python 实现A*算法

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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,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

技术分享图片    

其中n是路径上的最后一个节点,gn是从起始节点到n的路径的开销hn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

 

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