一、文章介绍

本文是针对吴飞教授在MOOC课程 ：《人工智能：模型与算法》 2.1节 启发式搜索的课前发散

在课程2.1节 启发式搜索章节中，吴飞教授以如何计算城市地图两点之间最短路径为例，重点讲授了贪婪最佳优先搜索和A*搜索算法；但并未使用“笨办法”：遍历查询的方式来解决该需求，对于算法初学者来讲无法直观比较出搜索算法带来的效率提升。故本文目的在于通过遍历查询不借助任何算法，利用python内建数据结构与方法实现任意两点的所有可能路径及开销。

二、信息收集

根据课件，我们可以知晓以下信息：

1. 城市地图
2. 相邻城市的实际距离

地图如下：

将以上信息录入python字典：

city_map = {'Arad':{'Zerind':75,'Sibiu':140,'Timisoara':118},'Zerind':{'Oradea':71},'Oradea':{'Sibiu':151},'Timisoara':{'Lugoj':111},'Lugoj':{'Mehadia':70},'Mehadia':{'Drobeta':75},'Drobeta':{'Craiova':120},'Craiova':{'Pitesti':138},'Sibiu':{'Fagaras':99,'Rimnicu Vilcea':80},'Rimnicu Vilcea':{'Craiova':146,'Pitesti':97},'Fagaras':{'Bucharest':211},'Pitesti':{'Bucharest':101},'Bucharest':{'Giurgiu':90,'Urziceni':85},'Urziceni':{'Hirsova':98,'Vaslui':142},'Hirsova':{'Eforie':86},'Vaslui':{'Iasi':92},'Iasi':{'Neamt':87},   }

问题1： 信息录入我们采取水平分割的录入方式，每个城市只录入下游相邻节点。 以Sibiu为例，其上游城市为Arad与Oradea; 但是并不录入，只录入Fagaras与Rimnicu Vilcea.

三、代码实现

3.1 数据处理

为了解决上述问题1，需要针对收集的城市数据进行处理，输出直观的全邻接信息。

# 统计city_map节点邻接关系
fullmesh_city_map={}      #  用于记录全互联地图# 遍历手工地图信息，正向解析下游城市
for k,v in city_map.items():next_hop={}for _k,_v in v.items():next_hop[_k]=_vif _k in city_map:   # 逆向解析上游城市if _k in fullmesh_city_map:fullmesh_city_map[_k].update({k:_v})else: # fullmesh_city_map[_k] = {k:_v}else:  # 处理边界城市fullmesh_city_map[_k] = {k:_v}if k in fullmesh_city_map:fullmesh_city_map[k].update(next_hop)else:fullmesh_city_map[k]=next_hop# 打印
for k,v in fullmesh_city_map.items():print(k,v)

输出结果如下：

Zerind {‘Arad’: 75, ‘Oradea’: 71}
Sibiu {‘Arad’: 140, ‘Oradea’: 151, ‘Fagaras’: 99, ‘Rimnicu Vilcea’: 80}
Timisoara {‘Arad’: 118, ‘Lugoj’: 111}
Arad {‘Zerind’: 75, ‘Sibiu’: 140, ‘Timisoara’: 118}
Oradea {‘Zerind’: 71, ‘Sibiu’: 151}
Lugoj {‘Timisoara’: 111, ‘Mehadia’: 70}
Mehadia {‘Lugoj’: 70, ‘Drobeta’: 75}
Drobeta {‘Mehadia’: 75, ‘Craiova’: 120}
Craiova {‘Drobeta’: 120, ‘Pitesti’: 138, ‘Rimnicu Vilcea’: 146}
Pitesti {‘Craiova’: 138, ‘Rimnicu Vilcea’: 97, ‘Bucharest’: 101}
Fagaras {‘Sibiu’: 99, ‘Bucharest’: 211}
Rimnicu Vilcea {‘Sibiu’: 80, ‘Craiova’: 146, ‘Pitesti’: 97}
Bucharest {‘Fagaras’: 211, ‘Pitesti’: 101, ‘Giurgiu’: 90, ‘Urziceni’: 85}
Giurgiu {‘Bucharest’: 90}
Urziceni {‘Bucharest’: 85, ‘Hirsova’: 98, ‘Vaslui’: 142}
Hirsova {‘Urziceni’: 98, ‘Eforie’: 86}
Vaslui {‘Urziceni’: 142, ‘Iasi’: 92}
Eforie {‘Hirsova’: 86}
Iasi {‘Vaslui’: 92, ‘Neamt’: 87}
Neamt {‘Iasi’: 87}

