from sys import stdin, argv
import unittest

track_previous = True

class weighted_digraph:
    class __edge(object):
        def __init__(self, to_node, weight):
            self.to_node = to_node
            self.weight = weight

    class __node(object):
        def __init__(self, value):
            self.value = value
            self.edges = []

        def __str__(self):
            result = str(self.value)
            for edge in self.edges:
                result += "->" + str(edge.to_node.value) + \
                    "(" + str(edge.weight) + ")"
            return(result)

        def add_edge(self, new_edge):
            if not self.is_adjacent(new_edge.to_node):
                    self.edges.append(new_edge)

        def remove_edge(self, to_node):
            for edge in self.edges:
                if edge.to_node == to_node:
                    self.edges.remove(edge)

        def is_adjacent(self, node):
            for edge in self.edges:
                if edge.to_node == node:
                    return(True)
            return(False)

    def __init__(self, directed=True):
        self.__nodes = []
        self.__directed = directed

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

    def __str__(self):
        result = ""
        for node in self.__nodes:
            result += str(node) + '\n'
        return(result)

    def __iter__(self): return iter(self.__nodes)

    def find(self, value):
        for node in self:
            if node.value == value:
                return(node)

        return(None)

    def add_nodes(self, nodes):
        for node in nodes:
            self.add_node(node)

    def add_node(self, value):
        if not self.find(value):
            self.__nodes.append(self.__node(value))

    def add_edges(self, edges):
        for edge in edges:
            self.add_edge(edge[0], edge[1], edge[2])

    def add_edge(self, from_value, to_value, weight):
        """
            Add an edge between two values. If the nodes for those values
            aren't already in the graph, add those.
        """
        from_node = self.find(from_value)
        to_node = self.find(to_value)

        if not from_node:
            self.add_node(from_value)
            from_node = self.find(from_value)
        if not to_node:
            self.add_node(to_value)
            to_node = self.find(to_value)

        from_node.add_edge(self.__edge(to_node, weight))
        if not self.__directed:
            to_node.add_edge(self.__edge(from_node, weight))

    def remove_edge(self, from_value, to_value, weight):
        from_node = self.find(from_value)
        to_node = self.find(to_value)

        from_node.remove_edge(to_node)
        if not self.__directed:
            to_node.remove_edge(from_node) 
    
    def are_adjacent(self, value1, value2):
        return(self.find(value1).is_adjacent(self.find(value2)))

    # I have no memory of this place.
    def dijkstra(self, start):
        for n in self.__nodes:
            n.distance = float('inf')
            n.previous = None 

        source = self.find(start)
        source.distance = 0

        todo = {source}
        res = []

        while todo:
            min_dist_node = next(iter(todo))

            for n in todo:
                if n.distance < min_dist_node.distance:
                    min_dist_node = n

            todo.remove(min_dist_node)
            path = [min_dist_node.distance, min_dist_node.value]
            prev = min_dist_node.previous
            while prev:
                path.append(prev.value)
                prev = prev.previous

            res.append(path)

            for e in min_dist_node.edges:
                n = self.find(e.to_node.value)
                new_distance = e.weight + min_dist_node.distance
                if new_distance < n.distance: 
                    n.distance = new_distance
                    n.previous = min_dist_node
                    todo.add(n)

        return res

class test_weighted_digraph(unittest.TestCase):
    def test_empty(self):
        self.assertEqual(len(weighted_digraph()), 0)

    def test_one(self):
        g = weighted_digraph()
        g.add_node(1)
        self.assertEqual(len(g), 1)

    def test_duplicate(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(1)
        self.assertEqual(len(g), 1)

    def test_two(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(2)
        self.assertEqual(len(g), 2)

    def test_edge(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(2)
        g.add_edge(1, 2, 3)
        self.assertEqual(str(g), '1->2(3)\n2\n')

    def test_adding_ints(self):
        g = weighted_digraph()
        g.add_nodes([1, 2])
        g.add_edges([(1, 2, 3), (2, 1, 3)])
        self.assertEqual(str(g), '1->2(3)\n2->1(3)\n')

    def test_adding_strings(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertEqual(str(g), 'Denver->Boston(1971.8)\nBoston->Denver(1971.8)\n')

    def test_are_adjacent(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_arent_adjacent(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston', 'Milano'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertFalse(g.are_adjacent('Denver', 'Milano'))

    def test_arent_adjacent_directed(self):
        g = weighted_digraph()
        g.add_edges([('Denver', 'Boston', 1971.8)])
        self.assertFalse(g.are_adjacent('Denver', 'Milano'))
        self.assertFalse(g.are_adjacent('Boston', 'Denver'))
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_arent_adjacent_undirected(self):
        g = weighted_digraph(False)
        g.add_edges([('Denver', 'Boston', 1971.8)])
        self.assertTrue(g.are_adjacent('Boston', 'Denver'))
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_add_edges_without_nodes(self):
        g = weighted_digraph()
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertEqual(str(g), \
            'Denver->Boston(1971.8)\nBoston->Denver(1971.8)\n')

    def test_dijkstra(self):
        # 
        #     2---1---4
        #    /|\      |\
        #   2 | \     | 6
        #  /  |  \    |  \
        # 1   1   2   3   6
        #  \  |    \  |  /
        #   1 |     \ | 1
        #    \|      \|/
        #     3---5---5
        # 
        
        g = weighted_digraph(False)
        g.add_edges([(1,2,2), (1,3,1), (2,3,1), (2,4,1), \
            (2,5,2), (3,5,5), (4,5,3), (4,6,6), (5,6,1)])
        if not track_previous:
            self.assertEqual(g.dijkstra(1), [[0, 1], [1, 3], [2, 2], \
                [3, 4], [4, 5], [5, 6]])
        else:
            # distance, path...
            self.assertEqual(g.dijkstra(1), [[0, 1], [1, 3, 1], [2, 2, 1], \
                [3, 4, 2, 1], [4, 5, 2, 1], [5, 6, 5, 2, 1]])

