Task 1: Assume you are a taxi driver. Your taxi can contain four passengers. Passengers pay the flat fee for a ride to the airport, so your goal is to pick up four passengers and take them to the airport in the smallest number of miles. Your world can be modelled as a graph of locations with distances between them. Some, but not all, of the locations have passengers which you can pick up.

problem1. describe the state space of this search problem.

problem2. What would be a good cost function for this search problem?

problem3. Now, consider a case where passengers have to pay according to how far away they are from the airport when they are picked up (note: they do not pay according to how long a ride they take in your taxi, but according to the length of the shortest path from their pickup point to airport). describe the state space for this search problem.

problem4. What would be a good cost function for this version of problem? You still have wanted to save petrol.

problem5. Is uniform cost search guaranteed to find optimal solution in either or both versions of the problem? Justify your answer.

problem6. Give concise definitions of following terms:

i) Constraint satisfaction problem,

ii) Back-tracking search

iii) Forward checking

iv) Arc consistency