Minimum cost to make an Array a permutation of first N natural numbers

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Given an array arr of positive integers of size N, the task is to find the minimum cost to make this array a permutation of first N natural numbers, where the cost of incrementing or decrementing an element by 1 is 1.
Examples:

Input: arr[] = {1, 1, 7, 4}
Output: 5
Explanation:
Perform increment operation on 1 one time
Perform decrement operation on 7 four times
Resultant array = {1, 2, 3, 4}
Input: arr[] = {1, 2, 3, 4, 5}
Output: 0
Explanation:
The array is already a permutation.

Approach:

Sort the array element in increasing order
Traverse the sorted array:
- Check if the element at ith index (0 ? i < N) is equals to i + 1.
- If not, then make it equal and increment the difference between the two as the cost of this operation.
When the traversal is complete, print the total cost of the operations performed.

Below is the implementation of the above approach:

C++

// C++ program to calculate minimum cost
// to make an Array a permutation
// of first N natural numbers
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate minimum cost
// for making permutation of size N
int make_permutation(int arr[], int n)
{
    // sorting the array in ascending order
    sort(arr, arr + n);
 
    // To store the required answer
    int ans = 0;
 
    // Traverse the whole array
    for (int i = 0; i < n; i++)
        ans += abs(i + 1 - arr[i]);
 
    // Return the required answer
    return ans;
}
 
// Driver code
int main()
{
    int arr[] = { 5, 3, 8, 1, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function call
    cout << make_permutation(arr, n);
}

Java

// Java program to calculate minimum cost
// to make an Array a permutation
// of first N natural numbers
import java.util.*;
 
class GFG{
  
// Function to calculate minimum cost
// for making permutation of size N
static int make_permutation(int arr[], int n)
{
    // sorting the array in ascending order
    Arrays.sort(arr);
  
    // To store the required answer
    int ans = 0;
  
    // Traverse the whole array
    for (int i = 0; i < n; i++)
        ans += Math.abs(i + 1 - arr[i]);
  
    // Return the required answer
    return ans;
}
  
// Driver code
public static void main(String[] args)
{
    int arr[] = { 5, 3, 8, 1, 1 };
    int n = arr.length;
  
    // Function call
    System.out.print(make_permutation(arr, n));
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python3 program to calculate minimum cost 
# to make an Array a permutation 
# of first N natural numbers 
 
# Function to calculate minimum cost 
# for making permutation of size N 
def make_permutation(arr,  n) :
 
    # sorting the array in ascending order 
    arr.sort(); 
 
    # To store the required answer 
    ans = 0; 
 
    # Traverse the whole array 
    for i in range(n) :
        ans += abs(i + 1 - arr[i]); 
 
    # Return the required answer 
    return ans; 
 
# Driver code 
if __name__ == "__main__" : 
 
    arr = [ 5, 3, 8, 1, 1 ]; 
    n = len(arr); 
 
    # Function call 
    print(make_permutation(arr, n)); 
 
    # This code is contributed by Yash_R

C#

// C# program to calculate minimum cost
// to make an Array a permutation
// of first N natural numbers
using System;
 
class GFG{
  
    // Function to calculate minimum cost
    // for making permutation of size N
    static int make_permutation(int []arr, int n)
    {
        // sorting the array in ascending order
        Array.Sort(arr);
      
        // To store the required answer
        int ans = 0;
      
        // Traverse the whole array
        for (int i = 0; i < n; i++)
            ans += Math.Abs(i + 1 - arr[i]);
      
        // Return the required answer
        return ans;
    }
      
    // Driver code
    public static void Main(string[] args)
    {
        int []arr = { 5, 3, 8, 1, 1 };
        int n = arr.Length;
      
        // Function call
        Console.WriteLine(make_permutation(arr, n));
    }
}
 
// This code is contributed by Yash_R

Javascript

<script>
// Java Script program to calculate minimum cost
// to make an Array a permutation
// of first N natural numbers
 
// Function to calculate minimum cost
// for making permutation of size N
function make_permutation(arr,n)
{
    // sorting the array in ascending order
    arr.sort();
 
    // To store the required answer
    let ans = 0;
 
    // Traverse the whole array
    for (let i = 0; i < n; i++)
        ans += Math.abs(i + 1 - arr[i]);
 
    // Return the required answer
    return ans;
}
 
// Driver code
 
    let arr = [ 5, 3, 8, 1, 1 ];
    let n = arr.length;
 
    // Function call
    document.write(make_permutation(arr, n));
// contributed by sravan kumar
</script>

Output:

Time Complexity: O(n*log(n))
Auxiliary Space: O(1)

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