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

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("已到達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