Kth Missing Positive Number

Given an array arr of positive integers sorted in a strictly increasing order, and an integer k.

Return the kth positive integer that is missing from this array.

Example 1:

Input: arr = [2,3,4,7,11], k = 5
Output: 9
Explanation: The missing positive integers are [1,5,6,8,9,10,12,13,...]. The 5th missing positive integer is 9.

Example 2:

Input: arr = [1,2,3,4], k = 2
Output: 6
Explanation: The missing positive integers are [5,6,7,...]. The 2nd missing positive integer is 6.

Constraints:

• 1 <= arr.length <= 1000
• 1 <= arr[i] <= 1000
• 1 <= k <= 1000
• arr[i] < arr[j] for 1 <= i < j <= arr.length

Follow up:

Could you solve this problem in less than O(n) complexity?

SOLUTION:

class Solution:
    def findKthPositive(self, arr: List[int], k: int) -> int:
        arr = set(arr)
        mx = max(arr) + k + 1
        ctr = 0
        for i in range(1, mx):
            if i not in arr:
                ctr += 1
            if ctr == k:
                return i