Went with a sort and index approach first, then they asked about optimizing it.
Start by clarifying the problem constraints (e.g., array size, value range, duplicates) and then present multiple solutions with trade-offs: sorting, min-heap, and Quickselect. Emphasize the optimal Quickselect approach with average O(n) time and O(1) space, and discuss how to handle worst-case scenarios.
Pro tip: Mention that Quickselect can be made worst-case O(n) using Median of Medians, but in practice, random pivot selection is often sufficient and simpler. Also, note that if k is small, a min-heap of size k+1 is a good alternative, especially for streaming data.
Ask about input size, value range, duplicates, and whether the array can be modified. Confirm the 0-indexed definition of k-th largest.
Mention sorting the array and returning the element at index n-1-k, which takes O(n log n) time. Also, consider a max-heap if k is large.
Explain the Quickselect algorithm: partition the array around a pivot, then recursively search the side that contains the k-th largest. Average time O(n), worst-case O(n^2).
Discuss using random pivot selection to avoid worst-case on sorted input, or Median of Medians for guaranteed O(n). Also, mention iterative implementation to avoid recursion overhead.
Compare time and space complexities of all approaches. Highlight that Quickselect is in-place and efficient for large arrays, while heap is better for streaming or when k is small.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sliding window, which I did eventually get to, but I burned a few minutes trying a DP approach that wasn't going anywhere.
Use a sliding window technique to find the longest subarray that contains at most K 'W' characters, where K is the number of PTO days. Expand the window by moving the right pointer, and when the count of 'W' exceeds K, shrink the window from the left until the count is within K. Keep track of the maximum window length seen.
Pro tip: Clarify edge cases upfront, such as when PTO days exceed the number of workdays or when the calendar is empty. Also, discuss how the solution scales for large inputs, emphasizing O(n) time and O(1) space.
Restate the problem: given a string of 'H' and 'W', and an integer K, find the longest contiguous substring that can be made all 'H' by converting at most K 'W's to 'H's. Confirm with the interviewer.
Recognize this as a sliding window problem: we need the longest subarray with at most K 'W's. Discuss why brute force is inefficient and why sliding window is optimal.
Initialize left and right pointers, a count of 'W's in the current window, and a variable for max length. Expand right, incrementing the 'W' count when encountering 'W'. While the count exceeds K, move left and decrement if the left character is 'W'. Update max length after each expansion.
Walk through a few examples, including edge cases like all 'H's, all 'W's, K=0, and K larger than the number of 'W's. Verify the algorithm returns the correct maximum streak.
State that the time complexity is O(n) because each character is visited at most twice (once by right, once by left), and space complexity is O(1) as we only use a few variables.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.