# 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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 = + + … + answer= Below is the implementation of above idea.

## C++

 `// CPP program to count number of subsequences ` `// which when multiplied result in a power of 2. ` `#include ` `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; ` `} `

## Java

 `// 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.*/`

## Python

 `# 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 `

## C#

 `// 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.*/`

## PHP

 ` `

Output:

```3
0
```

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