Took me embarrassingly long to realize this screams binary search on the answer.
Clarify the problem constraints and define the reduction process: each day, choose a window of k consecutive chapters and reduce each by up to p pages. Use binary search on the number of days, and for a given number of days, check feasibility by simulating the process greedily with a sliding window and difference array to track cumulative reductions.
Pro tip: During the simulation, maintain a running sum of reductions from active windows to efficiently compute the remaining pages for each chapter. This avoids O(n*k) time and demonstrates strong optimization skills.
Ask about constraints (e.g., array size, k, p) and confirm that each day you can choose any window of k consecutive chapters, and each chapter in that window can be reduced by at most p pages. Also confirm that chapters can be reduced independently within the window.
For a given number of days D, determine if it's possible to reduce all chapters to zero. Simulate day by day: for each chapter, compute how many more pages need to be reduced, and if it exceeds the maximum possible reductions from D days, return false.
Use a sliding window with a difference array to track the cumulative reductions applied to each chapter from previous windows. This allows O(n) feasibility check per D.
Binary search the minimum D between 0 and max possible days (e.g., ceil(total_pages / (k*p))). For each mid, run the feasibility check and adjust the search range accordingly.
State time complexity O(n log(max_days)) and space O(n). Discuss edge cases: k > n, p = 0, all pages zero, etc.
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