count of all possible pairs whose bitwise XOR value is greater than bitwise AND value

Examples:

Input : arr[]={ 12, 4, 15}
Output: 2
Explanation: 12 ^ 4 = 8, 12 & 4 = 4. so 12 ^ 4 > 12 & 4
4 ^ 15 = 11, 4 & 15 = 4. so 4 ^ 15 > 4 & 15 .
So, above two are valid pairs { 12, 4 }, {4, 15} .

Input: arr[] = { 1, 1, 3, 3 }
Output: 4

Approach: Refer to the below idea for the approach to solve this problem:

We know that, for an array of length N, there will be a total (N*(N-1))/2 pairs.

Therefore check for every pair, and increase count by one if a pair satisfy the given condition in the question.

Follow the below steps to solve this problem:

Check for every pair whether their bit wise XOR value is greater than bit wise AND or not.
If yes then increase the count
Return the count.

Below is the Implementation of the above approach:

C++

// C++ program to Count number of pairs
// whose bit wise XOR value is greater
// than bit wise AND value
 
#include <bits/stdc++.h>
using namespace std;
 
// Function that return count of pairs
// whose bitwise xor >= bitwise and
long long valid_pairs(int arr[], int N)
{
    long long cnt = 0;
    // check for all possible pairs
    for (int i = 0; i < N; i++) {
        for (int j = i + 1; j < N; j++) {
            if ((arr[i] ^ arr[j]) >= (arr[i] & arr[j]))
                cnt++;
        }
    }
 
    return cnt;
}
 
// Driver Code
int main()
{
    int N = 3;
    int arr[] = { 12, 4, 15 };
    cout << valid_pairs(arr, N);
}

Java

// Java program to Count number of pairs
// whose bit wise XOR value is greater
// than bit wise AND value
import java.io.*;
 
class GFG 
{
 
  // Function that return count of pairs
  // whose bitwise xor >= bitwise
  public static long valid_pairs(int arr[], int N)
  {
    long cnt = 0;
 
    // check for all possible pairs
    for (int i = 0; i < N; i++) {
      for (int j = i + 1; j < N; j++) {
        if ((arr[i] ^ arr[j]) >= (arr[i] & arr[j]))
          cnt++;
      }
    }
 
    return cnt;
  }
 
  // Driver code
  public static void main(String[] args)
  {
    int N = 3;
    int arr[] = { 12, 4, 15 };
    System.out.print(valid_pairs(arr, N));
  }
}
 
// This code is contributed by Rohit Pradhan.

Python3

# python3 program to Count number of pairs
# whose bit wise XOR value is greater
# than bit wise AND value
 
# Function that return count of pairs
# whose bitwise xor >= bitwise
def valid_pairs(arr, N):
 
    cnt = 0
     
    # check for all possible pairs
    for i in range(0, N):
        for j in range(i + 1, N):
            if ((arr[i] ^ arr[j]) >= (arr[i] & arr[j])):
                cnt += 1
 
    return cnt
 
# Driver Code
if __name__ == "__main__":
 
    N = 3
    arr = [12, 4, 15]
    print(valid_pairs(arr, N))
 
    # This code is contributed by rakeshsahni

C#

// C# program to Count number of pairs
// whose bit wise XOR value is greater
// than bit wise AND value
using System;
 
class GFG {
 
  // Function that return count of pairs
  // whose bitwise xor >= bitwise
  public static long valid_pairs(int[] arr, int N)
  {
    long cnt = 0;
 
    // check for all possible pairs
    for (int i = 0; i < N; i++) {
      for (int j = i + 1; j < N; j++) {
        if ((arr[i] ^ arr[j]) >= (arr[i] & arr[j]))
          cnt++;
      }
    }
 
    return cnt;
  }
 
  // Driver code
  public static void Main(string[] args)
  {
    int N = 3;
    int[] arr = { 12, 4, 15 };
    Console.Write(valid_pairs(arr, N));
  }
}
 
// This code is contributed by ukasp.

Javascript

<script>
       // JavaScript code for the above approach
 
 
       // Function that return count of pairs
       // whose bitwise xor >= bitwise
       function valid_pairs(arr, N) {
           let cnt = 0;
           // check for all possible pairs
           for (let i = 0; i < N; i++) {
               for (let j = i + 1; j < N; j++) {
                   if ((arr[i] ^ arr[j]) >= (arr[i] & arr[j]))
                       cnt++;
               }
           }
 
           return cnt;
       }
 
       // Driver Code
 
       let N = 3;
       let arr = [12, 4, 15];
       document.write(valid_pairs(arr, N));
 
   // This code is contributed by Potta Lokesh
   </script>