Minimum number of subsets with distinct elements - GeeksforGeeks

01 Jul, 2021
You are given an array of n-element. You have to make subsets from the array such that no subset contain duplicate elements. Find out minimum number of subset possible.Examples :  
Input : arr[] = {1, 2, 3, 4}
Output :1
Explanation : A single subset can contains all 
values and all values are distinct

Input : arr[] = {1, 2, 3, 3}
Output : 2
Explanation : We need to create two subsets
{1, 2, 3} and {3} [or {1, 3} and {2, 3}] such
that both subsets have distinct elements.
 
We basically need to find the most frequent element in the array. The result is equal to the frequency of the most frequent element.A simple solution is to run two nested loops to count frequency of every element and return the frequency of the most frequent element. Time complexity of this solution is O(n2).A better solution is to first sort the array and then start count number of repetitions of elements in an iterative manner as all repetition of any number lie beside the number itself. By this method you can find the maximum frequency or repetition by simply traversing the sorted array. This approach will cost O(nlogn) time complexity  
C++
Java
Python3
C#
PHP
Javascript
// A sorting based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.#include <bits/stdc++.h>using namespace std; // Function to count subsets such that all// subsets have distinct elements.int subset(int ar[], int n){    // Take input and initialize res = 0    int res = 0;     // Sort the array    sort(ar, ar + n);     // Traverse the input array and    // find maximum frequency    for (int i = 0; i < n; i++) {        int count = 1;         // For each number find its repetition / frequency        for (; i < n - 1; i++) {            if (ar[i] == ar[i + 1])                count++;            else                break;        }         // Update res        res = max(res, count);    }     return res;} // Driver codeint main(){    int arr[] = { 5, 6, 9, 3, 4, 3, 4 };    int n = sizeof(arr) / sizeof(arr[0]);    cout << subset(arr, n);    return 0;}
// A sorting based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.import java.util.*;import java.lang.*; public class GfG{         // Function to count subsets such that all    // subsets have distinct elements.    public static int subset(int ar[], int n)    {        // Take input and initialize res = 0        int res = 0;         // Sort the array        Arrays.sort(ar);         // Traverse the input array and        // find maximum frequency        for (int i = 0; i < n; i++) {            int count = 1;             // For each number find its repetition / frequency            for (; i < n - 1; i++) {                if (ar[i] == ar[i + 1])                    count++;                else                    break;            }             // Update res            res = Math.max(res, count);        }         return res;    }         // Driver function    public static void main(String argc[])    {        int arr[] = { 5, 6, 9, 3, 4, 3, 4 };        int n = 7;        System.out.println(subset(arr, n));    }     } /* This code is contributed by Sagar Shukla */
# A sorting based solution to find the# minimum number of subsets of a set# such that every subset contains distinct# elements. # function to count subsets such that all# subsets have distinct elements.def subset(ar, n):     # take input and initialize res = 0    res = 0     # sort the array    ar.sort()     # traverse the input array and    # find maximum frequency    for i in range(0, n) :        count = 1         # for each number find its repetition / frequency        for i in range(n - 1):            if ar[i] == ar[i + 1]:                count+=1            else:                break                     # update res        res = max(res, count)         return res  # Driver codear = [ 5, 6, 9, 3, 4, 3, 4 ]n = len(ar)print(subset(ar, n)) # This code is contributed by# Smitha Dinesh Semwal
// A sorting based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.using System; public class GfG {         // Function to count subsets such that all    // subsets have distinct elements.    public static int subset(int []ar, int n)    {        // Take input and initialize res = 0        int res = 0;         // Sort the array        Array.Sort(ar);         // Traverse the input array and        // find maximum frequency        for (int i = 0; i < n; i++) {            int count = 1;             // For each number find its            // repetition / frequency            for ( ; i < n - 1; i++) {                if (ar[i] == ar[i + 1])                    count++;                else                    break;            }             // Update res            res = Math.Max(res, count);        }         return res;    }         // Driver function    public static void Main()    {        int []arr = { 5, 6, 9, 3, 4, 3, 4 };        int n = 7;                 Console.WriteLine(subset(arr, n));    }     } /* This code is contributed by Vt_m */
<?php// A sorting based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements. // Function to count subsets such that all// subsets have distinct elements.function subset($ar, $n){    // Take input and initialize res = 0    $res = 0;     // Sort the array    sort($ar);     // Traverse the input array and    // find maximum frequency    for ($i = 0; $i < $n; $i++)    {        $count = 1;         // For each number find its        // repetition / frequency        for (; $i < $n - 1; $i++)        {            if ($ar[$i] == $ar[$i + 1])                $count++;            else                break;        }         // Update res        $res = max($res, $count);    }     return $res;} // Driver code$arr = array( 5, 6, 9, 3, 4, 3, 4 );$n = sizeof($arr);echo subset($arr, $n); // This code is contributed// by Sach_Code?>
