# Count subsets having distinct even numbers

Given a sequence of n numbers. The task is to count all the subsets of the given set which only have even numbers and all are distinct.

**Note:** By the property of sets, if two subsets have the same set of elements then they are considered as one. For example: [2, 4, 8] and [4, 2, 8] are considered to be the same.

Examples:

Input : {4, 2, 1, 9, 2, 6, 5, 3} Output : 7 The subsets are:[4],[2],[6],[4, 2],[2, 6],[4, 6],[4, 2, 6]Input : {10, 3, 4, 2, 4, 20, 10, 6, 8, 14, 2, 6, 9} Output : 127

A **simple approach** is to consider all the subsets and check whether they satisfy the given conditions or not. The time complexity will be in exponential.

An **efficient approach** is to count number of distinct even numbers. Let this be **ceven**. And then apply formula:

**2 ^{ceven} – 1**

This is similar to counting the number of subsets of a given set of n elements.

**1**is subtracted because the null set is not considered.

## C++

`// C++ implementation to count subsets having ` `// even numbers only and all are distinct ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// function to count the ` `// required subsets ` `int` `countSubsets(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `unordered_set<` `int` `> us; ` ` ` `int` `even_count = 0; ` ` ` ` ` `// inserting even numbers in the set 'us' ` ` ` `// single copy of each number is retained ` ` ` `for` `(` `int` `i=0; i<n; i++) ` ` ` `if` `(arr[i] % 2 == 0) ` ` ` `us.insert(arr[i]); ` ` ` ` ` `unordered_set<` `int` `>:: iterator itr; ` ` ` ` ` `// counting distinct even numbers ` ` ` `for` `(itr=us.begin(); itr!=us.end(); itr++) ` ` ` `even_count++; ` ` ` ` ` `// total count of required subsets ` ` ` `return` `(` `pow` `(2, even_count) - 1); ` `} ` ` ` `// Driver program to test above ` `int` `main() ` `{ ` ` ` `int` `arr[] = {4, 2, 1, 9, 2, 6, 5, 3}; ` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]); ` ` ` `cout << ` `"Number of subsets = "` ` ` `<< countSubsets(arr, n); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java implementation to count subsets having ` `// even numbers only and all are distinct ` `import` `java.util.*; ` ` ` `class` `GFG ` `{ ` ` ` `// function to count the ` `// required subsets ` `static` `int` `countSubsets(` `int` `arr[], ` `int` `n) ` `{ ` ` ` `HashSet<Integer> us = ` `new` `HashSet<>(); ` ` ` `int` `even_count = ` `0` `; ` ` ` ` ` `// inserting even numbers in the set 'us' ` ` ` `// single copy of each number is retained ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) ` ` ` `if` `(arr[i] % ` `2` `== ` `0` `) ` ` ` `us.add(arr[i]); ` ` ` ` ` ` ` `// counting distinct even numbers ` ` ` `even_count=us.size(); ` ` ` ` ` `// total count of required subsets ` ` ` `return` `(` `int` `) (Math.pow(` `2` `, even_count) - ` `1` `); ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `arr[] = {` `4` `, ` `2` `, ` `1` `, ` `9` `, ` `2` `, ` `6` `, ` `5` `, ` `3` `}; ` ` ` `int` `n = arr.length; ` ` ` `System.out.println(` `"Number of subsets = "` ` ` `+ countSubsets(arr, n)); ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji ` |

*chevron_right*

*filter_none*

## Python3

`# python implementation to count subsets having ` `# even numbers only and all are distinct ` ` ` `#function to count the required subsets ` `def` `countSubSets(arr, n): ` ` ` `us ` `=` `set` `() ` ` ` `even_count ` `=` `0` ` ` ` ` `# inserting even numbers in the set 'us' ` ` ` `# single copy of each number is retained ` ` ` `for` `i ` `in` `range` `(n): ` ` ` `if` `arr[i] ` `%` `2` `=` `=` `0` `: ` ` ` `us.add(arr[i]) ` ` ` ` ` `# counting distinct even numbers ` ` ` `for` `i ` `in` `us: ` ` ` `even_count ` `+` `=` `1` ` ` ` ` `# total count of required subsets ` ` ` `return` `pow` `(` `2` `, even_count)` `-` `1` ` ` ` ` `# Driver program ` `arr ` `=` `[` `4` `, ` `2` `, ` `1` `, ` `9` `, ` `2` `, ` `6` `, ` `5` `, ` `3` `] ` `n ` `=` `len` `(arr) ` `print` `(` `"Numbers of subset="` `, countSubSets(arr,n)) ` ` ` `# This code is contributed by Shrikant13 ` ` ` |

*chevron_right*

*filter_none*

## C#

`// C# implementation to count subsets having ` `// even numbers only and all are distinct ` `using` `System; ` `using` `System.Collections.Generic; ` ` ` `class` `GFG ` `{ ` ` ` `// function to count the ` `// required subsets ` `static` `int` `countSubsets(` `int` `[]arr, ` `int` `n) ` `{ ` ` ` `HashSet<` `int` `> us = ` `new` `HashSet<` `int` `>(); ` ` ` `int` `even_count = 0; ` ` ` ` ` `// inserting even numbers in the set 'us' ` ` ` `// single copy of each number is retained ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `if` `(arr[i] % 2 == 0) ` ` ` `us.Add(arr[i]); ` ` ` ` ` ` ` `// counting distinct even numbers ` ` ` `even_count = us.Count; ` ` ` ` ` `// total count of required subsets ` ` ` `return` `(` `int` `) (Math.Pow(2, even_count) - 1); ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `[] arr = {4, 2, 1, 9, 2, 6, 5, 3}; ` ` ` `int` `n = arr.Length; ` ` ` `Console.WriteLine(` `"Number of subsets = "` ` ` `+ countSubsets(arr, n)); ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji ` |

*chevron_right*

*filter_none*

**Output:**

Number of subsets = 7

**Time Complexity:** O(n)

This article is contributed by **Ayush Jauhari**. 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 write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

## Recommended Posts:

- Count minimum number of subsets (or subsequences) with consecutive numbers
- Count of distinct sums that can be obtained by adding prime numbers from given arrays
- Number of distinct subsets of a set
- Minimum number of subsets with distinct elements
- Number of distinct pair of edges such that it partitions both trees into same subsets of nodes
- Count number of subsets having a particular XOR value
- Count no. of ordered subsets having a particular XOR value
- Print all distinct integers that can be formed by K numbers from a given array of N numbers
- Count of all possible pairs of disjoint subsets of integers from 1 to N
- Sum of all subsets of a set formed by first n natural numbers
- Sum of sum of all subsets of a set formed by first N natural numbers
- Count number of subsets whose median is also present in the same subset
- Divide first N natural numbers into 3 equal sum subsets
- Partition an array of non-negative integers into two subsets such that average of both the subsets is equal
- Count distinct Bitwise OR of all Subarrays