Challenge: Maximum Amount of Gold

Problem

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Maximum Amount of Gold Problem

Given a set of gold bars of various weights and a backpack that can hold at most $W$ pounds, place as much gold as possible into the backpack.

Input: A set of $n$ gold bars of integer weights $w_{1},\ldots, w_{n}$ and a backpack that can hold at most $W$ pounds.

Output: A subset of gold bars of maximum total weight not exceeding $W$.