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This is the kind of problem where you either know the monotonic stack trick or you're cooked.
Start by clarifying the problem and edge cases, then propose an efficient O(n) solution using a monotonic stack to compute for each bar the maximum rectangle where it is the limiting height. Walk through the algorithm with a small example, and discuss time/space complexity and potential optimizations.
Pro tip: Emphasize the monotonic stack approach as it's optimal and commonly expected; also mention that a divide-and-conquer approach is possible but less efficient. Relate the problem to real-world applications like ad placement or image processing to show practical insight.
Restate the problem in your own words and confirm details: bars have width 1, heights are non-negative integers, and the rectangle must be axis-aligned within the histogram. Ask about input size and constraints to determine the expected complexity.
Mention that a brute force approach would consider all pairs of bars as boundaries and find the minimum height between them, resulting in O(n^2) time. This sets the stage for a more optimal solution.
Explain that for each bar, we need to find the nearest smaller bar to the left and right. A monotonic increasing stack can compute these boundaries in O(n) time by maintaining indices of bars with increasing heights.
Describe the steps: iterate through bars, while stack is not empty and current height is less than stack top's height, pop and calculate area using the popped bar's height and the width determined by current index and new stack top. Push current index. After iteration, pop remaining bars and calculate areas with right boundary at n.
State that time complexity is O(n) because each bar is pushed and popped at most once, and space complexity is O(n) for the stack. Discuss edge cases: empty array, all equal heights, strictly increasing/decreasing heights.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and edge cases, then propose a two-pointer solution that iterates through t while advancing a pointer in s when characters match. Analyze the time and space complexity, and discuss potential optimizations or alternative approaches like binary search for multiple queries.
Pro tip: Mention that this is a classic two-pointer problem and that the same pattern applies to many sequence alignment tasks in ML, such as matching user actions to a predefined funnel. Also, proactively discuss how you would handle follow-up scenarios like multiple queries or streaming data.
Restate the problem in your own words and ask clarifying questions about edge cases, such as empty strings, case sensitivity, and character set.
Explain that you will use two pointers: one for s and one for t. Iterate through t, and when characters match, advance the pointer in s. If the pointer in s reaches the end, s is a subsequence.
State that the time complexity is O(n) where n is the length of t, and space complexity is O(1). Mention that this is optimal for a single query.
Cover cases like empty s (always true), s longer than t (false), and multiple queries. For multiple queries, suggest preprocessing t into a dictionary of character positions and using binary search for O(m log n) per query.
Relate the problem to ML engineering tasks, such as verifying if a user's action sequence contains a target pattern, or matching tokens in NLP pipelines.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.