人工智能学习：python实现迭代加深的深度优先搜索

人工智能学习：python实现深度优先搜索算法

说明：

源码中的罗马尼亚城市地图与《人工智能学习：python实现宽度优先搜索算法》中的地图一致。

可以对比《人工智能学习：python实现深度优先搜索算法》。

迭代加深的深度优先搜索原理和伪代码：

算法流程分析：

流程：

深度逐渐加深，调用深度优先搜索进行搜索

算法性能分析：

有些状态被重复生成。但代价并非那么大，因为绝大多数节点都在底层，所以上层节点重复生成多次影响不大。生成的节点总数：

时间复杂度：

与宽度优先搜索想比，重复生成节点代价不大，举例：

源码：

import pandas as pd
from pandas import Series, DataFrame# 城市信息：city1 city2 path_cost
_city_info = None# 已探索集合
_explored = []# 节点数据结构
class Node:def __init__(self, state, parent, action, path_cost):self.state = stateself.parent = parentself.action = actionself.path_cost = path_costdef main():global _city_info, _exploredimport_city_info()while True:src_city = input('input src city\n')dst_city = input('input dst city\n')result = iterative_deepening_search(src_city, dst_city)if result == "failure" or result == "cutoff":print('from city: %s to city %s search failure' % (src_city, dst_city))else:print('from city: %s to city %s search success' % (src_city, dst_city))path = []while True:path.append(result.state)if result.parent is None:breakresult = result.parentsize = len(path)for i in range(size):if i < size - 1:print('%s->' % path.pop(), end='')else:print(path.pop())def import_city_info():global _city_infodata = [{'city1': 'Oradea', 'city2': 'Zerind', 'path_cost': 71},{'city1': 'Oradea', 'city2': 'Sibiu', 'path_cost': 151},{'city1': 'Zerind', 'city2': 'Arad', 'path_cost': 75},{'city1': 'Arad', 'city2': 'Sibiu', 'path_cost': 140},{'city1': 'Arad', 'city2': 'Timisoara', 'path_cost': 118},{'city1': 'Timisoara', 'city2': 'Lugoj', 'path_cost': 111},{'city1': 'Lugoj', 'city2': 'Mehadia', 'path_cost': 70},{'city1': 'Mehadia', 'city2': 'Drobeta', 'path_cost': 75},{'city1': 'Drobeta', 'city2': 'Craiova', 'path_cost': 120},{'city1': 'Sibiu', 'city2': 'Fagaras', 'path_cost': 99},{'city1': 'Sibiu', 'city2': 'Rimnicu Vilcea', 'path_cost': 80},{'city1': 'Rimnicu Vilcea', 'city2': 'Craiova', 'path_cost': 146},{'city1': 'Rimnicu Vilcea', 'city2': 'Pitesti', 'path_cost': 97},{'city1': 'Craiova', 'city2': 'Pitesti', 'path_cost': 138},{'city1': 'Fagaras', 'city2': 'Bucharest', 'path_cost': 211},{'city1': 'Pitesti', 'city2': 'Bucharest', 'path_cost': 101},{'city1': 'Bucharest', 'city2': 'Giurgiu', 'path_cost': 90},{'city1': 'Bucharest', 'city2': 'Urziceni', 'path_cost': 85},{'city1': 'Urziceni', 'city2': 'Vaslui', 'path_cost': 142},{'city1': 'Urziceni', 'city2': 'Hirsova', 'path_cost': 98},{'city1': 'Neamt', 'city2': 'Iasi', 'path_cost': 87},{'city1': 'Iasi', 'city2': 'Vaslui', 'path_cost': 92},{'city1': 'Hirsova', 'city2': 'Eforie', 'path_cost': 86}]_city_info = DataFrame(data, columns=['city1', 'city2', 'path_cost'])# print(_city_info)def iterative_deepening_search(src_state, dst_state):for i in range(100):result = depth_limited_search(src_state, dst_state, i)if result != "failure" and result != "cutoff":return resultreturn "cutoff"def depth_limited_search(src_state, dst_state, limit):global _explored_explored = []node = Node(src_state, None, None, 0)return recursive_dls(node, dst_state, limit)def recursive_dls(node, dst_state, limit):""":param node::param dst_state::param limit::return: "failure"：失败."cutoff"：被截至.node：成功"""global _city_info, _exploredif node.parent is not None:print('node state:%s parent state:%s' % (node.state, node.parent.state))else:print('node state:%s parent state:%s' % (node.state, None))_explored.append(node.state)# 目标测试if node.state == dst_state:print('this node is goal!')return nodeelif limit == 0:print('this node is cutoff!')return "cutoff"else:cutoff_occurred = False# 遍历子节点for i in range(len(_city_info)):dst_city = ''if _city_info['city1'][i] == node.state:dst_city = _city_info['city2'][i]elif _city_info['city2'][i] == node.state:dst_city = _city_info['city1'][i]if dst_city == '':continuechild = Node(dst_city, node, 'go', node.path_cost + _city_info['path_cost'][i])# 过滤已探索的点if child.state in _explored:continueprint('child node:state:%s path cost:%d' % (child.state, child.path_cost))result = recursive_dls(child, dst_state, limit - 1)if result == "cutoff":cutoff_occurred = Trueprint('search failure, child state: %s parent state: %s limit cutoff' %(child.state, child.parent.state))elif result != "failure":print('search success')return resultif cutoff_occurred:return "cutoff"else:return "failure"if __name__ == '__main__':main()

