# Product of all Subsets of a set formed by first N natural numbers

Given a number N, the task is to find the product of all the elements from all possible subsets of a set formed by first N natural numbers.

Examples:

Input: N = 2
Output: 4
Possible subsets are {{1}, {2}, {1, 2}}.
Product of elements in subsets = {1} * {2} * {1 * 2} = 4

Input: N = 3
Output: 1296
Possible subsets are {{1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}
Product of elements in subsets = 1 * 2 * 3 * (1 * 2) * (1 * 3) * (2 * 3) * (1 * 2 * 3) = 1296

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

Naive Approach: A simple solution is to generate all subsets of first N natural number. Then for every subset, compute its product and finally return overall product of each subset.

Efficient Approach:

• It can be observed that each element of the original array appears in 2(N – 1) times in all subsets.
• Therefore contribution of any element arri in the final answer will be
`i * 2(N – 1)`
• So, the Sum of cubes of all Subsets will be
```12N-1 * 22N-1 * 32N-1......N2N-1
```

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the product of all elements ` `// in all subsets in natural numbers from 1 to N ` `int` `product(``int` `N) ` `{ ` `    ``int` `ans = 1; ` `    ``int` `val = ``pow``(2, N - 1); ` ` `  `    ``for` `(``int` `i = 1; i <= N; i++) { ` `        ``ans *= ``pow``(i, val); ` `    ``} ` ` `  `    ``return` `ans; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `N = 2; ` ` `  `    ``cout << product(N); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `class` `GFG { ` ` `  `    ``// Function to find the product of all elements ` `    ``// in all subsets in natural numbers from 1 to N ` `    ``static` `int` `product(``int` `N) ` `    ``{ ` `        ``int` `ans = ``1``; ` `        ``int` `val = (``int``)Math.pow(``2``, N - ``1``); ` `     `  `        ``for` `(``int` `i = ``1``; i <= N; i++) { ` `            ``ans *= (``int``)Math.pow(i, val); ` `        ``} ` `     `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `N = ``2``; ` `     `  `        ``System.out.println(product(N)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to find the product of all elements ` `# in all subsets in natural numbers from 1 to N ` `def` `product(N) : ` `    ``ans ``=` `1``; ` `    ``val ``=` `2` `*``*``(N ``-` `1``); ` ` `  `    ``for` `i ``in` `range``(``1``, N ``+` `1``) : ` `        ``ans ``*``=` `(i``*``*``val); ` `     `  `    ``return` `ans; ` ` `  ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"` `: ` ` `  `    ``N ``=` `2``; ` ` `  `    ``print``(product(N)); ` `     `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Function to find the product of all elements ` `    ``// in all subsets in natural numbers from 1 to N ` `    ``static` `int` `product(``int` `N) ` `    ``{ ` `        ``int` `ans = 1; ` `        ``int` `val = (``int``)Math.Pow(2, N - 1); ` `     `  `        ``for` `(``int` `i = 1; i <= N; i++) { ` `            ``ans *= (``int``)Math.Pow(i, val); ` `        ``} ` `     `  `        ``return` `ans; ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main (``string``[] args) ` `    ``{ ` `        ``int` `N = 2; ` `     `  `        ``Console.WriteLine(product(N)); ` `    ``} ` `} ` ` `  `// This code is contributed by AnkitRai01 `

Output:

```4
```

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.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Improved By : AnkitRai01

Article Tags :
Practice Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.