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python实现A*寻路算法

A* 算法简介

A* 算法需要维护两个数据结构：OPEN 集和 CLOSED 集。OPEN 集包含所有已搜索到的待检测节点。初始状态，OPEN集仅包含一个元素：开始节点。CLOSED集包含已检测的节点。初始状态，CLOSED集为空。每个节点还包含一个指向父节点的指针，以确定追踪关系。

A* 算法会给每个搜索到的节点计算一个G+H 的和值F：

F = G + H
G：是从开始节点到当前节点的移动量。假设开始节点到相邻节点的移动量为1，该值会随着离开始点越来越远而增大。
H：是从当前节点到目标节点的移动量估算值。
- 如果允许向4邻域的移动，使用曼哈顿距离。
- 如果允许向8邻域的移动，使用对角线距离。

算法有一个主循环，重复下面步骤直到到达目标节点：
1 每次从OPEN集中取一个最优节点n（即F值最小的节点）来检测。
2 将节点n从OPEN集中移除，然后添加到CLOSED集中。
3 如果n是目标节点，那么算法结束。
4 否则尝试添加节点n的所有邻节点n'。

邻节点在CLOSED集中，表示它已被检测过，则无需再添加。
邻节点在OPEN集中：
- 如果重新计算的G值比邻节点保存的G值更小，则需要更新这个邻节点的G值和F值，以及父节点；
- 否则不做操作
否则将该邻节点加入OPEN集，设置其父节点为n，并设置它的G值和F值。

有一点需要注意，如果开始节点到目标节点实际是不连通的，即无法从开始节点移动到目标节点，那算法在第1步判断获取到的节点n为空，就会退出

关键代码介绍

保存基本信息的地图类

地图类用于随机生成一个供寻路算法工作的基础地图信息

先创建一个map类，初始化参数设置地图的长度和宽度，并设置保存地图信息的二维数据map的值为0，值为0表示能移动到该节点。

class Map():
	def __init__(self, width, height):
		self.width = width
		self.height = height
		self.map = [[0 for x in range(self.width)] for y in range(self.height)]

在map类中添加一个创建不能通过节点的函数，节点值为1表示不能移动到该节点。

	def createBlock(self, block_num):
		for i in range(block_num):
			x, y = (randint(0, self.width-1), randint(0, self.height-1))
			self.map[y][x] = 1

在map类中添加一个显示地图的函数，可以看到，这边只是简单的打印出所有节点的值，值为0或1的意思上面已经说明，在后面显示寻路算法结果时，会使用到值2，表示一条从开始节点到目标节点的路径。

	def showMap(self):
		print("+" * (3 * self.width + 2))
		for row in self.map:
			s = '+'
			for entry in row:
				s += ' ' + str(entry) + ' '
			s += '+'
			print(s)
		print("+" * (3 * self.width + 2))

添加一个随机获取可移动节点的函数

	def generatePos(self, rangeX, rangeY):
		x, y = (randint(rangeX[0], rangeX[1]), randint(rangeY[0], rangeY[1]))
		while self.map[y][x] == 1:
			x, y = (randint(rangeX[0], rangeX[1]), randint(rangeY[0], rangeY[1]))
		return (x , y)

搜索到的节点类

每一个搜索到将到添加到OPEN集的节点，都会创建一个下面的节点类，保存有entry的位置信息（x，y），计算得到的G值和F值，和该节点的父节点（pre_entry）。

class SearchEntry():
	def __init__(self, x, y, g_cost, f_cost=0, pre_entry=None):
		self.x = x
		self.y = y
		# cost move form start entry to this entry
		self.g_cost = g_cost
		self.f_cost = f_cost
		self.pre_entry = pre_entry
	
	def getPos(self):
		return (self.x, self.y)

算法主函数介绍

下面就是上面算法主循环介绍的代码实现，OPEN集和CLOSED集的数据结构使用了字典，在一般情况下，查找，添加和删除节点的时间复杂度为O(1), 遍历的时间复杂度为O(n), n为字典中对象数目。

def AStarSearch(map, source, dest):
	...
	openlist = {}
	closedlist = {}
	location = SearchEntry(source[0], source[1], 0.0)
	dest = SearchEntry(dest[0], dest[1], 0.0)
	openlist[source] = location
	while True:
		location = getFastPosition(openlist)
		if location is None:
			# not found valid path
			print("can't find valid path")
			break;
		
		if location.x == dest.x and location.y == dest.y:
			break
		
		closedlist[location.getPos()] = location
		openlist.pop(location.getPos())
		addAdjacentPositions(map, location, dest, openlist, closedlist)
	
