Count unordered pairs (i,j) such that product of a[i] and a[j] is power of two

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Given an array of N elements. The task is to count unordered pairs (i, j) in the array such that the product of a[i] and a[j] can be expressed as a power of two.

Examples:

Input : arr[] = {2, 3, 4, 8, 10}
Output : 3
Explanation: The pair of array element will be 
(2, 4), (2, 8), (4, 8) whose product are 
8, 16, 32 respectively which can be expressed 
as power of 2, like 2^3, 2^4, 2^5.

Input : arr[] = { 2, 5, 8, 16, 128 }
Output : 6

If you multiply $x$ and $y$ and their product become $z$ , then z=x*y, now if it’s possible to express $z$ as power of two then it can be proved that both $x$ and $y$ can be expressed as power of two. Basically z= 2^a = 2^(b+c) = 2^b * 2^c = x * y, where $b$ and $c$ both can hold a minimum value 0.

So now we have to count the number of elements in the array which can be expressed as a power of two. If the count is k, then answer will be kC2 = k*(k-1)/2, as we need the count of unordered pairs.

Below is the implementation of above approach:

C++

// C++ program to Count unordered pairs (i, j)
// in array such that product of a[i] and a[j]
// can be expressed as power of two
#include <bits/stdc++.h>
using namespace std;
 
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int x) 
{ 
  /* First x in the below expression is
     for the case when x is 0 */
  return x && (!(x&(x-1))); 
} 
 
// Function to Count unordered pairs
void Count_pairs(int a[], int n)
{
    int count = 0;
 
    for (int i = 0; i < n; i++) {
 
        // is a number can be expressed
        // as power of two
        if (isPowerOfTwo(a[i]))
            count++;
    }
 
    // count total number
    // of unordered pairs
    int ans = (count * (count - 1)) / 2;
 
    cout << ans << "\n";
}
 
// Driver code
int main()
{
    int a[] = { 2, 5, 8, 16, 128 };
 
    int n = sizeof(a) / sizeof(a[0]);
 
    Count_pairs(a, n);
 
    return 0;
}

Java

// Java program to Count unordered pairs (i, j)
// in array such that product of a[i] and a[j]
// can be expressed as power of two
 
import java.io.*;
 
class GFG {
 
 
/* Function to check if x is power of 2*/
static boolean isPowerOfTwo(int x) 
{ 
/* First x in the below expression is
    for the case when x is 0 */
return (x >0&& (!((x&(x-1))>0))); 
} 
 
// Function to Count unordered pairs
static void Count_pairs(int a[], int n)
{
    int count = 0;
 
    for (int i = 0; i < n; i++) {
 
        // is a number can be expressed
        // as power of two
        if (isPowerOfTwo(a[i]))
            count++;
    }
 
    // count total number
    // of unordered pairs
    int ans = (count * (count - 1)) / 2;
 
    System.out.println( ans);
}
 
// Driver code
 
    public static void main (String[] args) {
            int a[] = { 2, 5, 8, 16, 128 };
 
    int n = a.length;
    Count_pairs(a, n);
 
    }
}
 
// This code is contributed
// by shs

Python 3

# Python3 program to Count unordered pairs 
# (i, j) in array such that product of a[i] 
# and a[j] can be expressed as power of two 
 
# Function to check if x is power of 2
def isPowerOfTwo(x) :
 
    # First x in the below expression 
    # is for the case when x is 0 
    return (x and(not(x & (x - 1))))
 
# Function to Count unordered pairs 
def Count_pairs(a, n) :
 
    count = 0
 
    for i in range(n) :
 
        # is a number can be expressed 
        # as power of two 
        if isPowerOfTwo(a[i]) :
            count += 1
 
    # count total number 
    # of unordered pairs
    ans = (count * (count - 1)) / 2
 
    print(ans)
 
# Driver code     
if __name__ == "__main__" :
 
    a = [ 2, 5, 8, 16, 128]
 
    n = len(a)
 
    Count_pairs(a, n)
                 
# This code is contributed by ANKITRAI1

C#

// C# program to Count unordered pairs (i, j) 
// in array such that product of a[i] and a[j] 
// can be expressed as power of two 
 
using System;
 
public class GFG{
     
     
/* Function to check if x is power of 2*/
static bool isPowerOfTwo(int x) 
{ 
/* First x in the below expression is 
    for the case when x is 0 */
return (x >0&& (!((x&(x-1))>0))); 
} 
 
// Function to Count unordered pairs 
static void Count_pairs(int []a, int n) 
{ 
    int count = 0; 
 
    for (int i = 0; i < n; i++) { 
 
        // is a number can be expressed 
        // as power of two 
        if (isPowerOfTwo(a[i])) 
            count++; 
    } 
 
    // count total number 
    // of unordered pairs 
    int ans = (count * (count - 1)) / 2; 
 
    Console.WriteLine( ans); 
} 
 
// Driver code 
 
    static public void Main (){
            int []a = { 2, 5, 8, 16, 128 }; 
 
    int n = a.Length; 
    Count_pairs(a, n); 
 
    } 
} 
 
// This code is contributed 
// by Sach_Code

PHP

<?php
// PHP program to Count unordered 
// pairs (i, j) in array such that 
// product of a[i] and a[j] can be 
// expressed as power of two 
 
/* Function to check if x is power of 2*/
function isPowerOfTwo($x) 
{ 
    /* First x in the below expression is 
        for the case when x is 0 */
    return ($x && (!($x & ($x - 1)))); 
} 
 
// Function to Count unordered pairs 
function Count_pairs($a, $n) 
{ 
    $count = 0; 
 
    for ($i = 0; $i < $n; $i++) 
    { 
 
        // is a number can be expressed 
        // as power of two 
        if (isPowerOfTwo($a[$i])) 
            $count++; 
    } 
 
    // count total number 
    // of unordered pairs 
    $ans = ($count * ($count - 1)) / 2; 
 
    echo $ans , "\n"; 
} 
 
// Driver code 
$a = array( 2, 5, 8, 16, 128 ); 
 
$n = sizeof($a); 
 
Count_pairs($a, $n); 
 
// This code is contributed 
// by Sach_code
?>

Javascript

<script>
 
// JavaScript program to 
// Count unordered pairs (i, j)
// in array such that product of a[i] and a[j]
// can be expressed as power of two
 
 
 
/* Function to check if x is power of 2*/
function isPowerOfTwo( x)
{
/* First x in the below expression is
    for the case when x is 0 */
return (x >0&& (!((x&(x-1))>0)));
}
 
// Function to Count unordered pairs
function Count_pairs(a,n)
{
    let count = 0;
 
    for (let i = 0; i < n; i++) {
 
        // is a number can be expressed
        // as power of two
        if (isPowerOfTwo(a[i]))
            count++;
    }
 
    // count total number
    // of unordered pairs
    let ans = (count * (count - 1)) / 2;
 
    document.write( ans);
}
 
// Driver code
 
    let a = [ 2, 5, 8, 16, 128 ];
 
    let n = a.length;
    Count_pairs(a, n);
 
// This code is contributed by sravan kumar
 
</script>

Output

Complexity Analysis:

Time Complexity: O(N), where N is the number of elements in the array.
Auxiliary Space: O(1)

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