<script> // JavaScript program sorting based solution to find the// minimum number of subsets of a set// such that every subset contains distinct     // Function to count subsets such that all    // subsets have distinct elements.    function subset(ar, n)    {             // Take input and initialize res = 0        let res = 0;           // Sort the array        ar.sort();           // Traverse the input array and        // find maximum frequency        for (let i = 0; i < n; i++)        {            let count = 1;               // For each number find its repetition / frequency            for (; i < n - 1; i++)            {                if (ar[i] == ar[i + 1])                    count++;                else                    break;            }               // Update res            res = Math.max(res, count);        }        return res;    }      // Driver Code        let arr = [ 5, 6, 9, 3, 4, 3, 4 ];        let n = 7;        document.write(subset(arr, n)); // This code is contributed by chinmoy1997pal.</script>
Output:  
2
 An efficient solution is to use hashing. We count frequencies of all elements in a hash table. Finally we return the key with maximum value in hash table.  
C++
Java
Python3
C#
Javascript
// A hashing based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.#include <bits/stdc++.h>using namespace std; // Function to count subsets such that all// subsets have distinct elements.int subset(int arr[], int n){      // Traverse the input array and    // store frequencies of elements    unordered_map<int, int> mp;       for (int i = 0; i < n; i++)        mp[arr[i]]++;         // Find the maximum value in map.    int res = 0;    for (auto x : mp)       res = max(res, x.second);     return res;} // Driver codeint main(){    int arr[] = { 5, 6, 9, 3, 4, 3, 4 };    int n = sizeof(arr) / sizeof(arr[0]);    cout << subset(arr, n);    return 0;}
import java.util.HashMap;import java.util.Map; // A hashing based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.class GFG{     // Function to count subsets such that all// subsets have distinct elements.static int subset(int arr[], int n){    // Traverse the input array and    // store frequencies of elements    HashMap<Integer, Integer> mp = new HashMap<>();    for (int i = 0; i < n; i++)        mp.put(arr[i],mp.get(arr[i]) == null?1:mp.get(arr[i])+1);         // Find the maximum value in map.    int res = 0;    for (Map.Entry<Integer,Integer> entry : mp.entrySet())    res = Math.max(res, entry.getValue());     return res;} // Driver codepublic static void main(String[] args){    int arr[] = { 5, 6, 9, 3, 4, 3, 4 };    int n = arr.length;    System.out.println( subset(arr, n)); }} // This code is contributed by Rajput-Ji
# A hashing based solution to find the# minimum number of subsets of a set such # that every subset contains distinct# elements. # Function to count subsets such that# all subsets have distinct elements.def subset(arr, n):         # Traverse the input array and    # store frequencies of elements    mp = {i:0 for i in range(10)}    for i in range(n):        mp[arr[i]] += 1         # Find the maximum value in map.    res = 0    for key, value in mp.items():        res = max(res, value)     return res # Driver codeif __name__ == '__main__':    arr = [5, 6, 9, 3, 4, 3, 4]    n = len(arr)    print(subset(arr, n)) # This code is contributed by# Surendra_Gangwar
// A hashing based solution to find the// minimum number of subsets of a set// such that every subset contains distinct// elements.using System;using System.Collections.Generic; class GFG{     // Function to count subsets such that all// subsets have distinct elements.static int subset(int []arr, int n){    // Traverse the input array and    // store frequencies of elements    Dictionary<int,               int> mp = new Dictionary<int,                                        int>();    for (int i = 0 ; i < n; i++)    {        if(mp.ContainsKey(arr[i]))        {            var val = mp[arr[i]];            mp.Remove(arr[i]);            mp.Add(arr[i], val + 1);        }        else        {            mp.Add(arr[i], 1);        }    }         // Find the maximum value in map.    int res = 0;    foreach(KeyValuePair<int, int> entry in mp)        res = Math.Max(res, entry.Value);     return res;} // Driver codepublic static void Main(String[] args){    int []arr = { 5, 6, 9, 3, 4, 3, 4 };    int n = arr.Length;    Console.WriteLine(subset(arr, n));}} // This code is contributed by Rajput-Ji
<script>      // A hashing based solution to find the      // minimum number of subsets of a set      // such that every subset contains distinct      // elements.      // Function to count subsets such that all      // subsets have distinct elements.      function subset(arr, n) {        // Traverse the input array and        // store frequencies of elements        var mp = {};        for (var i = 0; i < n; i++) {          if (mp.hasOwnProperty(arr[i])) {            var val = mp[arr[i]];            delete mp[arr[i]];            mp[arr[i]] = val + 1;          } else {            mp[arr[i]] = 1;          }        }         // Find the maximum value in map.        var res = 0;        for (const [key, value] of Object.entries(mp)) {          res = Math.max(res, value);        }        return res;      }       // Driver code      var arr = [5, 6, 9, 3, 4, 3, 4];      var n = arr.length;      document.write(subset(arr, n));             // This code is contributed by rdtank.    </script>
Output :  
2
 
Sach_Code
SURENDRA_GANGWAR
Rajput-Ji
chinmoy1997pal
rdtank
Arrays
Hash
Sorting
Arrays
Hash
Sorting
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