# Maze Solving with Breadth-First Search¶

In this lab, we are going to solve a maze with an algorithm called breadth-first search. Before we do though, we need to get some terminology out of the way. There are two main ways that we will be storing data, known as data structures. These are:

• A graph is a data structure representing data that is interconnected. We will be representing our maze this way. Graphs are made of of nodes and edges. Think of edges as roads that connect different nodes together. In this maze, we will hopping from node to node via these edges.

• A queue is another commonly used data structure. Think of it as a line that we always take from the front of and always add to the back (no budging).

First, download the code template found in the `src/intermediate` folder of the repository, found here. Then, lets try and implement a solution to solve it!

One solution is breadth-first search, or BFS. BFS works by cycling through all possible nodes one hop away from your current position, adding them to a queue and then cycling through all of those nodes in the queue to see if they are the solution. Lets see how it is implemented below:

``````#Takes as input a Square object node in a graph of Square nodes.
# This will always be the Square node representing (0,0), the start position
#Performs BFS until the goal Square is found (the Square with color = "blue").
#Returns a list containing each Square node in the path from the start
# (0,0) to the goal node, inclusive, in order from start to goal.
def find_path(start_node):
start_node.set_color("gray")
start_node.prev = None

q = [] # Our queue of nodes visited
q.append(start_node) # Add starting node to the end of the queue
while len(q) != 0: # Runs when there are still nodes in the queue
start_node = q.pop(0) # Remove the node in the front of the queue
for node in start_node.adj:   # Look at every item in the current node's adjacency list
if node.get_color() == "white":  # If the color is white, we haven't visited this node before
node.set_color("grey")
node.depth = start_node.depth + 1
node.prev = start_node
q.append(node)  # Add this new node to the queue
elif node.get_color() == "blue":  # If the color is blue, we have reached our goal
node.prev = start_node
visited = [node]
cur = node.prev
while cur != None: # Backtrack our path, adding nodes to the visited list as we go
visited.insert(0, cur)
cur = cur.prev
return visited
start_node.set_color("black")
``````

There are other ways to find paths in mazes, one of which we will explore in the next lab!

• This lab was heavily inspired by Nathan Taylor's University of Minnesota CSCI 4041 assignment.