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

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>

Output

2

Time Complexity: O(N*N)
Auxiliary Space: O(1)