Sequence Optimization With Limited Flips
Asked of: Software Engineer
Last updated
What's being tested
Requires converting a constraint ("flip at most k rest days") into an algorithmic pattern that maximizes a numeric objective under limited operations. Interviewer checks for recognizing a sliding window/two-pointer reduction or a prefix-sum + greedy approach, implementing it in O(n) or O(n log n), and reasoning about edge cases (exact vs up-to-k flips, negative/zero weights).
Patterns & templates
- Sliding window on contiguous intervals: expand/contract while tracking flipped-rest count; yields
O(n)time,O(1)extra space. - Prefix sum for weighted days: precompute cumulative sums to compute any interval sum in
O(1)afterO(n)setup. - Two-pointer with count constraint: move right pointer, increment flip count for rest-days, advance left until flips ≤ k.
- Kadane variant with state: keep best subarray ending at i with j flips (small k → DP over flips) —
O(n*k)time. - Greedy + heap: pick top-k rest-day gains if flips need not create contiguity —
O(n + k log n)time. - Handle exact k vs up-to-k: if exact, enforce flipping additional minimal-loss days; if up-to-k, allow fewer flips.
- Watch weights: if daily pay can be negative, convert to max-subarray-with-limited-changes pattern, not plain zero/one.
Common pitfalls
Pitfall: Treating flips as independent gains — forgetting that flipping interior rest days merges paid segments and creates non-additive gains.
Pitfall: Implementing sliding window but not handling "exact k" requirement; off-by-one when left/right pointers move leads to wrong counts.
Pitfall: Using
O(n*k)DP without bounding k — declare constraints and switch to heap/greedy when k is large relative to n.
Practice these
the practice cards below cover the canonical variants — solve all of them and time yourself.
Practice questions
Related concepts
- Sliding Window And K-Flip OptimizationCoding & Algorithms
- Sliding Window, Binary Search, and Prefix ReasoningCoding & Algorithms
- String And Sliding Window AlgorithmsCoding & Algorithms
- Arrays, Sliding Windows, DP And Stack PatternsCoding & Algorithms
- Sliding Window Frequency MapsCoding & Algorithms
- Dynamic Programming, Backtracking, And Combinatorial SearchCoding & Algorithms