python 实现A_算法的示例代码

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python 实现A*算法的示例代码 A*作为最常用的路径搜索算法，值得我们去深刻的研究。路径规划项目。先看一下维基百科给的算法解释：http://en.wikipedia.org/wiki/A*_search_algorithm

A *是最佳优先搜索它通过在解决方案的所有可能路径(目标)中搜索导致成本最小(行进距离最短，时间最短等)的问题来解决问题。 )，并且在这些路径中，它首先考虑那些似乎最快速地引导到解决方案的路径。它是根据加权图制定的：从图的特定节点开始，它构造从该节点开始的路径树，一次一步地扩展路径，直到其一个路径在预定目标节点处结束。

在其主循环的每次迭代中，A *需要确定将其部分路径中的哪些扩展为一个或多个更长的路径。它是基于成本(总重量)的估计仍然到达目标节点。具体而言，A *选择最小化的路径

F(N)= G(N)+ H(n)

其中n是路径上的最后一个节点，g(n)是从起始节点到n的路径的开销，h(n)是一个启发式，用于估计从n到目标的最便宜路径的开销。启发式是特定于问题的。为了找到实际最短路径的算法，启发函数必须是可接受的，这意味着它永远不会高估实际成本到达最近的目标节点。

维基百科给出的伪代码：function A*(start, goal)

// The set of nodes already evaluated

closedSet := {} // The set of currently discovered nodes that are not evaluated yet.

// Initially, only the start node is known.

openSet := {start} // For each node, which node it can most efficiently be reached from.

// If a node can be reached from many nodes, cameFrom will eventually contain the

// most efficient previous step.

cameFrom := an empty map // For each node, the cost of getting from the start node to that node.

gScore := map with default value of Infinity // The cost of going from start to start is zero.

gScore[start] := 0 // For each node, the total cost of getting from the start node to the goal

// by passing by that node. That value is partly known, partly heuristic.

fScore := map with default value of Infinity // For the first node, that value is completely heuristic.

fScore[start] := heuristic_cost_estimate(start, goal) while openSet is not empty

current := the node in openSet having the lowest fScore[] value

if current = goal

return reconstruct_path(cameFrom, current) openSet.Remove(current)

closedSet.Add(current) for each neighbor of current

if neighbor in closedSet

continue // Ignore the neighbor which is already evaluated. if neighbor not in openSet // Discover a new node

openSet.Add(neighbor)

// The distance from start to a neighbor

//the "dist_between" function may vary as per the solution requirements.

tentative_gScore := gScore[current] + dist_between(current, neighbor)

if tentative_gScore >= gScore[neighbor]

continue // This is not a better path. // This path is the best until now. Record it!

cameFrom[neighbor] := current

gScore[neighbor] := tentative_gScore

fScore[neighbor] := gScore[neighbor] + heuristic_cost_estimate(neighbor, goal) return failurefunction reconstruct_path(cameFrom, current)

total_path := {current}

while current in cameFrom.Keys:

current := cameFrom[current]

total_path.append(current)

return total_path下面是UDACITY课程中路径规划项目，结合上面的伪代码，用python 实现A* import math

def shortest_path(M,start,goal):

sx=M.intersections[start][0]

sy=M.intersections[start][1]

gx=M.intersections[goal][0]

gy=M.intersections[goal][1]

h=math.sqrt((sx-gx)*(sx-gx)+(sy-gy)*(sy-gy))

closedSet=set()

openSet=set()

openSet.add(start)

gScore={}

gScore[start]=0

fScore={}

fScore[start]=h

cameFrom={}

sumg=0

NEW=0

BOOL=False

while len(openSet)!=0:

MAX=1000

for new in openSet:

print("new",new)

if fScore[new]MAX=fScore[new]

#print("MAX=",MAX)

NEW=new

current=NEW

print("current=",current)

if current==goal:

return reconstruct_path(cameFrom,current)

openSet.remove(current)

closedSet.add(current)

#dafult=M.roads(current)

for neighbor in M.roads[current]:

BOOL=False

print("key=",neighbor)

a={neighbor}

if len(a&closedSet)>0:

continue

print("key is not in closeSet")

if len(a&openSet)==0:

openSet.add(neighbor)

else:

BOOL=True

x= M.intersections[current][0]

y= M.intersections[current][1]

x1=M.intersections[neighbor][0]

y1=M.intersections[neighbor][1]

g=math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1))

h=math.sqrt((x1-gx)*(x1-gx)+(y1-gy)*(y1-gy))

new_gScore=gScore[current]+g

if BOOL==True:

if new_gScore>=gScore[neighbor]:

continue

print("new_gScore",new_gScore)

cameFrom[neighbor]=current

gScore[neighbor]=new_gScore

fScore[neighbor] = new_gScore+h

print("fScore",neighbor,"is",new_gScore+h)

print("fScore=",new_gScore+h)

print("__________++--------------++_________")

def reconstruct_path(cameFrom,current):

print("已到达lllll")

total_path=[]

total_path.append(current)

for key,value in cameFrom.items():

print("key",key,":","value",value)

while current in cameFrom.keys():

current=cameFrom[current]

total_path.append(current)

total_path=list(reversed(total_path))

return total_path

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