1539 Kth Missing Positive Number

Intuition

The fundamental idea here is that we can calculate the number of missing integers on an index.

In an “ideal” list where no number is missing, arr[i] = i+1. So, if there’s a mismatch in this logic, we can find number of missing numbers by missing = arr[i] - (i+1).

Code

Python3

def findKthPositive(self, arr: List[int], k: int) -> int:
    #   * * *     *        *
    # 1 2 3 4 5 6 7 8 9 10 11 12 13 14
    # ^
 
    if k > arr[-1] - len(arr):
        return k + len(arr)
 
    left, right = 0, len(arr)-1
 
    while left <= right:
        mid = (left + right) // 2
        missing = arr[mid] - (mid+1)
 
        if missing < k:
            left = mid + 1
        else:
            right = mid - 1
 
    return k + right + 1

Big O Analysis

• Runtime

  The runtime complexity here is $O(logN)$ since binary search and reducing the sample space by half every step.

• Memory

  The memory usage is $O(1)$ since no extra data structure is being used.

— A

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