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

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

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; 
      
    // distinct even numbers 
    even_count = us.size(); 
      
    // 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;      
}   

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 

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  
    even_count = len(us) 
  
    # 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 
  

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 

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.

Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.

My Personal Notes

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

C++

Java

Python3

C#

Recommended Posts: