# LeetCode 1539. Kth Missing Positive Number

## Description

https://leetcode.com/problems/kth-missing-positive-number/

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

Find 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`

## Explanation

We can first find a list of missing positives from the list and then we have to handle different scenarios to find kth missing positive. If the list of missing positives has a length greater than k, returns the kth positive from the list. If the list of missing positives is empty, the k th missing positive would be the largest number in the list + k. If the missing positives’ length is shorter than k, the kth missing positive would be the largest number in the original list + k – len(missing_positives).

## Python Solution

``````class Solution:
def findKthPositive(self, arr: List[int], k: int) -> int:

missing_positives = []

n = max(arr)

arr_set = set(arr)
for i in range(1, n + 1):
if i not in arr_set:
missing_positives.append(i)

if not missing_positives:
return arr[len(arr) - 1] + k

if k > len(missing_positives):
return arr[len(arr) - 1] + (k - len(missing_positives))

return missing_positives[k - 1]

``````
• Time Complexity: O(N).
• Space Complexity: O(N).