## Lab 1: Traffic JamDue Sept. 19 by midnight

Problem: How do you move the horizontal vehicles left or right and the vertical vehicles up or down to allow the red car to exit the grid out of the top side?

### Starting point code

From now on, you will be working with a partner to complete each lab. Log on to github.swarthmore.edu to see your partner assignment for this lab.

First change into your directory for this class. Then clone the GitHub repository for lab1, replacing USER1 and USER2 with the appropriate usernames:

```    cd cs63
git clone git@github.swarthmore.edu:cs63-f19/lab1-USER1-USER2.git
```

### Introduction

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

### Playing Traffic Jam and Fifteen Puzzle

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.

1. Try playing the Traffic Jam game from the command line. To invoke the traffic jam game do:
```python3 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.

2. Try playing the Fifteen Puzzle from the command line. To invoke the fifteen puzzle game do:
```python3 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 be able to solve his puzzle in four moves:
```2  3
1  0
moves: U, L
```
3. For each game, try a couple of other starting boards from the puzzles directory.

4. Make 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.

5. 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']]
```
Once you understand how the games work you can move on to implementing the search algorithms.

### Informed Search

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:

1. 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
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
```

2. 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.

### Heuristics

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:

python3 HeuristicsTests.py

1. 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.
2. 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.

3. Implement the displacedHeuristic and manhattanHeuristic functions in the file FifteenPuzzle.py. Optionally implement the bonusHeuristic.

4. 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.

### Experimental Comparison

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.