# 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 : 8Explanationthe 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.

## 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; ` `} ` |

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## 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. ` |

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## 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. ` |

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## 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. ` |

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## 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. ` `?> ` |

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**Output:**

8

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