Romanian Map

import math
import random
import bisect

"""
Defining a class for the problem structure that we will solve with a search.
The Problem class is an abstract class from which we make inheritance to define the basic
characteristics of every problem we want to solve
"""


class Problem:
    def __init__(self, initial, goal=None):
        self.initial = initial
        self.goal = goal

    def successor(self, state):
        """Given a state, return a dictionary of {action : state} pairs reachable
        from this state. If there are many successors, consider an iterator
        that yields the successors one at a time, rather than building them
        all at once.

        :param state: given state
        :return:  dictionary of {action : state} pairs reachable
                  from this state
        :rtype: dict
        """
        raise NotImplementedError

    def actions(self, state):
        """Given a state, return a list of all actions possible
        from that state

        :param state: given state
        :return: list of actions
        :rtype: list
        """
        raise NotImplementedError

    def result(self, state, action):
        """Given a state and action, return the resulting state

        :param state: given state
        :param action: given action
        :return: resulting state
        """
        raise NotImplementedError

    def goal_test(self, state):
        """Return True if the state is a goal. The default method compares
        the state to self.goal, as specified in the constructor. Implement
        this method if checking against a single self.goal is not enough.

        :param state: given state
        :return: is the given state a goal state
        :rtype: bool
        """
        return state == self.goal

    def path_cost(self, c, state1, action, state2):
        """Return the cost of a solution path that arrives at state2 from state1
        via action, assuming cost c to get up to state1. If the problem is such
        that the path doesn't matter, this function will only look at state2.
        If the path does matter, it will consider c and maybe state1 and action.
        The default method costs 1 for every step in the path.

        :param c: cost of the path to get up to state1
        :param state1: given current state
        :param action: action that needs to be done
        :param state2: state to arrive to
        :return: cost of the path after executing the action
        :rtype: float
        """
        return c + 1

    def value(self):
        """For optimization problems, each state has a value.
        Hill-climbing and related algorithms try to maximize this value.

        :return: state value
        :rtype: float
        """
        raise NotImplementedError


"""
Definition of the class for node structure of the search.
The class Node is not inherited
"""


class Node:
    def __init__(self, state, parent=None, action=None, path_cost=0):
        """Create node from the search tree,  obtained from the parent by
        taking the action

        :param state: current state
        :param parent: parent state
        :param action: action
        :param path_cost: path cost
        """
        self.state = state
        self.parent = parent
        self.action = action
        self.path_cost = path_cost
        self.depth = 0  # search depth
        if parent:
            self.depth = parent.depth + 1

    def __repr__(self):
        return "<Node %s>" % (self.state,)

    def __lt__(self, node):
        return self.state < node.state

    def expand(self, problem):
        """List the nodes reachable in one step from this node.

        :param problem: given problem
        :return: list of available nodes in one step
        :rtype: list(Node)
        """
        return [self.child_node(problem, action)
                for action in problem.actions(self.state)]

    def child_node(self, problem, action):
        """Return a child node from this node

        :param problem: given problem
        :param action: given action
        :return: available node  according to the given action
        :rtype: Node
        """
        next_state = problem.result(self.state, action)
        return Node(next_state, self, action,
                    problem.path_cost(self.path_cost, self.state,
                                      action, next_state))

    def solution(self):
        """Return the sequence of actions to go from the root to this node.

        :return: sequence of actions
        :rtype: list
        """
        return [node.action for node in self.path()[1:]]

    def solve(self):
        """Return the sequence of states to go from the root to this node.

        :return: list of states
        :rtype: list
        """
        return [node.state for node in self.path()[0:]]

    def path(self):
        """Return a list of nodes forming the path from the root to this node.

