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In this practical and assessment you will be creating a small ruby program to determine the winners of gunfights, as seen in old Western movies.

The rules governing these gunfights are very simple:

1. We have a bunch of cowboys
2. Each cowboy can aim a gun at any number of other cowboys
3. If a cowboy has a gun aimed at them, we say they are attacked, with the cowboy aiming the gun doing the attacking.
4. Given a group of cowboys, we say that a subset of this group is conflict-free if none of the cowboys in the subset are attacking each other.
5. A cowboy (let’s call him C is defended by some group of cowboys (let’s call this group X) if any cowboy attacking C is attacked by a member of X.
6. We say that a group of cowboys is self-defending if every cowboy in the group is defended by the group, and the group is conflict-free.

Create a ruby class called Fighters that takes in a set of cowboys and attacks between cowboys, e.g.

Fighters.new([:a,:b,:c],[[:a,:b],[:b,:c],[:c,:a]])

This represents the situation where we have 3 cowboys :a,:b,:c and :a aims at :b, :b aims at :c and :c aims at :a.

Write rspec tests (in a file called fighters_test.rb) for the following methods on this class, and then implement these methods.

1. conflict_free?(cowboys) which takes in a set of cowboys and returns true if this set is conflict-free and false otherwise.
2. defended?(cowboy,group) which returns true if the cowboy is defended by the group and false otherwise.
3. self_defended?(group) which, when given a group, returns true if the group is a self defending group.

We can identify several different groups of safe cowboys. First, there are those cowboys that are unconditionally alive. For example, given the following configuration of fighters

f=Fighters.new([:a,:b,:c],[[:a,:b],[:b,:c]])

Cowboys :a and :c will survive the fight as a would end up shooting b meaning that c would not be shot.

Create methods called unconditionally_alive and unconditionally_dead which compute (and return as an array) those cowboys which are definitely alive and dead.

To compute these, start with the cowboys which have no one aiming at them; these are unconditionally alive. Those cowboys being aimed at by these unconditionally alive cowboys are unconditionally dead, and those aimed at only by unconditionally dead cowboys are unconditionally alive and so on.

The problem described here actually stems from a very active research area in artificial intelligence called argumentation theory. If you’re interested in finding out more about these concepts, see the book ``Argumentation in Artificial Intelligence’’ edited by I. Rahwan and G. Simari. Chapter 6 is particularly relevant. This book is available as an e-book from the library.