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。
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:
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。
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")
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")