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：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

<strong>F（N）= G（N）+ H（n）</strong>

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

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