Note: For this lab, you can work together in teams of up to 4 students. However, this is not a necessity. The assignment is small enough to do it alone in which case you may get more experience. You can use Piazza to find team members and discuss problems.

You will need a Java Development Kit (JDK) and a Java IDE (any text editor should do as well).

Many environments have the property that there are several paths that lead to the same state.

1. Which of the search algorithms that we covered in class (breadth-first, depth-first and uniform-cost search) benefit from detecting repeated states? For each algorithm give a short explanation how detecting repeated states can make it better.
2. Which data structure is typically used for detecting repeated states and why?
3. Download the material below, implement a hash function for State objects that passes all the tests.
4. Report and comment on the results you get. How many hash collisions and bucket index collisions do you get?

Is this good or bad? (If the results are bad try to improve your hash function. If you only get very few collisions, increase the number of states that are generated in Main.java to 10000 or 100000 and see what happens.)

1. Why is it important to have few hash collisions if hashing is used to detect repeated states?

The Java project for the lab can be found on Skel. See, instructions below on how to get it.

The project contains a State class that could be thought of implementing a state of some robot. The state consists of a position, an orientation and a boolean holding the information of whether or not the robot is turned on. The project also contains code to test how good the hashCode() method of the State class is. To run the tests simply run the Main class or use “ant run” on the terminal.

• You need to implement the methods int hashCode() and boolean equals(Object o) in classes State and Position appropriately.
• For two states s1 and s2 that you'd consider the same, s1.equals(s2) must return true and false otherwise.
• For any two objects o1 and o2, if o1.equals(o2) then o1.hashCode() == o2.hashCode() must be true!
• Objects that are not equal are allowed have the same hash code. However, if that happens too often then hash maps become very inefficient.

Hand in a zip file containing:

• the answers to the questions above (1.,2. and 4.) (in a text/pdf/word file)
• your source code (ideally just the whole project directory)

To create the zip file you can just edit the “student” property in the build.xml and call the “zip” target using ant (execute “ant zip” in the directory containing the build.xml).