import heapq
import math


def length_haversine(p1, p2):
    lat1 = p1.lat
    lng1 = p1.lng
    lat2 = p2.lat
    lng2 = p2.lng
    lat1, lng1, lat2, lng2 = map(math.radians, [lat1, lng1, lat2, lng2])
    dlat = lat2 - lat1
    dlng = lng2 - lng1
    a = math.sin(dlat / 2) ** 2 + math.cos(lat1) * math.cos(lat2) * math.sin(dlng / 2) ** 2
    c = 2 * math.asin(math.sqrt(a))

    return 6372797.560856 * c  # return the distance in meters


def path_length(nodes, path):
    """ Calculate the length of a path of node IDs. """
    dist = 0
    for i in range(len(path)-1):
        dist += length_haversine(nodes[path[i]], nodes[path[i+1]])
    return dist


def get_closest_node_id(nodes, source_node):
    """ Search through all nodes and return the id of the node
    that is closest to 'source_node'. """
    min_node = None
    min_value = None

    for node_id, node in nodes.items():
        length = length_haversine(source_node, node)
        if min_node is None or length < min_value:
            min_node = node_id
            min_value = length

    return min_node


def find_shortest_path_dijkstra(nodes, source_id, target_id):
    """ Return the shortest path using Dijkstra's algorithm. """
    # queue contains multiple (walk_dist, (node_0, node_1, ... node_n))-tuples
    # where (node_0, node_1, ... node_n) is a walk to node_n
    # and walk_dist is the total length of the walk in meters
    queue = [(0, (source_id,))]
    visited = set()
    iterations = 0

    while queue:
        iterations += 1
        # consider an unchecked walk
        walk_dist, walk = heapq.heappop(queue)
        walk_end = walk[-1]
        if walk_end == target_id:
            # you have reached your destination
            return walk, iterations
        if walk_end in visited:
            # there exists a shorter walk to walk_end
            continue
        # otherwise this is the shortest walk to walk_end
        visited.add(walk_end)
        # consider all our neighbours
        for neighbour in nodes[walk_end].neighbours:
            if neighbour in visited:
                # there exists a shorter walk to neighbour
                continue
            # otherwise this MIGHT be the shortest walk to neighbour
            # so put it in the queue
            new_dist = walk_dist + length_haversine(nodes[walk_end], neighbour)
            new_walk = walk + (neighbour.id,)
            heapq.heappush(queue, (new_dist, new_walk))
    # no path found
    return None


def find_shortest_path_astar(nodes, source_id, target_id):
    """ Return the shortest path using A*. """
    queue = [(0, (source_id,))]
    visited = set()
    iterations = 0

    while queue:
        walk_dist, walk = heapq.heappop(queue)
        iterations += 1
        walk_end = walk[-1]
        if walk_end == target_id:
            return walk, iterations
        if walk_end in visited:
            continue
        visited.add(walk_end)
        for neighbour in nodes[walk_end].neighbours:
            if neighbour in visited:
                continue
            # simple heuristic
            new_dist = walk_dist + length_haversine(nodes[walk_end], neighbour) + length_haversine(neighbour, nodes[target_id])
            new_walk = walk + (neighbour.id,)
            heapq.heappush(queue, (new_dist, new_walk))
    return None