Skip to content
Related Articles

Related Articles

Count pairs with Bitwise-AND as even number
  • Last Updated : 19 Dec, 2018

Given an array of N integers. The task is to find the number of pairs (i, j) such that A[i] & A[j] is even.

Examples:

Input: N = 4, A[] = { 5, 1, 3, 2 }
Output: 3
Since pair of A[] are:
( 5, 1 ), ( 5, 3 ), ( 5, 2 ), ( 1, 3 ), ( 1, 2 ), ( 3, 2 )
5 AND 1 = 1, 5 AND 3 = 1, 5 AND 2 = 0,
1 AND 3 = 1, 1 AND 2 = 0,
3 AND 2 = 2
Total even pair A( i, j ) = 3

Input : N = 6, A[] = { 5, 9, 0, 6, 7, 3 }
Output : 9
Since pair of A[] =
( 5, 9 ) = 1, ( 5, 0 ) = 0, ( 5, 6 ) = 4, ( 5, 7 ) = 5, ( 5, 3 ) = 1,
( 9, 0 ) = 0, ( 9, 6 ) = 0, ( 9, 7 ) = 1, ( 9, 3 ) = 1,
( 0, 6 ) = 0, ( 0, 7 ) = 0, ( 0, 3 ) = 0,
( 6, 7 ) = 6, ( 6, 3 ) = 2,
( 7, 3 ) = 3

A Naive Approach is to check for every pair and print the count of pairs which are even.

Below is the implementation of the above approach:

C++




// C++ program to count pair with
// bitwise-AND as even number
  
#include <iostream>
using namespace std;
  
// Function to count number of pairs EVEN bitwise AND
int findevenPair(int A[], int N)
{
    int i, j;
  
    // variable for counting even pairs
    int evenPair = 0;
  
    // find all pairs
    for (i = 0; i < N; i++) {
        for (j = i + 1; j < N; j++) {
  
            // find AND operation
            // to check evenpair
            if ((A[i] & A[j]) % 2 == 0)
                evenPair++;
        }
    }
  
    // return number of even pair
    return evenPair;
}
  
// Driver Code
int main()
{
  
    int a[] = { 5, 1, 3, 2 };
    int n = sizeof(a) / sizeof(a[0]);
  
    cout << findevenPair(a, n) << endl;
  
    return 0;
}
Java



// Java program to count pair with
// bitwise-AND as even number
import java.io.*;
  
class GFG
{
  
// Function to count number of
// pairs EVEN bitwise AND
static int findevenPair(int []A,
                        int N)
{
    int i, j;
  
    // variable for counting even pairs
    int evenPair = 0;
  
    // find all pairs
    for (i = 0; i < N; i++) 
    {
        for (j = i + 1; j < N; j++)
        {
  
            // find AND operation
            // to check evenpair
            if ((A[i] & A[j]) % 2 == 0)
                evenPair++;
        }
    }
  
    // return number of even pair
    return evenPair;
}
  
// Driver Code
public static void main (String[] args)
{
    int []a = { 5, 1, 3, 2 };
    int n = a.length;
      
    System.out.println(findevenPair(a, n));
}
}
  
// This code is contributed by anuj_67..
Python3



# Python 3 program to count pair with
# bitwise-AND as even number
  
# Function to count number of 
# pairs EVEN bitwise AND
def findevenPair(A, N):
  
    # variable for counting even pairs
    evenPair = 0
  
    # find all pairs
    for i in range(0, N):
        for j in range(i + 1, N):
              
            # find AND operation to 
            # check evenpair
            if ((A[i] & A[j]) % 2 == 0):
                evenPair += 1
  
    # return number of even pair
    return evenPair
  
# Driver Code
a = [ 5, 1, 3, 2 ]
n = len(a)
  
print(findevenPair(a, n))
  
# This code is contributed 
# by PrinciRaj1992
C#



// C# program to count pair with
// bitwise-AND as even number
using System;
  
class GFG
{
  
// Function to count number of
// pairs EVEN bitwise AND
static int findevenPair(int []A,
                        int N)
{
    int i, j;
  
