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 = 5Output :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 = 4Output :4

Remove all elements. One can’t make subsequence of the form

{0, 1, 2, 3}

**Approach:**

- Let cnt
_{0}be the number of subsequences of [0], cnt_{1}be the number of subsequences [0, 1], cnt_{2}— the number of subsequences [0, 1, 2] and so on, and cnt_{k-1}is the number of completed subsequences [0, 1, 2, 3, …k-1]. - Iterate over all elements of arr in order from left to right.If the current element in the array is zero then increase the count of cnt
_{0}by 1. - If the current element in the array is not zero then check if its previous element in the sequence count is greater than zero or not.
- If its previous element in the sequence is greater than zero then decrement the count of the previous element by one and increment count of the current element by one.

Below is the implementation of the above approach:

## C++

`// C++ 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 decrement 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;` `}` |

## Java

`// 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 decrement 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` |

## Python3

`# 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` `] ` `*` `k ` ` ` ` ` `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 decrement 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` |

## C#

`// 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 decrement 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` |

**Output:**

2

**Time Complexity : **O(N)