**KNAPSACK:** Given a finite set *U*, a ``size''
and a ``value''
for each , a size constraint
, and a value goal
, is there a subset
such that
and
?

This can be seen as a knapsack, which has a size limit for the objects, as in the picture below.

The goal is to pick a collection of objects that will fit in the knapsack
and whose total value is at least *K* (*K* is input)

KNAPSACK =
subset *U*' of *U* such that
the sum of *s* values is at most *B*, and the sum of *v* values is at least
*K*}