	#mark the found path at the map
	while location is not None:
		map.map[location.y][location.x] = 2
		location = location.pre_entry

我们按照算法主循环的实现来一个个讲解用到的函数。
下面函数就是从OPEN集中获取一个F值最小的节点，如果OPEN集会空，则返回None。

	# find a least cost position in openlist, return None if openlist is empty
	def getFastPosition(openlist):
		fast = None
		for entry in openlist.values():
			if fast is None:
				fast = entry
			elif fast.f_cost > entry.f_cost:
				fast = entry
		return fast

addAdjacentPositions 函数对应算法主函数循环介绍中的尝试添加节点n的所有邻节点n'。

	# add available adjacent positions
	def addAdjacentPositions(map, location, dest, openlist, closedlist):
		poslist = getPositions(map, location)
		for pos in poslist:
			# if position is already in closedlist, do nothing
			if isInList(closedlist, pos) is None:
				findEntry = isInList(openlist, pos)
				h_cost = calHeuristic(pos, dest)
				g_cost = location.g_cost + getMoveCost(location, pos)
				if findEntry is None :
					# if position is not in openlist, add it to openlist
					openlist[pos] = SearchEntry(pos[0], pos[1], g_cost, g_cost+h_cost, location)
				elif findEntry.g_cost > g_cost:
					# if position is in openlist and cost is larger than current one,
					# then update cost and previous position
					findEntry.g_cost = g_cost
					findEntry.f_cost = g_cost + h_cost
					findEntry.pre_entry = location

getPositions 函数获取到所有能够移动的节点，这里提供了2种移动的方式：

允许上，下，左，右 4邻域的移动
允许上，下，左，右，左上，右上，左下，右下 8邻域的移动

	def getNewPosition(map, locatioin, offset):
		x,y = (location.x + offset[0], location.y + offset[1])
		if x  0 or x >= map.width or y  0 or y >= map.height or map.map[y][x] == 1:
			return None
		return (x, y)
		
	def getPositions(map, location):
		# use four ways or eight ways to move
		offsets = [(-1,0), (0, -1), (1, 0), (0, 1)]
		#offsets = [(-1,0), (0, -1), (1, 0), (0, 1), (-1,-1), (1, -1), (-1, 1), (1, 1)]
		poslist = []
		for offset in offsets:
			pos = getNewPosition(map, location, offset)
			if pos is not None:			
				poslist.append(pos)
		return poslist

isInList 函数判断节点是否在OPEN集或CLOSED集中

	# check if the position is in list
	def isInList(list, pos):
		if pos in list:
			return list[pos]
		return None

calHeuristic 函数简单得使用了曼哈顿距离，这个后续可以进行优化。
getMoveCost 函数根据是否是斜向移动来计算消耗（斜向就是2的开根号，约等于1.4）

	# imporve the heuristic distance more precisely in future
	def calHeuristic(pos, dest):
		return abs(dest.x - pos[0]) + abs(dest.y - pos[1])
		
	def getMoveCost(location, pos):
		if location.x != pos[0] and location.y != pos[1]:
			return 1.4
		else:
			return 1

代码的初始化

可以调整地图的长度，宽度和不可移动节点的数目。
可以调整开始节点和目标节点的取值范围。

WIDTH = 10
HEIGHT = 10
BLOCK_NUM = 15
map = Map(WIDTH, HEIGHT)
map.createBlock(BLOCK_NUM)
map.showMap()

source = map.generatePos((0,WIDTH//3),(0,HEIGHT//3))
dest = map.generatePos((WIDTH//2,WIDTH-1),(HEIGHT//2,HEIGHT-1))
print("source:", source)
print("dest:", dest)
AStarSearch(map, source, dest)
map.showMap()

