Find the minimum number of elements that should be removed to make an array good

Given an array of size N and an integer K. The array consists of only digits {0, 1, 2, 3, …k-1}. The task is to make array good by removing some of the elements. The array of length x is called good if x is divisible by k and one can split the given array into x/k subsequences and each of form {0, 1, 2, 3, …k-1}.

Note: An empty array is also a good array

Examples:



Input : a[] = {0, 1, 2, 3, 4, 0, 1, 0, 1, 2, 3, 4}, K = 5
Output : 2
First sequence is formed from first, second, third, fourth
and fifth element and second sequence is formed from eighth, ninth tenth, eleventh
and twelth. so, remove last fivth and sixth elements.

Input : a[] = {0, 2, 1, 3}, k = 4
Output : 4
Remove all elements. One can’t make subsequence of the form
{0, 1, 2, 3}

Approach:

Below is the implementation of the above approach:

filter_none

edit
close

play_arrow

link
brightness_4
code

// CPP program to remove minimum elements to
// make the given array good
#include <bits/stdc++.h>
using namespace std;
  
// Function to remove minimum elements to
// make the given array good
int MinRemove(int a[], int n, int k)
{
    // To store count of each subsequence
    vector<int> cnt(k, 0);
  
    for (int i = 0; i < n; i++) {
        // Increase the count of subsequence [0]
        if (a[i] == 0)
            cnt[0]++;
  
        // If Previous element subsequence count
        // is greater than zero then increment
        // subsequence count of current element
        // and increment subsequence count of
        // the previous element.
        else if (cnt[a[i] - 1] > 0) {
            cnt[a[i] - 1]--;
            cnt[a[i]]++;
        }
    }
  
    // Return the required answer
    return n - (k * cnt[k - 1]);
}
  
// Driver code
int main()
{
  
    int a[] = { 0, 1, 2, 3, 4, 0,
                1, 0, 1, 2, 3, 4 },
        k = 5;
  
    int n = sizeof(a) / sizeof(a[0]);
  
    // Function call
    cout << MinRemove(a, n, k);
  
    return 0;
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to remove minimum elements to
// make the given array good
import java.util.Collections;
import java.util.Vector;
  
class GFG
{
    // Function to remove minimum elements to
    // make the given array good
    static int MinRemove(int[] a, int n, int k)
    {
        // To store count of each subsequence
        int []cnt = new int[n];
        for (int i = 0; i < n; i++) 
        {
            // Increase the count of subsequence [0]
            if (a[i] == 0)
                cnt[0]++;
  
            // If Previous element subsequence count
            // is greater than zero then increment
            // subsequence count of current element
            // and increment subsequence count of
            // the previous element.
            else if (cnt[a[i] - 1] > 0)
            {
                cnt[a[i] - 1]--;
                cnt[a[i]]++;
            }
        }
  
        // Return the required answer
        return n - (k * cnt[k - 1]);
    }
  
    // Driver code
    public static void main(String[] args)
    {
  
  
        int a[] = { 0, 1, 2, 3, 4, 0,
                    1, 0, 1, 2, 3, 4 };
        int k = 5;
  
        int n = a.length;
  
        // Function call
        System.out.println(MinRemove(a, n, k));
    }
}
  
// This code contributed by Rajput-Ji
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 program to remove minimum elements to 
# make the given array good 
  
# Function to remove minimum elements to 
# make the given array good 
def MinRemove(a, n, k) : 
  
    # To store count of each subsequence 
    cnt = [0] *
  
    for i in range(n) :
        # Increase the count of subsequence [0] 
        if (a[i] == 0) :
            cnt[0] += 1
  
        # If Previous element subsequence count 
        # is greater than zero then increment 
        # subsequence count of current element 
        # and increment subsequence count of 
        # the previous element. 
        elif (cnt[a[i] - 1] > 0) :
            cnt[a[i] - 1] -= 1
            cnt[a[i]] += 1
  
    # Return the required answer 
    return n - (k * cnt[k - 1]); 
  
  
# Driver code 
if __name__ == "__main__"
  
    a = [ 0, 1, 2, 3, 4, 0
                1, 0, 1, 2, 3, 4
    k = 5
  
    n = len(a); 
  
    # Function call 
    print(MinRemove(a, n, k)); 
      
# This code is contributed by AnkitRai01
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to remove minimum elements to
// make the given array good
using System;
  
class GFG
{
    // Function to remove minimum elements to
    // make the given array good
    static int MinRemove(int[] a, int n, int k)
    {
        // To store count of each subsequence
        int []cnt = new int[n];
        for (int i = 0; i < n; i++) 
        {
            // Increase the count of subsequence [0]
            if (a[i] == 0)
                cnt[0]++;
  
            // If Previous element subsequence count
            // is greater than zero then increment
            // subsequence count of current element
            // and increment subsequence count of
            // the previous element.
            else if (cnt[a[i] - 1] > 0)
            {
                cnt[a[i] - 1]--;
                cnt[a[i]]++;
            }
        }
  
        // Return the required answer
        return n - (k * cnt[k - 1]);
    }
  
    // Driver code
    public static void Main(String[] args)
    {
        int []a = { 0, 1, 2, 3, 4, 0,
                    1, 0, 1, 2, 3, 4 };
        int k = 5;
        int n = a.Length;
  
        // Function call
        Console.WriteLine(MinRemove(a, n, k));
    }
}
  
// This code is contributed by 29AjayKumar
chevron_right

Output:
2

Time Complexity : O(N)





Check out this Author's contributed articles.

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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Improved By : Rajput-Ji, AnkitRai01, 29AjayKumar

Article Tags :
Practice Tags :