    // variable for counting even pairs
    int evenPair = 0;
  
    // find all pairs
    for (i = 0; i < N; i++) 
    {
        for (j = i + 1; j < N; j++)
        {
  
            // find AND operation
            // to check evenpair
            if ((A[i] & A[j]) % 2 == 0)
                evenPair++;
        }
    }
  
    // return number of even pair
    return evenPair;
}
  
// Driver Code
public static void Main ()
{
    int []a = { 5, 1, 3, 2 };
    int n = a.Length;
      
    Console.WriteLine(findevenPair(a, n));
}
}
  
// This code is contributed by anuj_67..
PHP



<?php
// PHP program to count pair with
// bitwise-AND as even number
  
// Function to count number of 
// pairs EVEN bitwise AND
function findevenPair($A, $N)
{
  
    // variable for counting even pairs
    $evenPair = 0;
      
    // find all pairs
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = $i + 1; $j < $N; $j++)
        {
            // find AND operation
            // to check evenpair
            if (($A[$i] & $A[$j]) % 2 == 0)
                $evenPair++;
        }
    }
  
    // return number of even pair
    return $evenPair;
}
  
// Driver Code
$a = array(5, 1, 3, 2 );
$n = sizeof($a);
echo findevenPair($a, $n);
  
// This code is contributed by akt_mit
?>
Output:


3

An Efficient Approach will be to observe that the bitwise AND of two numbers will be even if atleast one of the two numbers is even. So, count all the odd numbers in the array say count. Now, number of pairs with both odd elements will be count*(count-1)/2.
Therefore, number of elements with atleast one even element will be:
Total Pairs - Count of pair with both odd elements

Below is the implementation of the above approach:
C++



// C++ program to count pair with
// bitwise-AND as even number
  
#include <iostream>
using namespace std;
  
// Function to count number of pairs
// with EVEN bitwise AND
int findevenPair(int A[], int N)
{
    int count = 0;
  
    // count odd numbers
    for (int i = 0; i < N; i++)
        if (A[i] % 2 != 0)
            count++;
  
    // count odd pairs
    int oddCount = count * (count - 1) / 2;
  
    // return number of even pair
    return (N * (N - 1) / 2) - oddCount;
}
  
// Driver Code
int main()
{
  
    int a[] = { 5, 1, 3, 2 };
    int n = sizeof(a) / sizeof(a[0]);
  
    cout << findevenPair(a, n) << endl;
  
    return 0;
}
Java



// Java program to count pair with
// bitwise-AND as even number
  
  
import java.io.*;
  
class GFG {
   
  
  
// Function to count number of pairs
// with EVEN bitwise AND
static int findevenPair(int A[], int N)
{
    int count = 0;
  
    // count odd numbers
    for (int i = 0; i < N; i++)
        if (A[i] % 2 != 0)
            count++;
  
    // count odd pairs
    int oddCount = count * (count - 1) / 2;
  
    // return number of even pair
    return (N * (N - 1) / 2) - oddCount;
}
  
// Driver Code
  
    public static void main (String[] args) {
            int a[] = { 5, 1, 3, 2 };
    int n =a.length;
  
    System.out.print( findevenPair(a, n));
    }
}
// This code is contributed by anuj_67..
Python3



# Python 3 program to count pair with
# bitwise-AND as even number
  
# Function to count number of pairs
# with EVEN bitwise AND
def findevenPair(A, N):
    count = 0
  
    # count odd numbers
    for i in range(0, N):
        if (A[i] % 2 != 0):
            count += 1
  
    # count odd pairs
    oddCount = count * (count - 1) / 2
  
    # return number of even pair
    return (int)((N * (N - 1) / 2) - oddCount)
  
# Driver Code
a = [5, 1, 3, 2 ]
n = len(a)
  
print(findevenPair(a, n))
  
# This code is contributed 
# by PrinciRaj1992 
C#



// C# program to count pair with
// bitwise-AND as even number
  
using System;
  
public class GFG{
      
// Function to count number of pairs
// with EVEN bitwise AND
static int findevenPair(int []A, int N)
{
    int count = 0;
  
