Minimum operations to make the MEX of the given set equal to x

3.3

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.

Examples:

Input : n = 5, x = 3
        0 4 5 6 7
Output : 2
The MEX of the set {0, 4, 5, 6, 7} is 1 which is 
not equal to 3. So, we should add 1 and 2 to the
set. After adding 1 and 2, the set becomes 
{0, 1, 2, 4, 5, 6, 7} and 3 is the minimum
non-negative integer that doesn't exist in it.
So, the MEX of this set is 3 which is equal to
x i.e. 3. So, the output of this example is 2 
as we inserted 1 and 2 in the set.

Input : n = 1, x = 0
        1
Output : 0
In this example, the MEX of the given set {1}
is already 0. So, we do not need to perform 
any operation. So, the output is 0.

Approach:
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.

Below is the implementation of above approach:

// CPP program to perform minimal number
// of operations to make the MEX of the 
// set equal to the given number x.
#include <bits/stdc++.h>
using namespace std;

// function to find minimum number of
// operations required
int minOpeartions(int arr[], int n, int x)
{
    int k = x, i = 0;
    while (n--) {
    
        // if the element is less than x.
        if (arr[n] < x)
            k--;
    
        // if the element equals to x.
        if (arr[n] == x)
            k++;
    }
    return k;
}

// driver function
int main()
{
    int arr[] = { 0, 4, 5, 6, 7 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int x = 3;
    // output
    cout << minOpeartions(arr, n, x) << endl;
}

Output:

2

This article is contributed by Sagar Shukla. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geekforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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