使用字典的方式构建有向图,并搜索图中的路径。
提供了三种不同的操作函数:
不足点:只能够处理无权无向图
#这个图有6个节点(A-G)和8个弧。它可以通过下面的Python数据结构来表示:
graph = {'A': ['B', 'C','D'],
'B': ['E'],
'C': ['D','F'],
'D': ['B','E','G'],
'E': [],
'F': ['D','G'],
'G': ['E']}
# 找到一条从start到end的路径
def findPath(graph,start,end,path=[]):
path = path + [start]
if start == end:
return path
for node in graph[start]:
if node not in path:
newpath = findPath(graph,node,end,path)
if newpath:
return newpath
return None
# 找到所有从start到end的路径
def findAllPath(graph,start,end,path=[]):
path = path +[start]
if start == end:
return [path]
paths = [] #存储所有路径
for node in graph[start]:
if node not in path:
newpaths = findAllPath(graph,node,end,path)
for newpath in newpaths:
paths.append(newpath)
return paths
# 查找最短路径
def findShortestPath(graph,start,end,path=[]):
path = path +[start]
if start == end:
return path
shortestPath = []
for node in graph[start]:
if node not in path:
newpath = findShortestPath(graph,node,end,path)
if newpath:
if not shortestPath or len(newpath)<len(shortestPath):
shortestPath = newpath
return shortestPath
onepath = findPath(graph,'A','G')
print('一条路径:',onepath)
allpath = findAllPath(graph,'A','G')
print('\n所有路径:',allpath)
shortpath = findShortestPath(graph,'A','G')
print('\n最短路径:',shortpath)