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

• Last Updated : 26 Apr, 2021

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:
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:
Explanation:
The array is already a permutation.

Approach:

1. Sort the array element in increasing order
2. 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 inremenent the difference between the two as the cost of this operation.
3. 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 using namespace std; // Function to calculate minimum cost// for making permutation of size Nint 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 codeint main(){    int arr[] = { 5, 3, 8, 1, 1 };    int n = sizeof(arr) / sizeof(arr);     // Function call    cout << make_permutation(arr, n);}

Java

 // Java program to calculate minimum cost// to make an Array a permutation// of first N natural numbersimport java.util.*; class GFG{  // Function to calculate minimum cost// for making permutation of size Nstatic 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 codepublic 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 Ndef 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 codeif __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 numbersusing 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


Output:
5

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