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图由顶点和边组成。如果图中顶点是有序的，则称之为有向图。
由顶点组成的序列，称为路径。
除了可以对图进行遍历外，还可以搜索图中任意两个顶点之间的最短路径。
在python中，可利用字典 {键:值} 来创建图。
图中的每个顶点，都是字典中的键，该键对应的值为“该顶点所指向的图中其他的顶点”。
# -*- coding:utf-8 -*-
# file: pygraph.py
#
def searchGraph(graph, start, end): # 搜索树
results = []
generatePath(graph, [start], end, results) # 生成路径
results.sort(key=lambda x:len(x)) # 按路径长短排序
return results
def generatePath(graph, path, end, results): # 生成路径
state = path[-1]
if state == end:
results.append(path)
else:
for arc in graph[state]:
if arc not in path:
generatePath(graph, path + [arc], end, results)
if __name__ == '__main__':
Graph = {'A': ['B', 'C', 'D'], # 构建树
'B': ['E'],
'C': ['D', 'F'],
'D': ['B', 'E', 'G'],
'E': [],
'F': ['D', 'G'],
'G': ['E']}
r = searchGraph(Graph, 'A','D') # 搜索A到D的所有路径
print('************************')
print(' path A to D')
print('************************')
for i in r:
print(i)
r = searchGraph(Graph, 'A','E') # 搜索A到E的所有路径
print('************************')
print(' path A to E')
print('************************')
for i in r:
print(i)
r = searchGraph(Graph, 'C','E') # 搜索C到E的所有路径
print('************************')
print(' path C to E')
print('************************')
for i in r:
print(i)
运行结果如下：
Python 3.6.1 (v3.6.1:69c0db5, Mar 21 2017, 18:41:36) [MSC v.1900 64 bit (AMD64)] on win32
Type "copyright", "credits" or "license()" for more information.
>>>
== RESTART: G:\pygraph.py ==
************************
path A to D
************************
['A', 'D']
['A', 'C', 'D']
['A', 'C', 'F', 'D']
************************
path A to E
************************
['A', 'B', 'E']
['A', 'D', 'E']
['A', 'C', 'D', 'E']
['A', 'D', 'B', 'E']
['A', 'D', 'G', 'E']
['A', 'C', 'D', 'B', 'E']
['A', 'C', 'D', 'G', 'E']
['A', 'C', 'F', 'D', 'E']
['A', 'C', 'F', 'G', 'E']
['A', 'C', 'F', 'D', 'B', 'E']
['A', 'C', 'F', 'D', 'G', 'E']
************************
path C to E
************************
['C', 'D', 'E']
['C', 'D', 'B', 'E']
['C', 'D', 'G', 'E']
['C', 'F', 'D', 'E']
['C', 'F', 'G', 'E']
['C', 'F', 'D', 'B', 'E']
['C', 'F', 'D', 'G', 'E']
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