Tasks:

Part $1$: Basic pathfinding

To begin with, you will consider the problem of finding a path through a maze from a given start

state to a given goal state. This scenario is illustrated in the figure above, where the start position

is indicated by the "Pacman" icon and the goal state is a dot. The maze layout will be given to

you in a simple text format, where $\text{'}\%\text{'}$ stands for walls, $\text{'}$P$\text{'}$ for the starting position, and $\text{'}.\text{'}$ for the

goal $($see sample maze file$).$ For this part of the assignment, all step costs are equal to one.

To solve different mazes, please implement the two search algorithms in the following two

groups.

Group $1$:

Breadth$-$first search;

Group $2$:

$A^{**}$ search.

For A$*$ search, use the Manhattan distance from the current position to the goal as the heuristic

function.

Run each of the above algorithms on the small maze, medium maze, big maze, and the open

maze. For each problem instance and each search algorithm, report the following:

a$.$ The solution and its path cost;

b$.$ Number of nodes expanded;

c$.$ Maximum tree depth searched;

d$.$ Maximum size of the fringe.

You can display the solution by putting a $\text{'}.\text{'}$ in every maze square visited on the path $($example

solution to the big maze$).$