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Minimum operations to make the MEX of the 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
Updated on: 22-Nov-2019
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