        :return: list of states from the path
        :rtype: list(Node)
        """
        x, result = self, []
        while x:
            result.append(x)
            x = x.parent
        result.reverse()
        return result

    """We want the queue of nodes at breadth_first_search or
    astar_search to not contain states-duplicates, so the nodes that
    contain the same condition we treat as the same. [Problem: this can
    not be desirable in other situations.]"""

    def __eq__(self, other):
        return isinstance(other, Node) and self.state == other.state

    def __hash__(self):
        return hash(self.state)


"""
Definitions of helper structures for storing the list of generated, but not checked nodes
"""


class Queue:
    """Queue is an abstract class/interface. There are three types:
        Stack(): Last In First Out Queue (stack).
        FIFOQueue(): First In First Out Queue.
        PriorityQueue(order, f): QQueue in sorted order (default min-first).
    """

    def __init__(self):
        raise NotImplementedError

    def append(self, item):
        """Adds the item into the queue

        :param item: given element
        :return: None
        """
        raise NotImplementedError

    def extend(self, items):
        """Adds the items into the queue

        :param items: given elements
        :return: None
        """
        raise NotImplementedError

    def pop(self):
        """Returns the first element of the queue

        :return: first element
        """
        raise NotImplementedError

    def __len__(self):
        """Returns the number of elements in the queue

        :return: number of elements in the queue
        :rtype: int
        """
        raise NotImplementedError

    def __contains__(self, item):
        """Check if the queue contains the element item

        :param item: given element
        :return: whether the queue contains the item
        :rtype: bool
        """
        raise NotImplementedError


class Stack(Queue):
    """Last-In-First-Out Queue."""

    def __init__(self):
        self.data = []

    def append(self, item):
        self.data.append(item)

    def extend(self, items):
        self.data.extend(items)

    def pop(self):
        return self.data.pop()

    def __len__(self):
        return len(self.data)

    def __contains__(self, item):
        return item in self.data


class FIFOQueue(Queue):
    """First-In-First-Out Queue."""

    def __init__(self):
        self.data = []

    def append(self, item):
        self.data.append(item)

    def extend(self, items):
        self.data.extend(items)

    def pop(self):
        return self.data.pop(0)

    def __len__(self):
        return len(self.data)

    def __contains__(self, item):
        return item in self.data


class PriorityQueue(Queue):
    """A queue in which the minimum (or maximum) element is returned first
     (as determined by f and order). This structure is used in
     informed search"""

    def __init__(self, order=min, f=lambda x: x):
        """
        :param order: sorting function, if order is min, returns the element
                      with minimal f (x); if the order is max, then returns the
                      element with maximum f (x).
        :param f: function f(x)
        """
        assert order in [min, max]
        self.data = []
        self.order = order
        self.f = f

    def append(self, item):
        bisect.insort_right(self.data, (self.f(item), item))

    def extend(self, items):
        for item in items:
            bisect.insort_right(self.data, (self.f(item), item))

    def pop(self):
        if self.order == min:
            return self.data.pop(0)[1]
        return self.data.pop()[1]

    def __len__(self):
        return len(self.data)

    def __contains__(self, item):
        return any(item == pair[1] for pair in self.data)

    def __getitem__(self, key):
        for _, item in self.data:
            if item == key:
                return item

    def __delitem__(self, key):
        for i, (value, item) in enumerate(self.data):
            if item == key:
                self.data.pop(i)


def distance(a, b):
    """The distance between two (x, y) points."""
    return math.hypot((a[0] - b[0]), (a[1] - b[1]))


class Graph:
    """A graph connects nodes (verticies) by edges (links).  Each edge can also
    have a length associated with it.  The constructor call is something like:
        g = Graph({'A': {'B': 1, 'C': 2})
    this makes a graph with 3 nodes, A, B, and C, with an edge of length 1 from
    A to B,  and an edge of length 2 from A to C.  You can also do:
        g = Graph({'A': {'B': 1, 'C': 2}, directed=False)
    This makes an undirected graph, so inverse links are also added. The graph
    stays undirected; if you add more links with g.connect('B', 'C', 3), then
    inverse link is also added.  You can use g.nodes() to get a list of nodes,
    g.get('A') to get a dict of links out of A, and g.get('A', 'B') to get the
    length of the link from A to B.  'Lengths' can actually be any object at
    all, and nodes can be any hashable object."""