执行的效果图如下，第一个表示随机生成的地图，值为1的节点表示不能移动到该节点。
第二个图中值为2的节点表示找到的路径。

完整代码

使用python3.7编译

from random import randint

class SearchEntry():
	def __init__(self, x, y, g_cost, f_cost=0, pre_entry=None):
		self.x = x
		self.y = y
		# cost move form start entry to this entry
		self.g_cost = g_cost
		self.f_cost = f_cost
		self.pre_entry = pre_entry
	
	def getPos(self):
		return (self.x, self.y)

class Map():
	def __init__(self, width, height):
		self.width = width
		self.height = height
		self.map = [[0 for x in range(self.width)] for y in range(self.height)]
	
	def createBlock(self, block_num):
		for i in range(block_num):
			x, y = (randint(0, self.width-1), randint(0, self.height-1))
			self.map[y][x] = 1
	
	def generatePos(self, rangeX, rangeY):
		x, y = (randint(rangeX[0], rangeX[1]), randint(rangeY[0], rangeY[1]))
		while self.map[y][x] == 1:
			x, y = (randint(rangeX[0], rangeX[1]), randint(rangeY[0], rangeY[1]))
		return (x , y)

	def showMap(self):
		print("+" * (3 * self.width + 2))

		for row in self.map:
			s = '+'
			for entry in row:
				s += ' ' + str(entry) + ' '
			s += '+'
			print(s)

		print("+" * (3 * self.width + 2))
	

def AStarSearch(map, source, dest):
	def getNewPosition(map, locatioin, offset):
		x,y = (location.x + offset[0], location.y + offset[1])
		if x  0 or x >= map.width or y  0 or y >= map.height or map.map[y][x] == 1:
			return None
		return (x, y)
		
	def getPositions(map, location):
		# use four ways or eight ways to move
		offsets = [(-1,0), (0, -1), (1, 0), (0, 1)]
		#offsets = [(-1,0), (0, -1), (1, 0), (0, 1), (-1,-1), (1, -1), (-1, 1), (1, 1)]
		poslist = []
		for offset in offsets:
			pos = getNewPosition(map, location, offset)
			if pos is not None:			
				poslist.append(pos)
		return poslist
	
	# imporve the heuristic distance more precisely in future
	def calHeuristic(pos, dest):
		return abs(dest.x - pos[0]) + abs(dest.y - pos[1])
		
	def getMoveCost(location, pos):
		if location.x != pos[0] and location.y != pos[1]:
			return 1.4
		else:
			return 1

	# check if the position is in list
	def isInList(list, pos):
		if pos in list:
			return list[pos]
		return None
	
	# add available adjacent positions
	def addAdjacentPositions(map, location, dest, openlist, closedlist):
		poslist = getPositions(map, location)
		for pos in poslist:
			# if position is already in closedlist, do nothing
			if isInList(closedlist, pos) is None:
				findEntry = isInList(openlist, pos)
				h_cost = calHeuristic(pos, dest)
				g_cost = location.g_cost + getMoveCost(location, pos)
				if findEntry is None :
					# if position is not in openlist, add it to openlist
					openlist[pos] = SearchEntry(pos[0], pos[1], g_cost, g_cost+h_cost, location)
				elif findEntry.g_cost > g_cost:
					# if position is in openlist and cost is larger than current one,
					# then update cost and previous position
					findEntry.g_cost = g_cost
					findEntry.f_cost = g_cost + h_cost
					findEntry.pre_entry = location
	
	# find a least cost position in openlist, return None if openlist is empty
	def getFastPosition(openlist):
		fast = None
		for entry in openlist.values():
			if fast is None:
				fast = entry
			elif fast.f_cost > entry.f_cost:
				fast = entry
		return fast

	openlist = {}
	closedlist = {}
	location = SearchEntry(source[0], source[1], 0.0)
	dest = SearchEntry(dest[0], dest[1], 0.0)
	openlist[source] = location
	while True:
		location = getFastPosition(openlist)
		if location is None:
			# not found valid path
			print("can't find valid path")
			break;
		
		if location.x == dest.x and location.y == dest.y:
			break
		
		closedlist[location.getPos()] = location
		openlist.pop(location.getPos())
		addAdjacentPositions(map, location, dest, openlist, closedlist)
		
	#mark the found path at the map
	while location is not None:
		map.map[location.y][location.x] = 2
		location = location.pre_entry	

	
WIDTH = 10
HEIGHT = 10
BLOCK_NUM = 15
map = Map(WIDTH, HEIGHT)
map.createBlock(BLOCK_NUM)
map.showMap()

source = map.generatePos((0,WIDTH//3),(0,HEIGHT//3))
dest = map.generatePos((WIDTH//2,WIDTH-1),(HEIGHT//2,HEIGHT-1))
print("source:", source)
print("dest:", dest)
AStarSearch(map, source, dest)
map.showMap()

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