A*算法 学习记录

从某个国外的网站上看到了一篇介绍路径搜索算法的文章，使用python3编写，非常优秀。我使用的是python2，对代码稍作修改即可实现。作者还用C++和C#编写。

该文章源于一个游戏塔防的策略。点击打开链接

动画演示了不同墙壁下，图上随机生成的粒子点如何经过最短的路径到达目标位置。实际上每个粒子点并不是意义计算如何到达目标，而是当用户改变地图或者改变目标点位置后，重新计算了图上每个位置的最短运动方向。相当于生成了一张表格，粒子落在表格中的哪个区域，就对应项哪个方向运动。

在文章末尾有个链接，详细的介绍了路径搜索的各个思想和步骤。点击打开链接

下面给出python2.7的代码，作者给出的是python3。

首先是implementation.py文件的修改。修改如下

# Sample code from http://www.redblobgames.com/pathfinding/# Copyright 2014 Red Blob Games <[e-mail]>## Feel free to use this code in your own projects, including commercial projects# License: Apache v2.0 <http://www.apache.org/licenses/LICENSE-2.0.html>class SimpleGraph:    def __init__(self):        self.edges = {}        def neighbors(self, id):        return self.edges[id]example_graph = SimpleGraph()example_graph.edges = {    'A': ['B'],    'B': ['A', 'C', 'D'],    'C': ['A'],    'D': ['E', 'A'],    'E': ['B']}import collectionsclass Queue:    def __init__(self):        self.elements = collections.deque()        def empty(self):        return len(self.elements) == 0        def put(self, x):        self.elements.append(x)        def get(self):        return self.elements.popleft()# utility functions for dealing with square gridsdef from_id_width(id, width):    return (id % width, id // width)def draw_tile(graph, id, style, width):    r = "."    if 'number' in style and id in style['number']: r = "%d" % style['number'][id]    if 'point_to' in style and style['point_to'].get(id, None) is not None:        (x1, y1) = id        (x2, y2) = style['point_to'][id]        if x2 == x1 + 1: r = ("\u2192").decode('unicode_escape')        if x2 == x1 - 1: r = ("\u2190").decode('unicode_escape')        if y2 == y1 + 1: r = ("\u2193").decode('unicode_escape')        if y2 == y1 - 1: r = ("\u2191").decode('unicode_escape')    if 'start' in style and id == style['start']: r = "A"    if 'goal' in style and id == style['goal']: r = "Z"    if 'path' in style and id in style['path']: r = "@"    if id in graph.walls: r = "#" * width    return rdef draw_grid(graph, width=1, **style):    for y in range(graph.height):        for x in range(graph.width):            #print("%%-%ds" % width % draw_tile(graph, (x, y), style, width), end="")            print draw_tile(graph, (x, y), style, width),        print# data from main articleDIAGRAM1_WALLS = [from_id_width(id, width=30) for id in [21,22,51,52,81,82,93,94,111,112,123,124,133,134,141,142,153,154,163,164,171,172,173,174,175,183,184,193,194,201,202,203,204,205,213,214,223,224,243,244,253,254,273,274,283,284,303,304,313,314,333,334,343,344,373,374,403,404,433,434]]class SquareGrid:    def __init__(self, width, height):        self.width = width        self.height = height        self.walls = []        def in_bounds(self, id):        (x, y) = id        return 0 <= x < self.width and 0 <= y < self.height        def passable(self, id):        return id not in self.walls        def neighbors(self, id):        (x, y) = id        results = [(x+1, y), (x, y-1), (x-1, y), (x, y+1)]        if (x + y) % 2 == 0: results.reverse() # aesthetics        results = filter(self.in_bounds, results)        results = filter(self.passable, results)        return resultsclass GridWithWeights(SquareGrid):    def __init__(self, width, height):        #super().__init__(width, height)        SquareGrid.__init__(self, width, height)        self.weights = {}        def cost(self, from_node, to_node):        return self.weights.get(to_node, 1)diagram4 = GridWithWeights(10, 10)diagram4.walls = [(1, 7), (1, 8), (2, 7), (2, 8), (3, 7), (3, 8)]diagram4.weights = {loc: 5 for loc in [(3, 4), (3, 5), (4, 1), (4, 2),                                       (4, 3), (4, 4), (4, 5), (4, 6),                                        (4, 7), (4, 8), (5, 1), (5, 2),                                       (5, 3), (5, 4), (5, 5), (5, 6),                                        (5, 7), (5, 8), (6, 2), (6, 3),                                        (6, 4), (6, 5), (6, 6), (6, 7),                                        (7, 3), (7, 4), (7, 5)]}import heapqclass PriorityQueue:    def __init__(self):        self.elements = []        def empty(self):        return len(self.elements) == 0        def put(self, item, priority):        heapq.heappush(self.elements, (priority, item))        def get(self):        return heapq.heappop(self.elements)[1]def dijkstra_search(graph, start, goal):    frontier = PriorityQueue()    frontier.put(start, 0)    came_from = {}    cost_so_far = {}    came_from[start] = None    cost_so_far[start] = 0        while not frontier.empty():        current = frontier.get()                if current == goal:            break                for next in graph.neighbors(current):            new_cost = cost_so_far[current] + graph.cost(current, next)            if next not in cost_so_far or new_cost < cost_so_far[next]:                cost_so_far[next] = new_cost                priority = new_cost                frontier.put(next, priority)                came_from[next] = current        return came_from, cost_so_fardef reconstruct_path(came_from, start, goal):    current = goal    path = [current]    while current != start:        current = came_from[current]        path.append(current)    path.append(start) # optional    path.reverse() # optional    return pathdef heuristic(a, b):    (x1, y1) = a    (x2, y2) = b    return abs(x1 - x2) + abs(y1 - y2)def a_star_search(graph, start, goal):    frontier = PriorityQueue()    frontier.put(start, 0)    came_from = {}    cost_so_far = {}    came_from[start] = None    cost_so_far[start] = 0        while not frontier.empty():        current = frontier.get()                if current == goal:            break                for next in graph.neighbors(current):            new_cost = cost_so_far[current] + graph.cost(current, next)            if next not in cost_so_far or new_cost < cost_so_far[next]:                cost_so_far[next] = new_cost                priority = new_cost + heuristic(goal, next)                frontier.put(next, priority)                came_from[next] = current        return came_from, cost_so_far

主要修改的就是print函数，以及super。其中GridWithWeights中如果使用super(GridWithWeights).__init__(width, height)会出错，我不是很理解，于是用了笨的SquareGrid.__init__(self, width, height)，不会影响结果。

作者在代码中自己实现了一个简单地Queue，，不清楚为何不import python自带的Queue。

作者对于图的理解认为越简单表示越好，于是不定义任何图的class，用元组代替图中的每个节点，或者是边。

尤其要注意的是在作者提供的算法中，python里的字典变量起到了非常大的作用。

class SquareGrid中有一个filter的用法非常棒，作为python入门人员，这个函数值得学习吸收！

作者在画图时把墙壁的width设置为2，我们这儿设置为1即可。

文章最后给出了许多优化建议，以及链接，也都值得细读。