Due September 24th by midnight

First change into your directory for this class. Then clone the
GitHub repository for lab1, replacing ** USER1**
and

cd cs63 git clone git@github.swarthmore.edu:cs63-f19/lab1-Be sure both partners have a copy of the code, and that you keep your copies in synch using git push/pull.USER1-USER2.git

The objectives of this lab are to:

- Use informed search and heuristic knowledge to more efficiently find an optimal solution to state space search problems.
- Demonstrate experimentally that informed search outperforms uninformed search in terms of the number of nodes expanded.
- Demonstrate experimentally that heuristics that generate a closer approximation of the distance to the goal outperform other heuristics in terms of number of nodes expanded.

For this lab you will modify the following files:

`InformedSearch.py``TrafficJam.py``FifteenPuzzle.py``HeuristicsTests.py``experiments`

We will be using text-based versions of the Traffic Jam and Fifteen Puzzle games in this lab. Complete the following steps to familiarize yourself with the games.

- Try playing the Traffic Jam game from the command line.
To invoke the traffic jam game do:
./TrafficJam.py puzzles/traffic00.txt

You will see a picture of the board and a list of valid moves you may make (as shown below). In the case of traffic00, the gird is 6x6, but the grid size can change between puzzles. The exit is marked by two vertical bars. In a traffic jam puzzle, each car is represented by a unique number. In this example, cars 1, 2, and 6 are positioned horizontally and can only move left or right, while cars 0, 3, 4, and 5 are positioned vertically and can only move up or down. Cars may be different lengths but are always only one grid square wide. Empty locations are marked by a dash. The goal of the game is to move the car labeled 0 to the exit.

| | 1 1 2 2 3 - 0 - - - 3 - 0 - - - 3 - - - 4 - 5 - - - 4 - 5 - - - 4 6 6 - a: car0 down b: car4 up c: car6 right Select move (or q to quit):

You should be able to solve this particular puzzle in 7 moves.

- Try playing the Fifteen Puzzle from the command line. To invoke the fifteen puzzle game do:
./FifteenPuzzle.py puzzles/fifteen00.json

The file`fifteen00.json`contains a 2x2 puzzle. In a fifteen puzzle, each block is represented by a natural number, and the blank space is represented by a 0. The**goal**is to put the blocks in increasing order from the top left to the bottom right (with the blank at the bottom right), which for a 2x2 puzzle is the following state:1 2 3 0

Below is the**initial**state for`fifteen00.json`. The possible moves describe how the space should move. You should be2 3 1 0 moves: U, L

- For each game, try a couple of other starting boards from the
`puzzles`directory. - Try making a puzzle of your own for each game. Be sure you can solve it. You can find other example Traffic Jam boards at Dr. Mike's Math Games for Kids.
- Open the files
`TrafficJam.py`and`FifteenPuzzle.py`in an editor. Familiarize yourself with the interface so that you can call the appropriate methods within your search agent. Also be sure you understand how the boards of the game are represented. For example, the board from traffic00 would be represented as:[['1', '1', '2', '2', '3', '-'], ['0', '-', '-', '-', '3', '-'], ['0', '-', '-', '-', '3', '-'], ['-', '-', '4', '-', '5', '-'], ['-', '-', '4', '-', '5', '-'], ['-', '-', '4', '-', '6', '6']]

You will be implementing A* search. The key difference between informed searches, like A*, and uninformed searches, like BFS, is that they estimate the cost associated with each node. For A* this cost is the sum of how much work it took to get to a node and an estimate of how far it is to the goal from a node.

For the both games, the cost of getting to a node will simply be the number of actions taken, which is stored in the depth of the node. To estimate the distance to the goal you will use a heuristic function.

Complete the implementation of informed search as follows:

- Implement the
`InformedSearchAgent`class. The search algorithm is similar to the BFS algorithm you implemented in the previous lab. For A* you will use a priority queue, while in BFS you used a standard queue. Note that the`Queues.py`file contains a`Priority_Queue`class that you may use. When implementing the search function, you can initially test it with the`zeroHeuristic`. This heuristic is completely uninformative so the resulting search reduces to BFS.create a node to store the initial game board add this node to the PQ frontier with a priority of 0 + h(n) while frontier not empty get currNode from frontier if currNode's state is goal return goal node end if increment the expanded node counter if currNode's state is not in visited add state to visited find all possible moves from currNode's state for each move determine the nextState if nextState is not in visited create a node for nextState set priority based on depth and the heuristic add this node to the frontier with priority end if end for end if end while return None

- Test your informed search using the
`zero`heuristic, which adds no additional information. Thus the number of nodes expanded by informed search should be exactly the same as it would be for BFS, an uninformed search.

Now it's time to add some heuristic information. This will allow the informed search to expand less nodes to more efficiently find solutions.

Implement each heuristic described below. We have provided some
starting point unit tests for the heuristics in the
file `HeuristicTests.py`. **For each heuristic, you should
include four tests** using the game boards given in
the `puzzles` directory. To execute the tests do:

`./HeuristicsTests`

- Implement the
`blockingHeuristic`function in the file`TrafficJam.py`. This function takes in a Traffic Jam Game board. It locates car0, and returns the sum of the number of cars that are blocking car0 from reaching the exit plus the number of rows car0 needs to move to get to the exit. For example in the starting board for`traffic01.txt`there are two cars blocking the exit and car0 needs to move up two rows to reach the exit, so the heuristic should return 4. While in the starting board for`traffic02.txt`there are three cars blocking the exit and car0 needs to move up three rows to reach the exit, thus the heuristic should return 6. - Implement the
`betterHeuristic`function in the file`TrafficJam.py`. This heuristic must remain admissible (it must underestimate the cost to the goal), but must sometimes give a higher estimate than`blockingHeuristic`. Be sure to explain your new heuristic in the function comment and give an example where it gives a better estimate than`blockingHeuristic`. - Implement the
`displacedHeuristic`and`manhattanHeuristic`functions in the file`FifteenPuzzle.py`. Optionally implement the`bonusHeuristic`. - Test your informed search using all of the heuristics that
you've written. Here is some sample output. Notice that the number of
nodes expanded is much lower when using the
`blocking`heuristic versus the`zero`heuristic.

Once you've completed informed search you are ready to do some performance testing.

Complete the tables provided in the `experiments` file, and answer the questions that follow. Note that for the fifteen puzzle problems, uninformed search will become excruciatingly slow for any of the larger board sizes. Feel free to try it for yourself, though I won't ask you to record these results for the fifteen puzzle problems.