# Number of distinct subsets of a set

Given an array of n distinct elements, count total number of subsets.

**Examples: **

Input :{1, 2, 3}Output :8Explanation:the array contain total 3 element.its subset are {}, {1}, {2}, {3}, {1, 2}, {2, 3}, {3, 1}, {1, 2, 3}. so the output is 8..

We know number of subsets of set of size n is **2 ^{n}**

**How does this formula work?**

For every element, we have two choices, we either pick it or do not pick it. So in total we have 2 * 2 * … (n times) choices which is **2 ^{n}**

Alternate explanation is :

- Number of subsets of size 0 =
^{n}C_{0} - Number of subsets of size 1 =
^{n}C_{1} - Number of subsets of size 2 =
^{n}C_{2} - ………………..
- Total number of subsets =
^{n}C_{0}+^{n}C_{1}+^{n}C_{2}+ …. +^{n}C_{n}=**2**^{n}

Please refer Sum of Binomial Coefficients for details.

**Implementation:**

## C++

`// CPP program to count number of distinct` `// subsets in an array of distinct numbers` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Returns 2 ^ n` `int` `subsetCount(` `int` `arr[], ` `int` `n)` `{` ` ` `return` `1 << n;` `}` `/* Driver program to test above function */` `int` `main()` `{` ` ` `int` `A[] = { 1, 2, 3 };` ` ` `int` `n = ` `sizeof` `(A) / ` `sizeof` `(A[0]);` ` ` `cout << subsetCount(A, n);` ` ` `return` `0;` `}` |

## Java

`// Java program to count number of distinct` `// subsets in an array of distinct numbers` `class` `GFG {` ` ` ` ` `// Returns 2 ^ n` ` ` `static` `int` `subsetCount(` `int` `arr[], ` `int` `n)` ` ` `{` ` ` `return` `1` `<< n;` ` ` `}` ` ` ` ` `/* Driver program to test above function */` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `A[] = { ` `1` `, ` `2` `, ` `3` `};` ` ` `int` `n = A.length;` ` ` ` ` `System.out.println(subsetCount(A, n));` ` ` `}` `}` `// This code is contributed by Prerna Saini.` |

## Python3

`# Python3 program to count number` `# of distinct subsets in an` `# array of distinct numbers` `import` `math` `# Returns 2 ^ n` `def` `subsetCount(arr, n):` ` ` `return` `1` `<< n` ` ` `# driver code` `A ` `=` `[ ` `1` `, ` `2` `, ` `3` `]` `n ` `=` `len` `(A)` `print` `(subsetCount(A, n))` `# This code is contributed by Gitanjali.` |

## C#

`// C# program to count number of distinct` `// subsets in an array of distinct numbers` `using` `System;` `class` `GFG {` ` ` ` ` `// Returns 2 ^ n` ` ` `static` `int` `subsetCount(` `int` `[]arr, ` `int` `n)` ` ` `{` ` ` `return` `1 << n;` ` ` `}` ` ` ` ` `// Driver program` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[]A = { 1, 2, 3 };` ` ` `int` `n = A.Length;` ` ` ` ` `Console.WriteLine(subsetCount(A, n));` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to count` `// number of distinct` `// subsets in an array` `// of distinct numbers` `// Returns 2 ^ n` `function` `subsetCount(` `$arr` `, ` `$n` `)` `{` ` ` `return` `1 << ` `$n` `;` `}` `// Driver Code` `$A` `= ` `array` `( 1, 2, 3 );` `$n` `= sizeof(` `$A` `);` `echo` `(subsetCount(` `$A` `, ` `$n` `));` `// This code is contributed by Ajit.` `?>` |

## Javascript

`<script>` `// JavaScript program to count number of distinct` `// subsets in an array of distinct numbers` `// Returns 2 ^ n` ` ` `function` `subsetCount(arr, n)` ` ` `{` ` ` `return` `1 << n;` ` ` `}` ` ` `// Driver code` ` ` ` ` `let A = [ 1, 2, 3 ];` ` ` `let n = A.length;` ` ` ` ` `document.write(subsetCount(A, n));` `</script>` |

**Output:**

8