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:
2ceven – 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 non-adjacent subsets from numbers arranged in Circular fashion
- Find the count of distinct numbers in a range
- Count numbers whose maximum sum of distinct digit-sum is less than or equals M
- 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
- Print all distinct integers that can be formed by K numbers from a given array of N numbers
- Count no. of ordered subsets having a particular XOR value
- Count number of subsets having a particular XOR value
- Count of subsets with sum equal to X
- Count of subsets with sum equal to X using Recursion
- Count of subsets not containing adjacent elements
- Count of Subsets of a given Set with element X present in it