    def __init__(self, dictionary=None, directed=True):
        self.dict = dictionary or {}
        self.directed = directed
        if not directed:
            self.make_undirected()

    def make_undirected(self):
        """Make a digraph into an undirected graph by adding symmetric edges."""
        for a in list(self.dict.keys()):
            for (b, dist) in self.dict[a].items():
                self.connect1(b, a, dist)

    def connect(self, node_a, node_b, distance_val=1):
        """Add a link from node_a and node_b of given distance_val, and also add the inverse
        link if the graph is undirected."""
        self.connect1(node_a, node_b, distance_val)
        if not self.directed:
            self.connect1(node_b, node_a, distance_val)

    def connect1(self, node_a, node_b, distance_val):
        """Add a link from node_a to node_b of given distance_val, in one direction only."""
        self.dict.setdefault(node_a, {})[node_b] = distance_val

    def get(self, a, b=None):
        """Return a link distance or a dict of {node: distance} entries.
        .get(a,b) returns the distance or None;
        .get(a) returns a dict of {node: distance} entries, possibly {}."""
        links = self.dict.setdefault(a, {})
        if b is None:
            return links
        else:
            return links.get(b)

    def nodes(self):
        """Return a list of nodes in the graph."""
        return list(self.dict.keys())


def UndirectedGraph(dictionary=None):
    """Build a Graph where every edge (including future ones) goes both ways."""
    return Graph(dictionary=dictionary, directed=False)


def RandomGraph(nodes=list(range(10)), min_links=2, width=400, height=300,
                curvature=lambda: random.uniform(1.1, 1.5)):
    """Construct a random graph, with the specified nodes, and random links.
    The nodes are laid out randomly on a (width x height) rectangle.
    Then each node is connected to the min_links nearest neighbors.
    Because inverse links are added, some nodes will have more connections.
    The distance between nodes is the hypotenuse times curvature(),
    where curvature() defaults to a random number between 1.1 and 1.5."""
    g = UndirectedGraph()
    g.locations = {}
    # Build the cities
    for node in nodes:
        g.locations[node] = (random.randrange(width), random.randrange(height))
    # Build roads from each city to at least min_links nearest neighbors.
    for i in range(min_links):
        for node in nodes:
            if len(g.get(node)) < min_links:
                here = g.locations[node]

                def distance_to_node(n):
                    if n is node or g.get(node, n):
                        return math.inf
                    return distance(g.locations[n], here)

                neighbor = nodes.index(min(nodes, key=distance_to_node))
                d = distance(g.locations[neighbor], here) * curvature()
                g.connect(node, neighbor, int(d))
    return g


class GraphProblem(Problem):
    """The problem of searching a graph from one node to another."""

    def __init__(self, initial, goal, graph):
        super().__init__(initial, goal)
        self.graph = graph

    def actions(self, state):
        """The actions at a graph node are just its neighbors."""
        return list(self.graph.get(state).keys())

    def result(self, state, action):
        """The result of going to a neighbor is just that neighbor."""
        return action

    def path_cost(self, c, state1, action, state2):
        return c + (self.graph.get(state1, state2) or math.inf)

    def h(self, node):
        """h function is straight-line distance from a node's state to goal."""
        locs = getattr(self.graph, 'locations', None)
        if locs:
            return int(distance(locs[node.state], locs[self.goal]))
        else:
            return math.inf


"""
Uninformed tree search.
Within the tree we do not solve the loops.
"""


def tree_search(problem, fringe):
    """Search through the successors of a problem to find a goal.

    :param problem: given problem
    :param fringe:  empty queue
    :return: Node
    """
    fringe.append(Node(problem.initial))
    while fringe:
        node = fringe.pop()
        print(node.state)
        if problem.goal_test(node.state):
            return node
        fringe.extend(node.expand(problem))
    return None


def breadth_first_tree_search(problem):
    """Search the shallowest nodes in the search tree first.

    :param problem: given problem
    :return: Node
    """
    return tree_search(problem, FIFOQueue())


def depth_first_tree_search(problem):
    """Search the deepest nodes in the search tree first.