根据以上结果，可以发现任意城市都记录了上下游相邻城市。这便于后续代码的实现。

3.2 路径计算

本节代码用于计算任意两个给定城市间的可能路径和代价。因采用遍历的形式，且无任何标志用于判断程序是否已经得出两点之间的全部可能路径，故只能通过夸张的遍历次数来进行覆盖。

需求如下：
计算 城市’Oradea’与’Neamt’之间的可能路径与代价。

代码实现如下：

root = 'Oradea'
start = root
end = 'Neamt'path = []
finnal_path=[]
times = 0
update_pop =[None]while times<100000:    for k,v in fullmesh_city_map[start].items():if update_pop[0] == None:temp_path = [start,k,v]path.append(temp_path)else:if k in update_pop:path.append(update_pop)else:update_pop.insert(-1,k)update_pop[-1] += vpath.append(update_pop)update_pop=[]for i in x_copy:update_pop.append(i)for x in path:if x[-2] == end:_a = []for _x in x:_a.append(_x)if _a not in finnal_path:finnal_path.append(_a)else:passupdate_pop = path.pop(0)x_copy = []for i in update_pop:x_copy.append(i)start = update_pop[-2]    times+=1# 打印结果
path_number = 1
for i in finnal_path:print("线路{}: ".format(path_number),("--->".join(i[0:-1])),"距离 ",i[-1])path_number += 1

经过计算，共有12条可选路径。

四、完整代码

以下代码运行后会出现12条可选路径。大家可自行验证。 自此，大家在学习玩搜索算法后方便感知算法的带来的效率改善情况。

city_map = {'Arad':{'Zerind':75,'Sibiu':140,'Timisoara':118},'Zerind':{'Oradea':71},'Oradea':{'Sibiu':151},'Timisoara':{'Lugoj':111},'Lugoj':{'Mehadia':70},'Mehadia':{'Drobeta':75},'Drobeta':{'Craiova':120},'Craiova':{'Pitesti':138},'Sibiu':{'Fagaras':99,'Rimnicu Vilcea':80},'Rimnicu Vilcea':{'Craiova':146,'Pitesti':97},'Fagaras':{'Bucharest':211},'Pitesti':{'Bucharest':101},'Bucharest':{'Giurgiu':90,'Urziceni':85},'Urziceni':{'Hirsova':98,'Vaslui':142},'Hirsova':{'Eforie':86},'Vaslui':{'Iasi':92},'Iasi':{'Neamt':87},   }# 统计city_map节点邻接关系
fullmesh_city_map={}      #  用于记录全互联地图# 遍历手工地图信息，正向解析下游城市
for k,v in city_map.items():next_hop={}for _k,_v in v.items():next_hop[_k]=_vif _k in city_map:   # 逆向解析上游城市if _k in fullmesh_city_map:fullmesh_city_map[_k].update({k:_v})else: # fullmesh_city_map[_k] = {k:_v}else:  # 处理边界城市fullmesh_city_map[_k] = {k:_v}if k in fullmesh_city_map:fullmesh_city_map[k].update(next_hop)else:fullmesh_city_map[k]=next_hop# 打印
for k,v in fullmesh_city_map.items():print(k,v)root = 'Oradea'
start = root
end = 'Neamt'path = []
finnal_path=[]
times = 0
update_pop =[None]while times<100000:    for k,v in fullmesh_city_map[start].items():if update_pop[0] == None:temp_path = [start,k,v]path.append(temp_path)else:if k in update_pop:path.append(update_pop)else:update_pop.insert(-1,k)update_pop[-1] += vpath.append(update_pop)update_pop=[]for i in x_copy:update_pop.append(i)for x in path:if x[-2] == end:_a = []for _x in x:_a.append(_x)if _a not in finnal_path:finnal_path.append(_a)else:passupdate_pop = path.pop(0)x_copy = []for i in update_pop:x_copy.append(i)start = update_pop[-2]    times+=1# 打印结果
path_number = 1
for i in finnal_path:print("线路{}: ".format(path_number),("--->".join(i[0:-1])),"距离 ",i[-1])path_number += 1