I went straight to 2D DP which felt safe, but they pushed back asking if I could do better on space.
Start by clarifying the problem and edge cases, then present both DP and greedy solutions with their complexities. Emphasize the DP approach for its clarity and the greedy approach for its optimal space, and discuss trade-offs in terms of time, space, and implementation complexity.
Pro tip: Mention that the greedy approach with backtracking is often preferred in practice for its O(1) space, but be prepared to code the DP solution if asked for a more straightforward implementation. Also, highlight that the DP solution can be optimized to O(n) space using rolling arrays.
Ask clarifying questions about the input constraints, character sets, and expected behavior for edge cases like empty strings or patterns with consecutive asterisks.
Explain the dynamic programming solution with a 2D table where dp[i][j] indicates if the first i characters of the string match the first j characters of the pattern. Derive the recurrence relations and state the time and space complexity.
Describe the greedy algorithm that uses two pointers and backtracking for asterisks, achieving O(n) time and O(1) space. Explain how it handles multiple asterisks and why it works.
Discuss the trade-offs: DP is easier to reason about and implement but uses O(mn) space (or O(n) with optimization), while greedy is more space-efficient but trickier to get right. Mention that both have O(mn) worst-case time.
Mention potential optimizations like reducing DP space to O(n) using rolling arrays, or handling multiple consecutive asterisks by collapsing them. Also, briefly touch on extensions like regular expression matching.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This one tripped me up more than it should have.
Clarify the problem constraints and required operations, then propose a solution that maintains a frequency map of B values and uses a Fenwick tree (BIT) or segment tree over the value range to support point updates and range sum queries. For each query, iterate over distinct values in A and sum the frequencies of (total - a) in B, ensuring O((|A| + |B|) log V) or O(|A| log V) per query depending on the approach.
Pro tip: Mention that if the value range is large, you can compress coordinates or use a hash map combined with a balanced BST, but a Fenwick tree over compressed values is usually the most efficient and simplest to implement. Also, note that if A is static, precomputing its frequency map can reduce query time.
Ask about the range of values in A and B, the number of operations, and whether updates and queries are interleaved. Confirm that we need to count pairs (i, j) such that A[i] + B[j] = total after updates.
Maintain a frequency map of B's current values. Use a Fenwick tree (BIT) or segment tree over the value range (or compressed values) to support point updates (increment/decrement frequency) and range sum queries (count of values in a range).
When adding a value v to B[i], decrement the frequency of the old B[i] in the BIT and increment the frequency of the new value. Update the frequency map accordingly.
For a given total, iterate over distinct values in A (or all elements if A is small) and for each a, query the BIT for the frequency of (total - a). Sum these frequencies to get the total number of pairs.
Update is O(log V), query is O(|A| log V) where |A| is the number of distinct values in A. If |A| is large, consider precomputing A's frequency map and iterating over the smaller of the two sets. Discuss trade-offs and potential optimizations.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the requirements (capacity, O(1) operations) and then describe a design using a hash map and a doubly linked list. Explain how the hash map provides O(1) access to nodes, while the linked list maintains the order of usage for eviction. Walk through the get and put operations, highlighting edge cases and complexity.
Pro tip: Mention that you would use a doubly linked list with sentinel head and tail nodes to simplify edge cases and avoid null checks, and discuss how this design can be extended to support thread safety if needed.
Confirm the expected operations (get, put), capacity, and that both must be O(1). Ask about concurrency requirements or other constraints.
Select a hash map for O(1) key lookup and a doubly linked list to track usage order. Explain why a singly linked list or array would not work efficiently.
Describe how the hash map stores key -> node references, and the linked list maintains nodes in order of recent use (most recent at head). Include sentinel nodes to simplify operations.
For get: if key exists, move node to head and return value; else return -1. For put: if key exists, update value and move to head; else create new node, add to head, and if capacity exceeded, remove tail node and delete from map.
State that both operations are O(1) time and O(capacity) space. Discuss edge cases like capacity 0 or 1, updating existing keys, and handling null values.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Recognize that the optimal strategy is to neutralize threats in order of their arrival times (earliest deadline first). Sort threats by arrival time, then simulate minute by minute, neutralizing the next threat if it hasn't already arrived. Count how many you can neutralize before any threat arrives.
Pro tip: Clarify edge cases upfront, such as ties in arrival times and threats that arrive at time 0. Also, mention that if a threat arrives exactly at the minute you act, you can still neutralize it because the condition is 'at least' dist/speed.
Restate the problem: you have n threats with given distances and speeds. Each minute you can neutralize one threat. A threat arrives when elapsed time >= dist/speed. If any threat has arrived before you act at a minute, the process ends. Maximize neutralized threats.
Argue that to maximize the number, you should prioritize threats that arrive earliest (earliest deadline first). This greedy approach is optimal because neutralizing a later threat first could cause an earlier threat to arrive and end the process.
Compute arrival time for each threat as dist[i]/speed[i]. Sort threats in non-decreasing order of arrival time. If ties, any order works.
Iterate minute by minute (or over sorted threats). At minute t (starting from 0), if the next threat's arrival time <= t, it has already arrived, so stop. Otherwise, neutralize it and increment count. Continue until no more threats or a threat has arrived.
The number of threats neutralized before any arrival is the answer. Discuss time complexity: O(n log n) due to sorting, and space O(n) for storing arrival times.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.