Find Minimum Possible Number of Keyboards Stolen in C++

Suppose we have an array A with n elements. There was an electronic store, where a robbery has done on the last night. All keyboards which were present inside the store were numbered in ascending order from some integer number x. For example, for x=4 and there were 3 keyboards in the store, then the devices had indices 4, 5 and 6. If x=10 and there were 7 of them then the keyboards had indices 10, 11, 12, 13, 14, 15 and 16. After the robbery, only n keyboards are left. They have indices stored in array A. We have to find the minimum possible number of keyboards that have been stolen.

So, if the input is like A = [10, 13, 12, 8], then the output will be 2, because if x = 8 then minimum number of stolen keyboards is 2. The keyboards with indices 9 and 11 were stolen.

Steps

To solve this, we will follow these steps −

sort the array A
n := size of A
return A[n - 1] - A[0] + 1 - n

Example

Let us see the following implementation to get better understanding −

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

int solve(vector<int> A) {
      sort(A.begin(), A.end());
int n = A.size();
   return A[n - 1] - A[0] + 1 - n;
}
int main() {
   vector<int> A = { 10, 13, 12, 8 };
   cout << solve(A) << endl;
}

Input

{ 10, 13, 12, 8 }

Output

2