easyBinary SearchBinary Search

Kth Missing Positive Number

easyTime: O(log n)Space: O(1)

Recognize the pattern

kth missing positive integersorted array with gapsbinary search on missing count

Brute force idea

Iterate from 1 upward counting missing — O(n + k).

Better approach

Binary search: at index i, missing count = arr[i] - (i+1). Find leftmost index where missing ≥ k. Answer = k + left. O(log n).

Key invariant

Without gaps, arr[i] would be i+1. The difference arr[i] - (i+1) counts missing numbers before position i.

Watch out for

Off-by-one in the final answer — kth missing = k + left (the binary search result).

Binary Search Pattern