LA 3529

LA 3529 - Widget Factory

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Summary
There are N types of widgets, each type takes a fixed number of days (between 3 and 9) to be produced. In the factory there were several workers. For each of them we know the information "He started on weekday X, produced c1 widgets of type t1, ..., ck widgets of type tk and finished on weekday Y". The task is to determine the production time for each of the widgets.

There may be inputs where there is no answer or more than one answer, in these cases you just have to output a corresponding message.

Explanation
Note that if we want to know the number of days D a widget takes to be completed, it is enough to determine (D modulo 7).

Each worker's information can be translated into a linear congruence modulo 7. The resulting set of equations can be solved using Gaussian elimination.

Input
2 3 2 MON THU 1 2 3 MON FRI 1 1 2 3 MON SUN 1 2 2 10 2 1 MON TUE 3 1 MON WED 3 0 0

Output
8 3 Inconsistent data.