测试：从Zerind导航到Urziceni：

input src city
Zerind
input dst city
Urziceni
node state:Zerind parent state:None
this node iscutoff!
node state:Zerind parent state:None
child node:state:Oradea path cost:71
node state:Oradea parent state:Zerind
this node iscutoff!
search failure, child state: Oradea parent state: Zerind limitcutoff
child node:state:Arad path cost:75
node state:Arad parent state:Zerind
this node iscutoff!
search failure, child state: Arad parent state: Zerind limit cutoff
node state:Zerind parent state:None
child node:state:Oradea path cost:71
node state:Oradea parent state:Zerind
child node:state:Sibiu path cost:222
node state:Sibiu parent state:Oradea
this node iscutoff!
search failure, child state: Sibiu parent state: Oradea limitcutoff
search failure, child state: Oradea parent state: Zerind limitcutoff
child node:state:Arad path cost:75
node state:Arad parent state:Zerind
child node:state:Timisoara path cost:193
node state:Timisoara parent state:Arad
this node iscutoff!
search failure, child state: Timisoara parent state: Arad limitcutoff
search failure, child state: Arad parent state: Zerind limit cutoff
node state:Zerind parent state:None
child node:state:Oradea path cost:71
node state:Oradea parent state:Zerind
child node:state:Sibiu path cost:222
node state:Sibiu parent state:Oradea
child node:state:Arad path cost:362
node state:Arad parent state:Sibiu
this node iscutoff!
search failure, child state: Arad parent state: Sibiu limit cutoff
child node:state:Fagaras path cost:321
node state:Fagaras parent state:Sibiu
this node iscutoff!
search failure, child state: Fagaras parent state: Sibiu limitcutoff
child node:state:Rimnicu Vilcea path cost:302
node state:Rimnicu Vilcea parent state:Sibiu
this node iscutoff!
search failure, child state: Rimnicu Vilcea parent state: Sibiu limitcutoff
search failure, child state: Sibiu parent state: Oradea limitcutoff
search failure, child state: Oradea parent state: Zerind limit cutoff
node state:Zerind parent state:None
child node:state:Oradea path cost:71
node state:Oradea parent state:Zerind
child node:state:Sibiu path cost:222
node state:Sibiu parent state:Oradea
child node:state:Arad path cost:362
node state:Arad parent state:Sibiu
child node:state:Timisoara path cost:480
node state:Timisoara parent state:Arad
this node iscutoff!
search failure, child state: Timisoara parent state: Arad limitcutoff
search failure, child state: Arad parent state: Sibiu limit cutoff
child node:state:Fagaras path cost:321
node state:Fagaras parent state:Sibiu
child node:state:Bucharest path cost:532
node state:Bucharest parent state:Fagaras
this node iscutoff!
search failure, child state: Bucharest parent state: Fagaras limitcutoff
search failure, child state: Fagaras parent state: Sibiu limitcutoff
child node:state:Rimnicu Vilcea path cost:302
node state:Rimnicu Vilcea parent state:Sibiu
child node:state:Craiova path cost:448
node state:Craiova parent state:Rimnicu Vilcea
this node iscutoff!
search failure, child state: Craiova parent state: Rimnicu Vilcea limitcutoff
child node:state:Pitesti path cost:399
node state:Pitesti parent state:Rimnicu Vilcea
this node iscutoff!
search failure, child state: Pitesti parent state: Rimnicu Vilcea limitcutoff
search failure, child state: Rimnicu Vilcea parent state: Sibiu limitcutoff
search failure, child state: Sibiu parent state: Oradea limit cutoff
search failure, child state: Oradea parent state: Zerind limit cutoff
node state:Zerind parent state:None
child node:state:Oradea path cost:71
node state:Oradea parent state:Zerind
child node:state:Sibiu path cost:222
node state:Sibiu parent state:Oradea
child node:state:Arad path cost:362
node state:Arad parent state:Sibiu
child node:state:Timisoara path cost:480
node state:Timisoara parent state:Arad
child node:state:Lugoj path cost:591
node state:Lugoj parent state:Timisoara
this node iscutoff!
search failure, child state: Lugoj parent state: Timisoara limitcutoff
search failure, child state: Timisoara parent state: Arad limitcutoff
search failure, child state: Arad parent state: Sibiu limit cutoff
child node:state:Fagaras path cost:321
node state:Fagaras parent state:Sibiu
child node:state:Bucharest path cost:532
node state:Bucharest parent state:Fagaras
child node:state:Pitesti path cost:633
node state:Pitesti parent state:Bucharest
this node iscutoff!
search failure, child state: Pitesti parent state: Bucharest limitcutoff
child node:state:Giurgiu path cost:622
node state:Giurgiu parent state:Bucharest
this node iscutoff!
search failure, child state: Giurgiu parent state: Bucharest limitcutoff
child node:state:Urziceni path cost:617
node state:Urziceni parent state:Bucharest
this node isgoal!
search success
search success
search success
search success
search success
from city: Zerind to city Urziceni searchsuccess
Zerind->Oradea->Sibiu->Fagaras->Bucharest->Urziceni

可以看出，与深度优先搜索算法相比，本算法可以找出更优深度的路径。

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