kriskelly / knapsack

0/1 Knapsack solution implemented in Elixir

Knapsack

Implementation of a solution to the 0/1 Knapsack problem. The Knapsack problem is a combinatorial optimization problem: given a set of items I, each represented by a weight (w) and a value (v), and a knapsack with a maximum capacity W, the algorithm finds the optimal subset of I that will maximize sum(v) while maintaining sum(w) <= W.

Usage

require Knapsack.Knapsack01
alias Knapsack.Knapsack01

items = [
  %Knapsack01.Item{ weight: 10, value: 1, metadata: "any identifying data" },
  %Knapsack01.Item{ weight: 8, value: 2, metadata: "this one wins" },
]
capacity = 10
packed_items = Knapsack01.pack(items, capacity)

IO.inspect(packed_items)
[%Knapsack.Knapsack01.Item{metadata: "this one wins", value: 2, weight: 8}]

Note that this algorithm doesn't return the maximum value of the set, but it does return a list of items, you can get the max value like so:

Enum.reduce(packed_items, 0, fn(item, total) -> item.value + total end)

Installation

If available in Hex, the package can be installed as:

1. Add knapsack to your list of dependencies in mix.exs:

```elixir
def deps do
  [{:knapsack, "~> 0.1.0"}]
end
```

2. Ensure knapsack is started before your application:

```elixir
def application do
  [applications: [:knapsack]]
end
```