Breadth-First Search (BFS)

Breadth-First Search (BFS) is a popular graph traversal algorithm that explores all the vertices of a graph in breadth-first order. It starts from a source vertex and visits all its neighboring vertices before moving on to their neighbors. BFS uses a queue data structure to keep track of the vertices to be visited.

BFS can be applied to various problems in robotics and computer vision. One common application is navigation in a maze. By using BFS, we can find the shortest path between two points in a maze by exploring its cells in breadth-first order. Let's take a look at an example:

1import queue
2
3# Application: Navigation in a maze
4
5# This class represents a cell in the maze
6class Cell:
7  def __init__(self, row, col):
8    self.row = row
9    self.col = col
10    self.wall = False
11    self.visited = False
12    self.path = False
13    self.previous = None
14
15# Maze dimensions
16num_rows = 5
17num_cols = 5
18
19# Create the maze
20maze = [[Cell(row, col) for col in range(num_cols)] for row in range(num_rows)]
21
22# Set some walls in the maze
23def set_walls():
24  maze[1][1].wall = True
25  maze[1][3].wall = True
26  maze[2][2].wall = True
27  maze[3][1].wall = True
28
29# Function to print the maze
30
31# Function to get the neighbors of a cell
32
33# Breadth-First Search algorithm

In this example, we define a Cell class to represent each cell in the maze. Each cell has attributes such as its row and column position, whether it is a wall, whether it has been visited, whether it is part of the path, and a reference to its previous cell. We then create a maze with the specified dimensions and set some walls.

To implement BFS, we need a queue data structure to store the cells to be visited. We start from a source cell and enqueue it in the queue. While the queue is not empty, we dequeue a cell, mark it as visited, and enqueue its unvisited neighboring cells. We repeat this process until we reach the destination cell or the queue becomes empty. This guarantees that we visit all cells in the maze in breadth-first order.

Next, we will write functions to print the maze, get the neighbors of a cell, and implement the BFS algorithm.

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# Breadth-First Search algorithm

import queue

​

# Application: Navigation in a maze

​

# This class represents a cell in the maze

class Cell:

  def __init__(self, row, col):

    self.row = row

    self.col = col

    self.wall = False

    self.visited = False

    self.path = False

    self.previous = None

​

# Maze dimensions

num_rows = 5

num_cols = 5

​

# Create the maze

maze = [[Cell(row, col) for col in range(num_cols)] for row in range(num_rows)]

​

# Set some walls in the maze

def set_walls():

  maze[1][1].wall = True

  maze[1][3].wall = True

  maze[2][2].wall = True

  maze[3][1].wall = True

​

# Function to print the maze