python 实现A*算法

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：https://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

    

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 failure

function 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:
                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