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 : 8
Explanation
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 2n
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 2n

Alternate explanation is :
Number of subsets of size 0 = nC0
Number of subsets of size 1 = nC1
Number of subsets of size 2 = nC2
………………..

Total number of subsets = nC0 + nC1 + nC2 + …. + nCn = 2n

Please refer Sum of Binomial Coefficients for details.

C++

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// 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

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// 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

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# 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#

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// 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

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<?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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