This is the LFU cache problem and it's nasty if you haven't seen it.
Start by clarifying the requirements: O(1) average time for get and put, eviction of least frequently used key, and ties broken by recency. Then propose a design combining a hash map for O(1) access to nodes and a frequency-based doubly linked list structure (or a min-heap with lazy updates) to track LFU order. Walk through the get and put operations, explaining how frequency updates and eviction work in O(1) average time.
Pro tip: Mention that a naive min-heap gives O(log n) for updates, so to achieve O(1) average you need a hash map plus a doubly linked list of frequency buckets, each containing a doubly linked list of keys with that frequency. This shows you understand the trade-offs and can optimize beyond the obvious.
Confirm that get and put must be O(1) average, eviction is LFU with LRU tie-breaking, and discuss edge cases like capacity 0 or 1, and updating existing keys.
Use a hash map for O(1) key lookup, mapping to nodes. Use a doubly linked list of frequency buckets, each bucket containing a doubly linked list of keys with that frequency, ordered by recency.
Each node stores key, value, frequency, and pointers to prev/next in its frequency list. Each bucket stores frequency and pointers to prev/next bucket, plus head/tail of its key list.
For get: if key exists, increment its frequency, move it to the appropriate bucket (create if needed), and return value. For put: if key exists, update value and increment frequency; if new, insert with frequency 1; if capacity exceeded, evict the least frequent and least recently used key (tail of lowest frequency bucket).
Explain that all operations are O(1) average due to hash map and constant-time list manipulations. Discuss handling of capacity limits, updating existing keys, and tie-breaking by recency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sliding window, classic minimum window substring.
Use a sliding window with two pointers to expand and contract the window while tracking character frequencies. Maintain a count of matched characters to know when the window contains all required characters, and update the minimum length when a valid window is found.
Pro tip: Clarify edge cases upfront (e.g., empty strings, case sensitivity, character set) and discuss trade-offs between approaches (e.g., sliding window vs. brute force). Mention that the sliding window approach is optimal with O(n) time and O(k) space, where k is the number of unique characters in the second string.
Restate the problem in your own words and ask clarifying questions about input constraints, character set, and expected output. Identify edge cases such as empty strings, no valid substring, or duplicate characters.
Explain that a brute-force approach would be O(n^2 * m) and inefficient. Propose the sliding window technique with frequency maps to achieve O(n) time.
Describe how to use two pointers (left and right) to represent a window. Expand right to include characters until the window is valid, then contract left to minimize the window while keeping it valid.
Explain how to maintain a frequency map of the target string and a count of matched characters. When the count equals the number of unique characters in the target, the window is valid.
State the time and space complexity (O(n) time, O(k) space). Walk through a small example to demonstrate correctness and handle edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Use a min-heap to efficiently merge the two sorted arrays by sums, starting with the smallest possible pair (0,0). Push the next candidates (i+1,j) and (i,j+1) into the heap, avoiding duplicates, and extract k pairs. This approach runs in O(k log k) time and handles the case where fewer than k pairs exist by returning all extracted pairs.
Pro tip: Clarify with the interviewer whether the arrays can contain duplicates and if the output should be sorted by sum; also mention that using a visited set or index tracking prevents duplicate pairs in the heap.
Ask about input constraints (array sizes, possible duplicates, k value) and expected output format (order of pairs, handling fewer than k pairs).
Select a min-heap (priority queue) to efficiently retrieve the smallest sum pairs, since the arrays are sorted and we need the k smallest sums.
Push the initial pair (0,0) into the heap. While the heap is not empty and we have fewer than k pairs, pop the smallest sum, add it to the result, and push the next possible pairs (i+1,j) and (i,j+1) if within bounds and not already visited.
Use a visited set or a boolean matrix to avoid pushing the same pair multiple times. Ensure indices do not exceed array lengths.
After extracting up to k pairs, return the list of pairs. If fewer than k pairs exist, return all extracted pairs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.