Search algorithms play a crucial role in various fields, including robotics and computer vision. These algorithms enable us to efficiently explore and find solutions within large datasets and complex environments. In this lesson, we will delve into two fundamental search algorithms: Breadth-First Search (BFS) and Depth-First Search (DFS). Understanding these algorithms is essential for solving many problems in the fields of robotics and computer vision.

In BFS, we start exploring from the initial node and expand the search breadth-wise, visiting all the neighboring nodes before moving to the next level. This approach allows us to traverse the search space systematically and is particularly useful for finding the shortest path.

On the other hand, DFS explores as far as possible before backtracking. It traverses to the deepest level of a tree or graph before exploring other branches. DFS is often used to explore all possible paths in a search space and is useful for tasks such as exhaustive search and cycle detection.

By mastering BFS and DFS, you will have the tools to solve a wide range of problems in robotics and computer vision. Let's dive in and explore these algorithms in more detail!

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

Depth-First Search (DFS)

Depth-First Search (DFS) is a graph traversal algorithm that explores all vertices of a graph by traversing as far as possible along each branch before backtracking. It starts at a selected source node and explores as far as possible along each branch before backtracking.

In DFS, a stack data structure is used to keep track of the vertices to be visited. The algorithm starts by pushing the source vertex onto the stack. While the stack is not empty, the top vertex is popped from the stack and marked as visited. Then, for each neighbor of the current vertex that has not been visited, it is pushed onto the stack.

DFS can be applied to various problems in robotics and computer vision. One common application is image processing, where DFS can be used to explore nearby pixels and identify connected components. Another application is path planning in a maze, where DFS can be used to find a path from the start to the goal by exploring the maze in depth-first order.

Let's take a look at an example implementation of DFS in Python:

1# Python code for Depth-First Search (DFS)
2
3# DFS function
4def dfs(graph, start, visited):
5    visited.add(start)
6    print(start)
7    for neighbor in graph[start]:
8        if neighbor not in visited:
9            dfs(graph, neighbor, visited)
10
11# Example usage
12
13# Create a graph
14code_here
15
16# Call DFS on the graph
17visited = set()
18dfs(graph, start, visited)

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# Python code for Depth-First Search (DFS)

​

# DFS function

def dfs(graph, start, visited):

    visited.add(start)

    print(start)

    for neighbor in graph[start]:

        if neighbor not in visited:

            dfs(graph, neighbor, visited)

​

# Example usage

​

# Create a graph

graph = {

    'A': ['B', 'C'],

    'B': ['D', 'E'],

    'C': ['F', 'G'],

    'D': [],

    'E': ['H', 'I'],

    'F': [],

    'G': ['J'],

    'H': [],

    'I': [],

    'J': []

}

​

# Call DFS on the graph

visited = set()

dfs(graph, 'A', visited)