Count of subsequences having maximum distinct elements
Given an arr of size n. The problem is to count all the subsequences having maximum number of distinct elements.
Examples:
Input : arr[] = {4, 7, 6, 7}
Output : 2
The indexes for the subsequences are:
{0, 1, 2} - Subsequence is {4, 7, 6} and
{0, 2, 3} - Subsequence is {4, 6, 7}
Input : arr[] = {9, 6, 4, 4, 5, 9, 6, 1, 2}
Output : 8
Naive Approach: Consider all the subsequences having distinct elements and count the one’s having maximum distinct elements.
Efficient Approach: Create a hash table to store the frequency of each element of the array. Take product of all the frequencies.
The solution is based on the fact that there is always 1 subsequence possible when all elements are distinct. If elements repeat, every occurrence of repeating element makes a mew subsequence of distinct elements.
C++
// C++ implementation to count subsequences having// maximum distinct elements#include <bits/stdc++.h>using namespace std; typedef unsigned long long int ull; // function to count subsequences having// maximum distinct elementsull countSubseq(int arr[], int n){ // unordered_map 'um' implemented as // hash table unordered_map<int, int> um; ull count = 1; // count frequency of each element for (int i = 0; i < n; i++) um[arr[i]]++; // traverse 'um' for (auto itr = um.begin(); itr != um.end(); itr++) // multiply frequency of each element // and accumulate it in 'count' count *= (itr->second); // required number of subsequences return count;} // Driver program to test aboveint main(){ int arr[] = { 4, 7, 6, 7 }; int n = sizeof(arr) / sizeof(arr[0]); cout << "Count = " << countSubseq(arr, n); return 0;} |
Java
// Java implementation to count subsequences having // maximum distinct elementsimport java.util.HashMap; class geeks{ // function to count subsequences having // maximum distinct elements public static long countSubseq(int[] arr, int n) { // unordered_map 'um' implemented as // hash table HashMap<Integer, Integer> um = new HashMap<>(); long count = 1; // count frequency of each element for (int i = 0; i < n; i++) { if (um.get(arr[i]) != null) { int a = um.get(arr[i]); um.put(arr[i], ++a); } else um.put(arr[i], 1); } // traverse 'um' for (HashMap.Entry<Integer, Integer> entry : um.entrySet()) { // multiply frequency of each element // and accumulate it in 'count' count *= entry.getValue(); } // required number of subsequences return count; } // Driver Code public static void main(String[] args) { int[] arr = { 4, 7, 6, 7 }; int n = arr.length; System.out.println("Count = " + countSubseq(arr, n)); }} // This code is contributed by// sanjeev2552 |
Python3
# Python 3 implementation to count subsequences # having maximum distinct elements # function to count subsequences having# maximum distinct elementsdef countSubseq(arr, n): # unordered_map 'um' implemented # as hash table # take range equal to maximum # value of arr um = {i:0 for i in range(8)} count = 1 # count frequency of each element for i in range(n): um[arr[i]] += 1 # traverse 'um' for key, values in um.items(): # multiply frequency of each element # and accumulate it in 'count' if(values > 0): count *= values # required number of subsequences return count # Driver Codeif __name__ == '__main__': arr = [4, 7, 6, 7] n = len(arr) print("Count =", countSubseq(arr, n)) # This code is contributed by# Surendra_Gangwar |
C#
// C# implementation to count subsequences// having maximum distinct elementsusing System;using System.Collections.Generic; class GFG{ // function to count subsequences having // maximum distinct elements public static long countSubseq(int[] arr, int n) { // unordered_map 'um' implemented as // hash table Dictionary<int, int> um = new Dictionary<int, int>(); long count = 1; // count frequency of each element for (int i = 0; i < n; i++) { if (um.ContainsKey(arr[i])) { int a = um[arr[i]]; um.Remove(arr[i]); um.Add(arr[i], ++a); } else um.Add(arr[i], 1); } // traverse 'um' foreach(KeyValuePair<int, int> entry in um) { // multiply frequency of each element // and accumulate it in 'count' count *= entry.Value; } // required number of subsequences return count; } // Driver Code public static void Main(String[] args) { int[] arr = { 4, 7, 6, 7 }; int n = arr.Length; Console.WriteLine("Count = " + countSubseq(arr, n)); }} // This code is contributed by Princi Singh |
Output:
Count = 2
Time Complexity: O(n).
Auxiliary Space: O(n).
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