Started with the linear scan and it worked, but they pushed me on efficiency.
Clarify the problem constraints and edge cases, then propose an efficient binary search solution that leverages the sorted array to find the k-th missing number in O(log n) time. Explain how to compute the number of missing integers up to any index using the formula arr[i] - (i+1), and use binary search to locate the smallest index where this count is at least k.
Pro tip: Mention that you would first check if k is larger than the total missing numbers; if so, return the appropriate value beyond the array. Also, discuss how to handle duplicates if they are allowed, though the problem states positive integers and sorted, so duplicates might be present—clarify this.
Ask about array size, range of values, whether duplicates are allowed, and if k is guaranteed to be within bounds. Discuss what to return if k exceeds total missing numbers.
For a 0-indexed array, the number of missing positive integers up to index i is arr[i] - (i + 1). This works because in a perfect sequence 1,2,3,..., arr[i] would be i+1.
Binary search for the smallest index i such that missing count >= k. If found, the k-th missing number is arr[i] - (missing count - k + 1). If no such index, the answer is arr[n-1] + (k - missing count at last index).
If the array is empty, return k. If k is less than or equal to the first missing number, handle accordingly. Ensure the formula works for indices at boundaries.
State time complexity O(log n) and space O(1). Walk through examples like [2,3,4,7,11], k=5 to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.