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A problem in combinatorial optimization. Given a set of items with both weight and value, determine the number of each item to include in a collection so that the total weight is at most a given limit and the value of the collection is maximized.

5 votes
2 answers
165 views

Detecting conservation, loss, or gain in a crafting game with items and recipes

Suppose we're designing a game like Minecraft where we have lots of items $i_1,i_2,...,i_n\in I$ and a bunch of recipes $r_1,r_2,...,r_m\in R$. Recipes are functions $r:(I\times\mathbb{N})^n\rightarro …