python 实现A*算法的示例代码

Python  /  管理员 发布于 7年前   174

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

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 mathdef 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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