Minimize deletion or insertions of Array elements such that arr[i] have frequency as its value

Given an array arr[] of length N, the task is to find the minimum number of operations to change the array such that each arr[i] occurs arr[i] times where in each operation either one element can be deleted from the array or one element can be inserted in the array.

Examples:

Input: N = 4, arr[ ] = {1, 1, 3, 3}
Output: 2
Explanation: Delete one occurrence of 1 from the array in one operation.
In another operation, insert element 3 in the array.
The final array will be [ 1, 3, 3, 3 ] where 1 occurs 1 time and 3 occurs 3 times.
Minimum 2 operations are needed. It cannot be reconstructed in less than 2 moves.
Input: N = 6, arr[ ] = {3, 3, 5,, 3, 2, 4}
Output: 3

Approach: The solution to the problem is based on the following idea:

For each array element (arr[i]), there are two choices: either delete all the occurrences of arr[i] or insert arr[i] such that number of occurrences is not same as its value.
Choose the minimum among the required number of deletions and insertions to minimize the total number of operations.

Follow the steps mentioned below to implement the idea:

Store the frequency of all the elements
Check if the frequency of the element is higher or greater than its value:
- If the frequency is higher than the best choice is to remove the element until the frequency becomes same as the current element.
- Else there are two choices:
  - Delete all the occurrences of the element.
  - Insert the element such that the frequency is same as its value.
- Add the minimum of these two in the final count of operations.
Return the final count as the answer.

Below is the implementation for the above approach:

C++

// C++ code to implement the approach
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find out minimum
// number of operation
int minOperations(int N, vector<int>& a)
{
   
    // Map for storing frequency
    // of the array elements
    unordered_map<int, int> mp;
 
    for (auto x : a) {
        mp[x]++;
    }
 
    // Variable to store the answer
    int operations = 0;
    for (auto x : mp) {
        int occurrences = x.second;
 
        // If the occurrence is greater
        // than number then the greedy
        // move is to remove extra occurrences
        if (occurrences > x.first) {
            operations += (occurrences - x.first);
        }
 
        // Else you can remove all the
        // occurrences of the number or
        // add the number sometimes until
        // the occurrences of the number are
        // not equal to the number itself so
        // you have to take the minimum of
        // all the occurrences
        else if (occurrences < x.first) {
            operations += min(occurrences,
                              x.first - occurrences);
        }
    }
 
    // Return the operations
    return operations;
}
 
// Driver code
int main()
{
    int N = 6;
    vector<int> arr = { 3, 3, 5, 3, 2, 4 };
 
    // Function call
    cout << minOperations(N, arr) << endl;
    return 0;
}

Java

// Java code to implement the approach
import java.io.*;
import java.util.HashMap;
import java.util.Map;
  
 
class GFG {
 
// Function to find out minimum
// number of operation
static int minOperations(int N, int a[])
{
   
    // Map for storing frequency
    // of the array elements
    HashMap<Integer, Integer> mp = new HashMap<Integer, Integer>();
 
    for(int i = 0; i < N; i++){
          if(mp.containsKey(a[i])){
              mp.put(a[i], mp.get(a[i]) + 1);
        }
       else{
              mp.put(a[i], 1);
       }
    }
 
    // Variable to store the answer
    int operations = 0;
      int occurrences = 0;
    for (Map.Entry<Integer, Integer> x : mp.entrySet()){       
           occurrences = x.getValue();
 
        // If the occurrence is greater
        // than number then the greedy
        // move is to remove extra occurrences
        if (occurrences > x.getKey()) {
            operations += (occurrences - x.getKey());
        }
 
        // Else you can remove all the
        // occurrences of the number or
        // add the number sometimes until
        // the occurrences of the number are
        // not equal to the number itself so
        // you have to take the minimum of
        // all the occurrences
        else if (occurrences < x.getKey()) {
            operations += Math.min(occurrences,
                              x.getKey() - occurrences);
        }
    }
    // Return the operations
    return operations;
}
 
// Driver code
    public static void main (String[] args) {
           int N = 6;
         int arr[] = { 3, 3, 5, 3, 2, 4 };
 
        // Function call
        System.out.print(minOperations(N, arr));
    }
}

Python3

# Python3 code to implement the above approach
from collections import Counter
 
# function to calculate the no of operations
def minOperations(N, a):
    # a dictionary that stores the frequencies
    mp = dict(Counter(a))
     
    # variable to store the operations
    operations = 0
     
    # if occurrence > x, then the greedy move is
    # to remove extra occurrences
    for x in mp:
        occurrences = mp[x]
         
        if occurrences > x:
            operations += occurrences - x
             
        # else, you can remove all the occurrences of the no
        # or add x until the occurrences
        # of x are not equal to x itself.
        elif occurrences < x:
            operations += min(occurrences, x - occurrences)
    # return the operations
    return operations
     
# Driver Code
N = 6
arr = [3, 3, 5, 3, 2, 4]
print(minOperations(N, arr))
 
# This code is contributed by phasing17

C#

// C# code to implement the approach
using System;
using System.Collections.Generic;
 
class GFG {
 
  // Function to find out minimum
  // number of operation
  static int minOperations(int N, int[] a)
  {
 
    // Map for storing frequency
    // of the array elements
    Dictionary<int, int> mp
      = new Dictionary<int, int>();
 
    for (int i = 0; i < a.Length; i++) {
      if (mp.ContainsKey(a[i])) {
        mp[a[i]] = mp[a[i]] + 1;
      }
      else {
        mp.Add(a[i], 1);
      }
    }
 
    // Variable to store the answer
    int operations = 0;
    foreach(KeyValuePair<int, int> x in mp)
    {
 
      int occurrences = x.Value;
 
      // If the occurrence is greater
      // than number then the greedy
      // move is to remove extra occurrences
      if (occurrences > x.Key) {
        operations += (occurrences - x.Key);
      }
 
      // Else you can remove all the
      // occurrences of the number or
      // add the number sometimes until
      // the occurrences of the number are
      // not equal to the number itself so
      // you have to take the minimum of
      // all the occurrences
      else if (occurrences < x.Key) {
        operations += Math.Min(occurrences,
                               x.Key - occurrences);
      }
    }
 
    // Return the operations
    return operations;
  }
 
  // Driver code
  public static void Main()
  {
    int N = 6;
    int[] arr = { 3, 3, 5, 3, 2, 4 };
 
    // Function call
    Console.Write(minOperations(N, arr));
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
    // JavaScript code to implement the approach
 
    // Function to find out minimum
    // number of operation
    const minOperations = (N, a) => {
     
        // Map for storing frequency
        // of the array elements
        let mp = {};
 
        for (let x in a) {
            mp[a[x]] = a[x] in mp ? mp[a[x]] + 1 : 1;
        }
 
        // Variable to store the answer
        let operations = 0;
        for (let x in mp) {
            let occurrences = mp[x];
 
            // If the occurrence is greater
            // than number then the greedy
            // move is to remove extra occurrences
            if (occurrences > x) {
                operations += (occurrences - x);
            }
 
            // Else you can remove all the
            // occurrences of the number or
            // add the number sometimes until
            // the occurrences of the number are
            // not equal to the number itself so
            // you have to take the minimum of
            // all the occurrences
            else if (occurrences < x) {
                operations += Math.min(occurrences,
                    x - occurrences);
            }
        }
 
        // Return the operations
        return operations;
    }
 
    // Driver code
    let N = 6;
    let arr = [3, 3, 5, 3, 2, 4];
 
    // Function call
    document.write(minOperations(N, arr));
 
// This code is contributed by rakeshsahni
 
</script>