    // count odd numbers
    for (int i = 0; i < N; i++)
        if (A[i] % 2 != 0)
            count++;
  
    // count odd pairs
    int oddCount = count * (count - 1) / 2;
  
    // return number of even pair
    return (N * (N - 1) / 2) - oddCount;
}
  
// Driver Code
  
    static public void Main (){
    int []a = { 5, 1, 3, 2 };
    int n =a.Length;
    Console.WriteLine( findevenPair(a, n));
    }
}
// This code is contributed by ajit
PHP



<?php
// PHP program to count pair with
// bitwise-AND as even number
  
// Function to count number of pairs
// with EVEN bitwise AND
function findevenPair($A, $N)
{
    $count = 0;
  
    // count odd numbers
    for ($i = 0; $i < $N; $i++)
        if ($A[$i] % 2 != 0)
            $count++;
  
    // count odd pairs
    $oddCount = $count * ($count - 1) / 2;
  
    // return number of even pair
    return ($N * ($N - 1) / 2) - $oddCount;
}
  
// Driver Code
$a = array(5, 1, 3, 2);
$n = sizeof($a);
  
echo findevenPair($a, $n) . "\n";
  
// This code is contributed 
// by Akanksha Rai
?>
Output:
3

Time Complexity: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.
My Personal Notes
arrow_drop_up
Next
last_page
Count of pairs whose bitwise AND is a power of 2
Recommended Articles
Page :
Maximize count of pairs whose bitwise XOR is even by replacing such pairs with their Bitwise XOR
22, Feb 21
Count pairs with Bitwise XOR as EVEN number
28, Nov 18
Count pairs with Bitwise OR as Even number
22, Aug 18
Count of even and odd power pairs in an Array
25, Jan 20
Count even sum pairs possible by selecting two integers from two given ranges respectively
22, Jan 21
Maximize count of pairs whose Bitwise AND exceeds Bitwise XOR by replacing such pairs with their Bitwise AND
22, Feb 21
Count of pairs {X, Y} from an array such that sum of count of set bits in X ⊕ Y and twice the count of set bits in X & Y is M
12, Mar 21
Number of pairs such that path between pairs has the two vertices A and B
10, Apr 20
Maximum sum of even indexed elements obtained by right shift on an even sized subarray
30, Jun 20
Sum of Array Divisible by Size with Even and Odd Numbers at Odd and Even Index in Java
02, Dec 20
Minimize increments required to make differences between all pairs of array elements even
19, Feb 21
Count of binary strings of length N with even set bit count and at most K consecutive 1s
25, Jun 20
Ways to form n/2 pairs such that difference of pairs is minimum
20, Nov 18
Count of binary strings of length N having equal count of 0's and 1's and count of 1's ≥ count of 0's in each prefix substring
25, Jul 20
Count Numbers with N digits which consists of even number of 0’s
29, Nov 18
Range Queries to count the number of even parity values with updates
12, May 20
Check whether count of odd and even factors of a number are equal
03, Jul 20
Count the number of pairs that have column sum greater than row sum
04, Feb 19
Count pairs (A, B) such that A has X and B has Y number of set bits and A+B = C
27, Nov 18
Count number of pairs (i, j) such that arr[i] * arr[j] > arr[i] + arr[j]
02, Jan 19
Count of pairs in an Array with same number of set bits
21, May 20
Count pairs with Bitwise XOR as ODD number
23, Aug 18
Count pairs with Bitwise AND as ODD number
22, Aug 18
Count number of pairs (i, j) from an array such that arr[i] * j = arr[j] * i
10, Mar 21
Article Contributed By :
https://media.geeksforgeeks.org/auth/avatar.png
VishalBachchas
@VishalBachchas
Vote for difficulty





Improved By :
Article Tags :
Practice Tags :
Report Issue

We use cookies to ensure you have the best browsing experience on our website. By using our site, you
acknowledge that you have read and understood our
Cookie Policy &
        Privacy Policy

Lightbox