Minimum Operations to Make the MEX of a Given Set Equal to X in C++

Problem statement

Given a set of n integers, perform minimum number of operations (you can insert/delete elements into/from the set) to make the MEX of the set equal to x (that is given).

Note − The MEX of a set of integers is the minimum non-negative integer that doesn’t exist in it. For example, the MEX of the set {0, 2, 4} is 1 and the MEX of the set {1, 2, 3} is 0

Example

If n = 5 and x = 3 and array is {0, 4, 5, 6, 7} then we require minimum 2 operations

Algorithm

• The approach is to see that in the final set all the elements less than x should exist, x shouldn’t exist and any element greater than x doesn’t matter.
• So, we will count the number of elements less than x that don’t exist in the initial set and add this to the answer.
• If x exists we will add 1 to the answer because x should be removed.

Example

#include <iostream>
using namespace std;
int getMinOperations(int *arr, int n, int x) {
   int k = x, i = 0;
   while (n--) {
      if (arr[n] < x) {
         --k;
      }
      if (arr[n] == x) {
         ++k;
      }  
   }
   return k;
}
int main() {
   int arr[] = {0, 4, 5, 6, 7};
   int n = sizeof(arr) / sizeof(arr[0]); int x = 3;
   cout << "Minimum required operations = " << getMinOperations(arr, n, x) << endl;
   return 0;
}

Output

When you compile and execute above program. It generates following output −

Minimum required operations = 2