【深度优先搜索】和【广度优先搜索】的区别介绍

一. 前言

深度优先搜索(Depth-First Search,DFS)和广度优先搜索(Breadth-First Search,BFS)是两种常见的图搜索算法。它们的主要区别在于搜索的方式和顺序不同。

二. 区别

1. DFS的搜索方式是:

从某个节点出发,沿着一条路径直到底部,然后返回到前一个节点,继续搜索下一条路径,直到搜索完整张图。DFS使用栈或者递归来实现搜索过程。

具体步骤如下:

  • 访问起始结点;
  • 递归地访问第一个未被访问的相邻结点,如果没有未被访问的相邻结点,则回溯到上一个结点继续递归;
  • 依次访问和递归每个未被访问的相邻结点,直到找到目标结点或到达叶子结点为止。

2. BFS的搜索方式是:

从某个节点出发,将其所有邻接节点加入到队列中,然后依次访问队列中的节点,将其邻接节点加入到队列中,以此类推,直到搜索完整张图。BFS使用队列来实现搜索过程。

具体步骤如下:

  • 将起始结点放入队列中;

  • 访问队列头部结点,将其未访问过的相邻结点加入队列尾部;

  • 将队列头部结点出队列;

  • 重复步骤 2 和 3,直到队列为空或找到目标结点。

三. 代码示例

1. 深度优先搜索代码示例:

示例一

def dfs(graph, start, target, path=[]):
    # 记录路径
    path = path + [start]
    # 到达目标结点,返回路径
    if start == target:
        return path
    # 遍历相邻结点
    for node in graph[start]:
        if node not in path:
            newpath = dfs(graph, node, target, path)
            if newpath:
                return newpath
    return None

示例二

class Graph:
    def __init__(self, graph_dict=None):
        if graph_dict is None:
            graph_dict = {}
        self.__graph_dict = graph_dict
 
    def add_vertex(self, vertex):
        if vertex not in self.__graph_dict:
            self.__graph_dict[vertex] = []
 
    def add_edge(self, edge):
        edge = set(edge)
        (vertex1, vertex2) = tuple(edge)
        if vertex1 in self.__graph_dict:
            self.__graph_dict[vertex1].append(vertex2)
        else:
            self.__graph_dict[vertex1] = [vertex2]
 
    def dfs(self, start, visited=None):
        if visited is None:
            visited = set()
        visited.add(start)
        print(start)
        for next in self.__graph_dict[start] - visited:
            self.dfs(next, visited)
        return visited
 
 
graph = {"A": {"B", "C"},
         "B": {"A", "D", "E"},
         "C": {"A", "F"},
         "D": {"B"},
         "E": {"B", "F"},
         "F": {"C", "E"}}
 
g = Graph(graph)
print("Depth First Search:")
g.dfs("A")

运行结果
【深度优先搜索】和【广度优先搜索】的区别介绍_第1张图片

2. 广度优先搜索代码示例:

示例一

from collections import deque

# 使用队列实现 BFS
def bfs(graph, start, target):
    # 使用 deque 实现双端队列
    queue = deque()
    queue.append(start)
    visited = set()
    visited.add(start)
    while queue:
        # 出队列
        node = queue.popleft()
        # 到达目标结点,返回
        if node == target:
            return True
        # 遍历相邻结点
        for neighbor in graph[node]:
            # 未访问过的结点入队列
            if neighbor not in visited:
                visited.add(neighbor)
                queue.append(neighbor)
    # 没有找到目标结点
    return False

示例二

from collections import deque
 
 
class Graph:
    def __init__(self, graph_dict=None):
        if graph_dict is None:
            graph_dict = {}
        self.__graph_dict = graph_dict
 
    def add_vertex(self, vertex):
        if vertex not in self.__graph_dict:
            self.__graph_dict[vertex] = []
 
    def add_edge(self, edge):
        edge = set(edge)
        (vertex1, vertex2) = tuple(edge)
        if vertex1 in self.__graph_dict:
            self.__graph_dict[vertex1].append(vertex2)
        else:
            self.__graph_dict[vertex1] = [vertex2]
 
    def bfs(self, start):
        visited, queue = set(), deque([start])
        visited.add(start)
        while queue:
            vertex = queue.popleft()
            print(vertex)
            for neighbour in self.__graph_dict[vertex]:
                if neighbour not in visited:
                    visited.add(neighbour)
                    queue.append(neighbour)
 
 
graph = {"A": {"B", "C"},
         "B": {"A", "D", "E"},
         "C": {"A", "F"},
         "D": {"B"},
         "E": {"B", "F"},
         "F": {"C", "E"}}
 
g = Graph(graph)
print("Breadth First Search:")
g.bfs("A")

运行结果
【深度优先搜索】和【广度优先搜索】的区别介绍_第2张图片

四. 总结:

  • 深度优先搜索:倾向于深度遍历图中的分支,直到遇到叶子节点或目标节点;
  • 广度优先搜索:倾向于先遍历离起始节点较近的节点,然后逐步向下遍历。

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