Minimize sum of numbers required to convert an array into a permutation of first N natural numbers

Minimize sum of numbers required to convert an array into a permutation of first N natural numbers

Given an array A[] of size N, the task is to find the minimum sum of numbers required to be added to array elements to convert the array into a permutation of 1 to N. If the array can not be converted to desired permutation, print -1.

Examples:

Input: A[] = {1, 1, 1, 1, 1}
Output: 10
Explanation: Increment A[1] by 1, A[2] by 2, A[3] by 3, A[4] by 4, thus A[] becomes {1, 2, 3, 4, 5}.
Minimum additions required = 1 + 2 + 3 + 4 = 10

Input: A[] = {2, 2, 3}
Output: -1

Approach: The idea is to use sorting. Follow these steps to solve this problem:

Below is the implementation of the above approach:

C++

#include <bits/stdc++.h> using namespace std;    int minimumAdditions(int a[], int n) {          sort(a, a + n);     int ans = 0;             for (int i = 0; i < n; i++) {                     if ((i + 1) - a[i] < 0) {             return -1;         }         if ((i + 1) - a[i] > 0) {                             ans += (i + 1 - a[i]);         }     }             return ans; }    int main() {          int A[] = { 1, 1, 1, 1, 1 };     int n = sizeof(A) / sizeof(A[0]);             cout << minimumAdditions(A, n);        return 0; }

Output:

10

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

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