Powers of two and subsequences

Given an array of size N, find count of subsequences which when multiplied result in a number which is a power of 2.

Examples:

Input : A[] = {1, 2, 3}
Output : 3
Explanation: There are 3 such subsequences {1}, 
{2} and {1, 2}.

Input : A[] = {3, 5, 9}
Output : 0
Explanation: There is no such subsequence.

From the properties of power of two, we can see that it can be expressed only as a product of numbers which itself is power of 2. So first we traverse the array and count the total of numbers in the array which are power of two. Let’s say there are N such numbers in the array. We can either choose 1 or 2 or 3 or … or N such numbers to get a subsequence which is when multiplied results in a number which is power of two.
Therefore the required answer will be:



answer = {{N}\choose{1}} + {{N}\choose{2}} + … + {{N}\choose{N}}

answer= 2^{N}-1

Below is the implementation of above idea.

C++

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// CPP program to count number of subsequences
// which when multiplied result in a power of 2.
#include <bits/stdc++.h>
using namespace std;
  
// Function to check if num is power of 
// two or not.
bool isPowerOf2(int num)
{
    if (num == 0)
        return false;
  
    if (num == 1)
        return true;
  
    if (num & (num - 1))
        return false;
  
    return true;
}
  
// counting all subsequences whose product
// is power of 2.
int countSubsequence(int a[], int size)
{
    int count = 0;
    for (int i = 0; i < size; i++) 
        if (isPowerOf2(a[i]))
            count++;
    return (int)(pow(2, count)) - 1;
}
  
// Driver code
int main()
{
    int a[] = { 1, 2, 3 };
    cout << countSubsequence(a, 3) << endl;
    int b[] = { 3, 5, 9 };
    cout << countSubsequence(b, 3) << endl;
    return 0;
}

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Java

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// JAVA program to count number of 
// subsequences which when multiplied 
// result in a power of 2.
import java.io.*;
import java.math.*;
  
class GFG {
      
    // Function to check if num is 
    // power of two or not.
    static boolean isPowerOf2(int num)
    {
        if (num == 0)
            return false;
       
        if (num == 1)
            return true;
       
        if (num / 2 == (num - 1) / 2)
            return false;
       
        return true;
    }
       
    // counting all subsequences whose
    // product is power of 2.
    static int countSubsequence(int a[], 
                                int size)
    {
        int count = 0;
        for (int i = 0; i < size; i++) 
            if (isPowerOf2(a[i]))
                count++;
        return (int)(Math.pow(2, count)) - 1;
    }
       
    // Driver 
    public static void main(String args[])
    {
        int a[] = { 1, 2, 3 };
        System.out.println(countSubsequence(a, 3));
        int b[] = { 3, 5, 9 };
        System.out.println(countSubsequence(b, 3)) ;
    }
}
  
/*This code is contributed by Nikita Tiwari.*/

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Python

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# Python program to count number of 
# subsequences which when multiplied
# result in a power of 2.
  
# Function to check if num is power
# of two or not.
def isPowerOf2(num) :
    if (num == 0) :
        return False
   
    if (num == 1) :
        return True
   
    if (num & (num - 1)) :
        return False
   
    return True
  
# counting all subsequences whose
# product is power of 2.
def countSubsequence(a, size) :
    count = 0
    for i in range(0,size) :
        if (isPowerOf2(a[i])) :
            count = count + 1
    return (int)(pow(2, count)) - 1
   
# Driver code
a = [ 1, 2, 3 ];
print countSubsequence(a, 3)
b = [ 3, 5, 9 ]
print countSubsequence(b, 3)
  
# This code is contributed by Nikita Tiwari

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C#

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// C# program to count number of 
// subsequences which when multiplied 
// result in a power of 2.
using System;
  
class GFG {
      
    // Function to check if num is 
    // power of two or not.
    static bool isPowerOf2(int num)
    {
        if (num == 0)
            return false;
      
        if (num == 1)
            return true;
      
        if (num / 2 == (num - 1) / 2)
            return false;
      
        return true;
    }
      
    // counting all subsequences whose
    // product is power of 2.
    static int countSubsequence(int []a, 
                                int size)
    {
        int count = 0;
        for (int i = 0; i < size; i++) 
            if (isPowerOf2(a[i]))
                count++;
        return (int)(Math.Pow(2, count)) - 1;
    }
      
    // Driver  code
    public static void Main()
    {
        int []a = { 1, 2, 3 };
        Console.WriteLine(countSubsequence(a, 3));
        int []b = { 3, 5, 9 };
        Console.WriteLine(countSubsequence(b, 3)) ;
    }
}
  
/*This code is contributed by vt_m.*/

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PHP

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<?php
// PHP program to count number
// of subsequences which when 
// multiplied result in a power
// of 2.
  
// Function to check if num 
// is power of  two or not.
function isPowerOf2( $num)
{
    if ($num == 0)
        return false;
  
    if ($num == 1)
        return true;
  
    if ($num & ($num - 1))
        return false;
  
    return true;
}
  
// counting all subsequences whose 
// product is power of 2.
function countSubsequence( $a, $size)
{
    $count = 0;
    for($i = 0; $i < $size; $i++) 
        if (isPowerOf2($a[$i]))
            $count++;
    return pow(2, $count) - 1;
}
  
    // Driver Code
    $a = array(1, 2, 3);
    echo countSubsequence($a, 3) ,"\n";
    $b = array(3, 5, 9);
    echo countSubsequence($b, 3) ;
  
// This code is contributed by anuj_67.
?>

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Output:

3
0

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Improved By : vt_m



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