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++ 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 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 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# 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 |
<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> |
5
Time Complexity: O(n*log(n))
Auxiliary Space: O(1)