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Fewest Days to Read a Book When Chapters Cannot Be Split Across Days

OtherSoftware Engineer · Online Assessment
EasySoftware EngineerOnline AssessmentCoding & Algorithms

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Given the reading time available on each day and the time each chapter of a book takes, find the fewest days needed to read every chapter in order when a chapter can never be split across days, or report that the book cannot be finished. It tests simulation with per-day capacity, ordering constraints, and impossible cases.

On any day you may read more than one chapter if you have enough time, but every chapter must be read completely within a single day; a chapter can never be split across days. Return the number of days needed to finish the whole book, or -1 if the book cannot be finished within the given days.

Function Signature

def days_to_finish(time: list[int], book: list[int]) -> int:

Rules

  • Chapters are read in order: chapter j + 1 can be started only after chapter j has been finished.
  • Days are used in order starting from day 0. You may read nothing on a day.
  • Reading time does not carry over: time left unused at the end of a day is lost.
  • The answer is the smallest d such that the whole book can be read using only days 0 through d - 1 under these rules. If no such d <= len(time) exists, return -1.
  • An empty book needs 0 days.

Constraints

  • 1 <= len(time) <= 100000
  • 0 <= len(book) <= 100000
  • 0 <= time[i] <= 10000
  • 1 <= book[j] <= 10000

Examples

Example 1

  • Input: time = [3, 5, 2, 6], book = [2, 2, 3, 4]
  • Output: 4
  • Explanation: Day 0 has 3 units: chapter 0 (2 units) fits, but adding chapter 1 would need 4. Day 1 has 5 units: chapters 1 and 2 need exactly 5. Day 2 has 2 units, too few for chapter 3 (4 units). Day 3 has 6 units, and chapter 3 is finished. The book is finished using days 0 through 3, so 4 days are needed, and it cannot be done in fewer.

Example 2

  • Input: time = [4, 4], book = [5]
  • Output: -1
  • Explanation: The only chapter needs 5 units, but no day offers more than 4, and a chapter cannot be split.

Example 3

  • Input: time = [10, 1], book = [3, 3, 4]
  • Output: 1
  • Explanation: All three chapters need 10 units in total, which fits on day 0.