使数组成为前N个自然数的排列的最低成本

给定大小为N的正整数的数组arr ，任务是找到使该数组成为前N个自然数的排列的最小开销，其中将元素递增或递减1的开销为1。

例子：

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.

方法：

1. 按升序对数组元素进行排序
2. 遍历排序后的数组：
   • 检查第i个索引(0≤i 的元素是否等于i +1 。
   • 如果不是，则使其相等，并且将两者之间的差额视为该操作的成本。
3. 遍历完成后，打印所执行操作的总成本。

下面是上述方法的实现：

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 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

输出：

5