What is the difference between breadth-first search and depth-first search in Python?

Question

Jayant Kumar · Accepted Answer

Table of Contents
Introduction
Breadth-First Search (BFS) and Depth-First Search (DFS) are two fundamental graph traversal algorithms used to explore nodes and edges in a graph or tree. Both have unique characteristics, traversal methods, and applications. Understanding the differences can help in selecting the appropriate algorithm for specific tasks.
1. Traversal Methods
1.1 Breadth-First Search (BFS)
BFS explores nodes level by level, starting from the root or starting node and moving outward. It uses a queue to keep track of nodes to be explored next.

Traversal Method:

Start at the root or source node.
Explore all neighbor nodes at the present depth level before moving on to nodes at the next depth level.
This approach guarantees the shortest path in an unweighted graph.

Use Cases:

Finding the shortest path in an unweighted graph.
Level-order traversal in trees.
Solving puzzles or problems involving layers or levels.

1.2 Depth-First Search (DFS)
DFS explores as far down a branch as possible before backtracking. It uses a stack (or recursion) to keep track of nodes to be explored next.

Traversal Method:

Start at the root or source node.
Explore as deeply as possible along each branch before backtracking.
Can be implemented using recursion or an explicit stack.

Use Cases:

Pathfinding in mazes or puzzles where the path does not need to be the shortest.
Topological sorting in directed graphs.
Detecting cycles in graphs.

2. Python Implementation
2.1 Breadth-First Search (BFS)
Here’s a Python implementation of BFS using a queue:
from collections import deque

class Graph:
    def __init__(self):
        self.graph = {}

def add_edge(self, u, v):
        if u not in self.graph:
            self.graph[u] = []
        if v not in self.graph:
            self.graph[v] = []
        self.graph[u].append(v)
        self.graph[v].append(u)

def bfs(self, start):
        visited = set()
        queue = deque([start])
        visited.add(start)
        
        while queue:
            vertex = queue.popleft()
            print(vertex, end=' ')
            for neighbor in self.graph[vertex]:
                if neighbor not in visited:
                    visited.add(neighbor)
                    queue.append(neighbor)

# Example usage
g = Graph()
g.add_edge(1, 2)
g.add_edge(1, 3)
g.add_edge(2, 4)
g.add_edge(2, 5)
g.add_edge(3, 6)
g.add_edge(3, 7)

print("BFS Traversal:")
g.bfs(1)  # Output: 1 2 3 4 5 6 7

2.2 Depth-First Search (DFS)
Here’s a Python implementation of DFS using recursion:
class GraphDFS:
    def __init__(self):
        self.graph = {}

def add_edge(self, u, v):
        if u not in self.graph:
            self.graph[u] = []
        if v not in self.graph:
            self.graph[v] = []
        self.graph[u].append(v)
        self.graph[v].append(u)

def dfs(self, start):
        visited = set()
        self._dfs_recursive(start, visited)

def _dfs_recursive(self, vertex, visited):
        visited.add(vertex)
        print(vertex, end=' ')
        for neighbor in self.graph[vertex]:
            if neighbor not in visited:
                self._dfs_recursive(neighbor, visited)

# Example usage
g_dfs = GraphDFS()
g_dfs.add_edge(1, 2)
g_dfs.add_edge(1, 3)
g_dfs.add_edge(2, 4)
g_dfs.add_edge(2, 5)
g_dfs.add_edge(3, 6)
g_dfs.add_edge(3, 7)

print("
DFS Traversal:")
g_dfs.dfs(1)  # Output: 1 2 4 5 3 6 7

3. Comparison of BFS and DFS

BFS:

Data Structure: Queue.
Traversal: Level by level.
Shortest Path: Guarantees shortest path in an unweighted graph.
Memory Usage: Can be high for wide graphs with many nodes at each level.

DFS:

Data Structure: Stack or recursion.
Traversal: Deepest nodes first, then backtrack.
Shortest Path: Does not guarantee shortest path.
Memory Usage: Can be high for deep graphs with many nodes in one branch.

Conclusion
Breadth-First Search (BFS) and Depth-First Search (DFS) are essential graph traversal algorithms with distinct characteristics and use cases. BFS is ideal for finding the shortest path and level-order traversal, while DFS is suited for deep path exploration and topological sorting. By understanding their differences and applications, you can effectively choose the appropriate algorithm for your specific needs in Python.

What is the difference between breadth-first search and depth-first search in Python?

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