1539. Kth Missing Positive Number

Problem Link

Description

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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

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Python3

class Solution:
    def findKthPositive(self, arr: List[int], k: int) -> int:
        N = len(arr)
        left, right = 0, N
 
        def good(mid):
            return arr[mid] - 1 - mid >= k
 
        while left < right:
            mid = left + (right - left) // 2
 
            if good(mid):
                right = mid
            else:
                left = mid + 1
        
        return left + k