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Maximize total score of all scanned books.

  • Each library needs to be signed up before it can ship books

Books

B books with ID's 0 -> B-1. Multiple copies of the same book exist, we only need one scanned.

  • Books scanned must be unique. IE points only awarded for each unique books.

Libraries

L librareis from 0 -> L-1.

Attributes - set of Books - time in days so sign the library up - Number of Books that can be scanned each day

Time

0 to D-1 : can ship books. First library signup on day 0

Library signup (Basically a mutex lock)

  • Each library must be signed up.
  • Only one may be signed up at a time
  • Libraries can be signed up in any order
  • On the first day after signed up Books can be scanned

Scanning

  • Scanning is measured in 1 day intervals.
  • The Scanning facility can scan an infinite number of books in a day
  • Bottleneck is the libraries

Example

6 2 7 - Books, Libraries, Days 1 2 3 6 5 4 - Score of each respective book

->lib 0 5 2 2 - number of books, number of days for signup, scannable books per day 0 1 2 3 4 - book ids

->lib 1 4 3 1 - number of books, number of days for signup, scannable books per day 0 2 3 5 - book ids

In short

X days, each library needs to signup before we can start shipping books.

Signup 1 library at a time, scanning books happens concurrently & each library has a max quota.