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Count pairs with bitwise OR less than Max
  • Difficulty Level : Basic
  • Last Updated : 02 Apr, 2019
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Given an array arr[] of N integers, the task is to count the pairs of indices (i, j) such that 0 ≤ i < j ≤ N and arr[i] | arr[j] ≤ max(arr[i], arr[j]) where | is the bitwise OR.

Examples:

Input: arr[] = {1, 2, 3}
Output: 2
(1, 3) and (2, 3) are the only valid pairs.

Input: arr[] = {11, 45, 12, 14, 5}
Output: 3

Approach: Run two nested loops and check for every possible pair. If arr[i] | arr[j] <= max(arr[i], arr[j]) then increment the count.



Below is the implementation of the above approach:

C++




// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the count of valid pairs
int countPairs(int arr[], int n)
{
    int cnt = 0;
  
    // Check all possible pairs
    for (int i = 0; i < n - 1; i++)
        for (int j = i + 1; j < n; j++)
            if ((arr[i] | arr[j]) <= max(arr[i], arr[j]))
                cnt++;
  
    return cnt;
}
  
// Driver code
int main()
{
    int arr[] = { 1, 2, 3 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << countPairs(arr, n);
  
    return 0;
}

Java




// Java implementation of the approach
  
class GFG
{
      
// Function to return the count of valid pairs
static int countPairs(int arr[], int n)
{
    int cnt = 0;
  
    // Check all possible pairs
    for (int i = 0; i < n - 1; i++)
        for (int j = i + 1; j < n; j++)
            if ((arr[i] | arr[j]) <= Math.max(arr[i], arr[j]))
                cnt++;
  
    return cnt;
}
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 1, 2, 3 };
    int n = arr.length;
    System.out.println(countPairs(arr, n));
}
}
  
// This code is Contributed by Code_Mech.

Python3




# Python 3 implementation of the approach
  
# Function to return the count 
# of valid pairs
def countPairs(arr, n):
    cnt = 0
  
    # Check all possible pairs
    for i in range(n - 1):
        for j in range(i + 1, n, 1):
            if ((arr[i] | arr[j]) <= max(arr[i], 
                                         arr[j])):
                cnt += 1
  
    return cnt
  
# Driver code
if __name__ == '__main__':
    arr = [1, 2, 3]
    n = len(arr)
    print(countPairs(arr, n))
      
# This code is contributed by
# Surendra_Gangwar

C#




// C# implementation of the approach
using System;
  
class GFG
{
      
// Function to return the count of valid pairs
static int countPairs(int []arr, int n)
{
    int cnt = 0;
  
    // Check all possible pairs
    for (int i = 0; i < n - 1; i++)
        for (int j = i + 1; j < n; j++)
            if ((arr[i] | arr[j]) <= Math.Max(arr[i], arr[j]))
                cnt++;
  
    return cnt;
}
  
// Driver code
static void Main()
{
    int []arr = { 1, 2, 3 };
    int n = arr.Length;
    Console.WriteLine(countPairs(arr, n));
}
}
  
// This code is Contributed by mits.

PHP




<?php
// PHP implementation of the approach
  
// Function to return the count of valid pairs
function countPairs($arr, $n)
{
    $cnt = 0;
  
    // Check all possible pairs
    for ($i = 0; $i < $n - 1; $i++)
        for ($j = $i + 1; $j < $n; $j++)
            if (($arr[$i] | 
                 $arr[$j]) <= max($arr[$i], 
                                  $arr[$j]))
                $cnt++;
  
    return $cnt;
}
  
// Driver code
$arr = array(1, 2, 3);
$n = sizeof($arr);
echo countPairs($arr, $n);
  
// This code is contributed 
// by Akanksha Rai
?>
Output:
2

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