// A* Search Algorithm
1.  Initialize the open list
2.  Initialize the closed list
    put the starting node on the open 
    list (you can leave its f at zero)
3.  while the open list is not empty
    a) find the node with the least f on 
       the open list, call it "q"
    b) pop q off the open list
    c) generate q's 8 successors and set their 
       parents to q
    d) for each successor
        i) if successor is the goal, stop search
        ii) else, compute both g and h for successor
          successor.g = q.g + distance between 
                              successor and q
          successor.h = distance from goal to 
          successor (This can be done using many 
          ways, we will discuss three heuristics- 
          Manhattan, Diagonal and Euclidean 
          Heuristics)
          successor.f = successor.g + successor.h
        iii) if a node with the same position as 
            successor is in the OPEN list which has a 
           lower f than successor, skip this successor
        iV) if a node with the same position as 
            successor  is in the CLOSED list which has
            a lower f than successor, skip this successor
            otherwise, add  the node to the open list
     end (for loop)
    e) push q on the closed list
    end (while loop)

from collections import defaultdict
H_dist ={}
def aStarAlgo(start_node, stop_node):
    open_set = set(start_node)
    closed_set = set()
    g = {}               #store distance from starting node
    parents = {}         # parents contains an adjacency map of all nodes
    #distance of starting node from itself is zero
    g[start_node] = 0

#start_node is root node i.e it has no parent nodes
#so start_node is set to its own parent node

parents[start_node] = start_node
while len(open_set) > 0:
    n = None
    #node with lowest f() is found
    for v in open_set:
        if n == None or g[v] + heuristic(v) < g[n] + heuristic(n):
            n = v
    if n == stop_node or Graph_nodes[n] == None:
        pass
    else:
        for (m, weight) in get_neighbors(n):
            #nodes 'm' not in first and last set are added to first
            #n is set its parent
            if m not in open_set and m not in closed_set:
                open_set.add(m)
                parents[m] = n
                g[m] = g[n] + weight
            #for each node m,compare its distance from start i.e g(m) to the
            #from start through n node
            else:
                if g[m] > g[n] + weight:
                    #update g(m)
                    g[m] = g[n] + weight
                    #change parent of m to n
                    parents[m] = n
                    #if m in closed set,remove and add to open
                    if m in closed_set:
                        closed_set.remove(m)
                        open_set.add(m)
    if n == None:
        print('Path does not exist!')
        return None
        
# if the current node is the stop_node
# then we begin reconstructin the path from it to the start_node

    if n == stop_node:
        path = []
        while parents[n] != n:
            path.append(n)
            n = parents[n]
        path.append(start_node)
        path.reverse()
        print('Path found: {}'.format(path))
        return path
    # remove n from the open_list, and add it to closed_list
    # because all of his neighbors were inspected
    open_set.remove(n)
    closed_set.add(n)
print('Path does not exist!')
return None

#define fuction to return neighbor and its distance
#from the passed node
def get_neighbors(v):
    if v in Graph_nodes:
        return Graph_nodes[v]
    else:
        return None
def heuristic(n):
    return H_dist[n]
          
'''Graph_nodes = {
    'A': [('B', 6), ('F', 3)],
    'B': [('A', 6), ('C', 3), ('D', 2)],
    'C': [('B', 3), ('D', 1), ('E', 5)],
    'D': [('B', 2), ('C', 1), ('E', 8)],
    'E': [('C', 5), ('D', 8), ('I', 5), ('J', 5)],
    'F': [('A', 3), ('G', 1), ('H', 7)],
    'G': [('F', 1), ('I', 3)],
    'H': [('F', 7), ('I', 2)],
    'I': [('E', 5), ('G', 3), ('H', 2), ('J', 3)],
}
graph = defaultdict(list)
n,e = map(int,input().split())
for i in range(e):
    u,v,cost = map(str,input().split())
    t=(v,float(cost))
    graph[u].append(t)
    t1=(u,float(cost))
    graph[v].append(t1)
for i in range(n):
    node,h=map(str,input().split())
    H_dist[node]=float(h)
print(H_dist)
Graph_nodes=graph
print(graph)
aStarAlgo('S', 'G')