Minimum steps to convert an Array into permutation of numbers from 1 to N

Given an array arr of length N, the task is to count the minimum number of operations to convert given sequence into a permutation of first N natural numbers (1, 2, …., N). In each operation, increment or decrement an element by one.
Examples:

Input: arr[] = {4, 1, 3, 6, 5} 
Output: 4 
Apply decrement operation four times on 6
Input : arr[] = {0, 2, 3, 4, 1, 6, 8, 9} 
Output : 7 

Approach: An efficient approach is to sort the given array and for each element, find the difference between the arr[i] and i(1 based indexing). Find the sum of all such difference, and this will be the minimum steps required.
Below is the implementation of the above approach:

CPP

// C++ program to find minimum number of steps to
// convert a given sequence into a permutation

#include <bits/stdc++.h>
using namespace std;

// Function to find minimum number of steps to
// convert a given sequence into a permutation
int get_permutation(int arr[], int n)
{
    // Sort the given array
    sort(arr, arr + n);

    // To store the required minimum
    // number of operations
    int result = 0;

    // Find the operations on each step
    for (int i = 0; i < n; i++) {
        result += abs(arr[i] - (i + 1));
    }

    // Return the answer
    return result;
}

// Driver code
int main()
{
    int arr[] = { 0, 2, 3, 4, 1, 6, 8, 9 };

    int n = sizeof(arr) / sizeof(arr[0]);

    // Function call
    cout << get_permutation(arr, n);

    return 0;
}

Java

// Java program to find minimum number of steps to
// convert a given sequence into a permutation
import java.util.*;

class GFG{

// Function to find minimum number of steps to
// convert a given sequence into a permutation
static int get_permutation(int arr[], int n)
{
    // Sort the given array
    Arrays.sort(arr);

    // To store the required minimum
    // number of operations
    int result = 0;

    // Find the operations on each step
    for (int i = 0; i < n; i++) {
        result += Math.abs(arr[i] - (i + 1));
    }

    // Return the answer
    return result;
}

// Driver code
public static void main(String[] args)
{
    int arr[] = { 0, 2, 3, 4, 1, 6, 8, 9 };

    int n = arr.length;

    // Function call
    System.out.print(get_permutation(arr, n));

}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program to find minimum number of steps to
# convert a given sequence into a permutation

# Function to find minimum number of steps to
# convert a given sequence into a permutation
def get_permutation(arr, n):

    # Sort the given array
    arr = sorted(arr)

    # To store the required minimum
    # number of operations
    result = 0

    # Find the operations on each step
    for i in range(n):
        result += abs(arr[i] - (i + 1))

    # Return the answer
    return result

# Driver code
if __name__ == '__main__':
    arr=[0, 2, 3, 4, 1, 6, 8, 9]
    n = len(arr)

    # Function call
    print(get_permutation(arr, n))

# This code is contributed by mohit kumar 29

C#

// C# program to find minimum number of steps to
// convert a given sequence into a permutation
using System;

class GFG{

// Function to find minimum number of steps to
// convert a given sequence into a permutation
static int get_permutation(int []arr, int n)
{
    // Sort the given array
    Array.Sort(arr);

    // To store the required minimum
    // number of operations
    int result = 0;

    // Find the operations on each step
    for (int i = 0; i < n; i++) {
        result += Math.Abs(arr[i] - (i + 1));
    }

    // Return the answer
    return result;
}

// Driver Code
public static void Main()
{
    int []arr = { 0, 2, 3, 4, 1, 6, 8, 9 };

    int n = arr.Length;

    // Function call
    Console.Write(get_permutation(arr, n));
}
}

// This code is contributed by shivanisinghss2110

Javascript

<script>
// javascript program to find minimum number of steps to
// convert a given sequence into a permutation

// Function to find minimum number of steps to
// convert a given sequence into a permutation
function get_permutation(arr , n)
{

    // Sort the given array
    arr.sort();

    // To store the required minimum
    // number of operations
    var result = 0;

    // Find the operations on each step
    for (i = 0; i < n; i++) {
        result += Math.abs(arr[i] - (i + 1));
    }

    // Return the answer
    return result;
}

// Driver code
var arr = [ 0, 2, 3, 4, 1, 6, 8, 9 ];
var n = arr.length;

// Function call
document.write(get_permutation(arr, n));

// This code is contributed by Amit Katiyar
</script>

Output:

7

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