    :param problem: given problem
    :return: Node
    """
    return tree_search(problem, Stack())


"""
Uninformed graph search
The main difference is that here we do not allow loops,
i.e. repetition of states
"""


def graph_search(problem, fringe):
    """Search through the successors of a problem to find a goal.
     If two paths reach a state, only use the best one.

    :param problem: given problem
    :param fringe: empty queue
    :return: Node
    """
    closed = set()
    fringe.append(Node(problem.initial))
    while fringe:
        node = fringe.pop()
        if problem.goal_test(node.state):
            return node
        if node.state not in closed:
            closed.add(node.state)
            fringe.extend(node.expand(problem))
    return None


def breadth_first_graph_search(problem):
    """Search the shallowest nodes in the search tree first.

    :param problem: given problem
    :return: Node
    """
    return graph_search(problem, FIFOQueue())


def depth_first_graph_search(problem):
    """Search the deepest nodes in the search tree first.

    :param problem: given problem
    :return: Node
    """
    return graph_search(problem, Stack())


def depth_limited_search(problem, limit=50):
    def recursive_dls(node, problem, limit):
        """Helper function for depth limited"""
        cutoff_occurred = False
        if problem.goal_test(node.state):
            return node
        elif node.depth == limit:
            return 'cutoff'
        else:
            for successor in node.expand(problem):
                result = recursive_dls(successor, problem, limit)
                if result == 'cutoff':
                    cutoff_occurred = True
                elif result is not None:
                    return result
        if cutoff_occurred:
            return 'cutoff'
        return None

    return recursive_dls(Node(problem.initial), problem, limit)


def iterative_deepening_search(problem):
    for depth in range(sys.maxsize):
        result = depth_limited_search(problem, depth)
        if result is not 'cutoff':
            return result


def uniform_cost_search(problem):
    """Search the nodes in the search tree with lowest cost first."""
    return graph_search(problem, PriorityQueue(min, lambda a: a.path_cost))

def memoize(fn, slot=None):
    """ Запамети ја пресметаната вредност за која била листа од
    аргументи. Ако е специфициран slot, зачувај го резултатот во
    тој slot на првиот аргумент. Ако slot е None, зачувај ги
    резултатите во речник.

    :param fn: зададена функција
    :param slot: име на атрибут во кој се чуваат резултатите од функцијата
    :return: функција со модификација за зачувување на резултатите
    """
    if slot:
        def memoized_fn(obj, *args):
            if hasattr(obj, slot):
                return getattr(obj, slot)
            else:
                val = fn(obj, *args)
                setattr(obj, slot, val)
                return val
    else:
        def memoized_fn(*args):
            if args not in memoized_fn.cache:
                memoized_fn.cache[args] = fn(*args)
            return memoized_fn.cache[args]

        memoized_fn.cache = {}
    return memoized_fn


def best_first_graph_search(problem, f):
    """Пребарувај низ следбениците на даден проблем за да најдеш цел. Користи
     функција за евалуација за да се одлучи кој е сосед најмногу ветува и
     потоа да се истражи. Ако до дадена состојба стигнат два пата, употреби
     го најдобриот пат.

    :param problem: даден проблем
    :param f: дадена функција за евристика
    :return: Node or None
    """
    f = memoize(f, 'f')
    node = Node(problem.initial)
    if problem.goal_test(node.state):
        return node
    frontier = PriorityQueue(min, f)
    frontier.append(node)
    explored = set()
    while frontier:
        node = frontier.pop()
        if problem.goal_test(node.state):
            return node
        explored.add(node.state)
        for child in node.expand(problem):
            if child.state not in explored and child not in frontier:
                frontier.append(child)
            elif child in frontier:
                incumbent = frontier[child]
                if f(child) < f(incumbent):
                    del frontier[incumbent]
                    frontier.append(child)
    return None


def greedy_best_first_graph_search(problem, h=None):
    """ Greedy best-first пребарување се остварува ако се специфицира дека f(n) = h(n).

