COMP30024 Artificial Intelligence
Week 7 Problem Sheet
Weekly Topic Review
There was no new examinable lecture content introduced last week, so this week we are going to focus on the project. In part B of the project you will be required to write an agent to play a game of Cachex. Today you are going to analyse the Cachex game to get you thinking about possible game-playing agent strategies. You are not required to do these activities with your actual project partner – these are just warm-up questions, and you may collaborate with anyone in the class.
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Before approaching these questions please make sure you understand the rules of the game. You might like to re-visit them on Canvas (the original document was updated to clarify some rules)!
1. Game analysis [T] Recall that we denote the size of the board using the variable n. It is important to consider how it impacts the size of the search space, since this could determine what sorts of agent strategies are feasible.
(a) What is the branching factor of a game of Cachex in terms of n?
(b) Derive an upper bound on the size of the state space in terms of n.
(c) Classify the task environment of the Cachex game (you might want to revisit the work- shop in week 2). Discuss what this means for the types of game-playing strategies that could be used.
2. Win detection [T] Given a Cachex game board, design an algorithm to determine if a player has won the game, and if so, which player. You may assume the “input” is a game board represented as an n × n array, where ‘r’ or ‘b’ denotes an occupied cell for the respective player (or None for an empty cell).
3. Diamond captures [T] For a given coordinate on the game board, what is the maximum number of ‘diamonds’ it could be a part of? Discuss how you might detect diamond-captures given some arbitrary board, and a move that has just been played.
4. Agent strategies [T] Discuss how game-playing strategies introduced in recent lectures could be used to write a Cachex agent. Are these feasible for any game board size n?
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