Four soccer teams have to take part in a round-robin tournament. The problem is to determine...
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Four soccer teams have to take part in a round-robin tournament. The problem is to determine a schedule of matches so that each team plays each other team once in the minimum number of rounds. Matches can take place in parallel. There are many ways to solve this problem, one of which is to specify it as a state space and search for the goal state. Say we number the teams 1, 2, 3 and 4. For each team, we can keep track of which other teams it has played so far by means of a set. So for team 1, the set {2, 4} means it has played against teams 2 and 4 so far. The entire state of which teams have played which other teams can then be represented by an ordered 4-tuple, where each element is a set of the teams that a team has played. The start/initial state is therefore s1 = ({}, {},{}, {}) because initially, team 1 has not played any other teams, team 2 hasn't played any other teams, etc. (2.1) What is the goal state of the state space? (2.2) Define an action called Schedule which can be applied to a state to get to a successor state. Hint: it helps to consider how you want the action to transform a state into a successor state. Explain what an applicable action means (the rules for transforming a state into another state) for your Schedule action. (2.3) What are the successor states of the start state? (2.4) What are the applicable actions to the state S1,1 = ({2}, {1}, {4}, {3})? (2.5) Specify the transition model for the applicable actions you specified for state S1,1 above. (2.6) Calculate the size of the search space (include the initial state in your calculation). Justify your answer. Four soccer teams have to take part in a round-robin tournament. The problem is to determine a schedule of matches so that each team plays each other team once in the minimum number of rounds. Matches can take place in parallel. There are many ways to solve this problem, one of which is to specify it as a state space and search for the goal state. Say we number the teams 1, 2, 3 and 4. For each team, we can keep track of which other teams it has played so far by means of a set. So for team 1, the set {2, 4} means it has played against teams 2 and 4 so far. The entire state of which teams have played which other teams can then be represented by an ordered 4-tuple, where each element is a set of the teams that a team has played. The start/initial state is therefore s1 = ({}, {},{}, {}) because initially, team 1 has not played any other teams, team 2 hasn't played any other teams, etc. (2.1) What is the goal state of the state space? (2.2) Define an action called Schedule which can be applied to a state to get to a successor state. Hint: it helps to consider how you want the action to transform a state into a successor state. Explain what an applicable action means (the rules for transforming a state into another state) for your Schedule action. (2.3) What are the successor states of the start state? (2.4) What are the applicable actions to the state S1,1 = ({2}, {1}, {4}, {3})? (2.5) Specify the transition model for the applicable actions you specified for state S1,1 above. (2.6) Calculate the size of the search space (include the initial state in your calculation). Justify your answer.
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Related Book For
Principles of Information Systems
ISBN: 978-0324665284
9th edition
Authors: Ralph M. Stair, George W. Reynolds
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