    :param problem: даден проблем
    :param h: дадена функција за евристика
    :return: Node or None
    """
    h = memoize(h or problem.h, 'h')
    return best_first_graph_search(problem, h)


def astar_search(problem, h=None):
    """ A* пребарување е best-first graph пребарување каде f(n) = g(n) + h(n).

    :param problem: даден проблем
    :param h: дадена функција за евристика
    :return: Node or None
    """
    h = memoize(h or problem.h, 'h')
    return best_first_graph_search(problem, lambda n: n.path_cost + h(n))


def recursive_best_first_search(problem, h=None):
    """Recursive best first search - ја ограничува рекурзијата
    преку следење на f-вредноста на најдобриот алтернативен пат
    од било кој јазел предок (еден чекор гледање нанапред).

    :param problem: даден проблем
    :param h: дадена функција за евристика
    :return: Node or None
    """
    h = memoize(h or problem.h, 'h')

    def RBFS(problem, node, flimit):
        if problem.goal_test(node.state):
            return node, 0  # (втората вредност е неважна)
        successors = node.expand(problem)
        if len(successors) == 0:
            return None, infinity
        for s in successors:
            s.f = max(s.path_cost + h(s), node.f)
        while True:
            # Подреди ги според најниската f вредност
            successors.sort(key=lambda x: x.f)
            best = successors[0]
            if best.f > flimit:
                return None, best.f
            if len(successors) > 1:
                alternative = successors[1].f
            else:
                alternative = infinity
            result, best.f = RBFS(problem, best, min(flimit, alternative))
            if result is not None:
                return result, best.f

    node = Node(problem.initial)
    node.f = h(node)
    result, bestf = RBFS(problem, node, infinity)
    return result

romania_map = UndirectedGraph(dict(
    Arad=dict(Zerind=25, Sibiu=240, Timisoara=118),
    Bucharest=dict(Urziceni=85, Pitesti=101, Giurgiu=90, Fagaras=211),
    Craiova=dict(Drobeta=120, Rimnicu=146, Pitesti=138),
    Drobeta=dict(Mehadia=75),
    Eforie=dict(Hirsova=86),
    Fagaras=dict(Sibiu=99),
    Hirsova=dict(Urziceni=98),
    Iasi=dict(Vaslui=92, Neamt=87),
    Lugoj=dict(Timisoara=111, Mehadia=70),
    Oradea=dict(Zerind=31, Sibiu=21),
    Pitesti=dict(Rimnicu=97),
    Rimnicu=dict(Sibiu=80),
    Urziceni=dict(Vaslui=142)))

romania_map.locations = dict(
    Arad=(91, 492), Bucharest=(400, 327), Craiova=(253, 288),
    Drobeta=(165, 299), Eforie=(562, 293), Fagaras=(305, 449),
    Giurgiu=(375, 270), Hirsova=(534, 350), Iasi=(473, 506),
    Lugoj=(165, 379), Mehadia=(168, 339), Neamt=(406, 537),
    Oradea=(131, 571), Pitesti=(320, 368), Rimnicu=(233, 410),
    Sibiu=(207, 457), Timisoara=(94, 410), Urziceni=(456, 350),
    Vaslui=(509, 444), Zerind=(108, 531))

pocetok = input()
stanica1 = input()
stanica2 = input()
kraj = input()

pat1=GraphProblem(pocetok,stanica1,romania_map)
pat3=GraphProblem(stanica2,kraj,romania_map)

ans1=astar_search(pat1)
#ans2=astar_search(pat2)
ans3=astar_search(pat3)

sol1 = ans1.solve()
#sol2 = ans2.solve()
sol3 = ans3.solve()

sol = sol1 + sol3

#print(sol1)
#print(sol2)
#print(sol3)


cost1=ans1.path_cost
cost2=romania_map.get(stanica1,stanica2)
cost3=ans3.path_cost

print(cost1,cost2,cost3)
cost=cost1+cost2+cost3
print(sol, cost)