if '__main__' == __name__:
    g = weighted_digraph(False)
    file = open(argv[1], "r")
    for line in file:
        a = line.strip().split(" ")
        g.add_edge(a[0], a[1], int(a[2]))
    result = g.dijkstra("Denver")
    for city in result:
        print(city[1], "is", city[0], 'miles from Denver')
        if track_previous:
            for path in city[2:]:
                print("     ", path)

from sys import stdin, argv
import unittest

track_previous = True

class weighted_digraph:
    class __edge(object):
        def __init__(self, to_node, weight):
            self.to_node = to_node
            self.weight = weight

    class __node(object):
        def __init__(self, value):
            self.value = value
            self.edges = []

        def __str__(self):
            result = str(self.value)
            for edge in self.edges:
                result += "->" + str(edge.to_node.value) + \
                    "(" + str(edge.weight) + ")"
            return(result)

        def add_edge(self, new_edge):
            if not self.is_adjacent(new_edge.to_node):
                    self.edges.append(new_edge)

        def remove_edge(self, to_node):
            for edge in self.edges:
                if edge.to_node == to_node:
                    self.edges.remove(edge)

        def is_adjacent(self, node):
            for edge in self.edges:
                if edge.to_node == node:
                    return(True)
            return(False)

    def __init__(self, directed=True):
        self.__nodes = []
        self.__directed = directed

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

    def __str__(self):
        result = ""
        for node in self.__nodes:
            result += str(node) + '\n'
        return(result)

    def __iter__(self): return iter(self.__nodes)

    def find(self, value):
        for node in self:
            if node.value == value:
                return(node)

        return(None)

    def add_nodes(self, nodes):
        for node in nodes:
            self.add_node(node)

    def add_node(self, value):
        if not self.find(value):
            self.__nodes.append(self.__node(value))

    def add_edges(self, edges):
        for edge in edges:
            self.add_edge(edge[0], edge[1], edge[2])

    def add_edge(self, from_value, to_value, weight):
        """
            Add an edge between two values. If the nodes for those values
            aren't already in the graph, add those.
        """
        from_node = self.find(from_value)
        to_node = self.find(to_value)

        if not from_node:
            self.add_node(from_value)
            from_node = self.find(from_value)
        if not to_node:
            self.add_node(to_value)
            to_node = self.find(to_value)

        from_node.add_edge(self.__edge(to_node, weight))
        if not self.__directed:
            to_node.add_edge(self.__edge(from_node, weight))

    def remove_edge(self, from_value, to_value, weight):
        from_node = self.find(from_value)
        to_node = self.find(to_value)

        from_node.remove_edge(to_node)
        if not self.__directed:
            to_node.remove_edge(from_node) 
    
    def are_adjacent(self, value1, value2):
        return(self.find(value1).is_adjacent(self.find(value2)))

    # I have no memory of this place.
    def dijkstra(self, start):
        for n in self.__nodes:
            n.distance = float('inf')
            n.previous = None 

        source = self.find(start)
        source.distance = 0

        todo = {source}
        res = []

        while todo:
            min_dist_node = next(iter(todo))

            for n in todo:
                if n.distance < min_dist_node.distance:
                    min_dist_node = n

            todo.remove(min_dist_node)
            path = [min_dist_node.distance, min_dist_node.value]
            prev = min_dist_node.previous
            while prev:
                path.append(prev.value)
                prev = prev.previous

            res.append(path)

            for e in min_dist_node.edges:
                n = self.find(e.to_node.value)
                new_distance = e.weight + min_dist_node.distance
                if new_distance < n.distance: 
                    n.distance = new_distance
                    n.previous = min_dist_node
                    todo.add(n)

        return res

class test_weighted_digraph(unittest.TestCase):
    def test_empty(self):
        self.assertEqual(len(weighted_digraph()), 0)

    def test_one(self):
        g = weighted_digraph()
        g.add_node(1)
        self.assertEqual(len(g), 1)

    def test_duplicate(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(1)
        self.assertEqual(len(g), 1)

    def test_two(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(2)
        self.assertEqual(len(g), 2)

    def test_edge(self):
        g = weighted_digraph()
        g.add_node(1)
        g.add_node(2)
        g.add_edge(1, 2, 3)
        self.assertEqual(str(g), '1->2(3)\n2\n')

    def test_adding_ints(self):
        g = weighted_digraph()
        g.add_nodes([1, 2])
        g.add_edges([(1, 2, 3), (2, 1, 3)])
        self.assertEqual(str(g), '1->2(3)\n2->1(3)\n')

    def test_adding_strings(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertEqual(str(g), 'Denver->Boston(1971.8)\nBoston->Denver(1971.8)\n')

    def test_are_adjacent(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_arent_adjacent(self):
        g = weighted_digraph()
        g.add_nodes(['Denver', 'Boston', 'Milano'])
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertFalse(g.are_adjacent('Denver', 'Milano'))

    def test_arent_adjacent_directed(self):
        g = weighted_digraph()
        g.add_edges([('Denver', 'Boston', 1971.8)])
        self.assertFalse(g.are_adjacent('Denver', 'Milano'))
        self.assertFalse(g.are_adjacent('Boston', 'Denver'))
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_arent_adjacent_undirected(self):
        g = weighted_digraph(False)
        g.add_edges([('Denver', 'Boston', 1971.8)])
        self.assertTrue(g.are_adjacent('Boston', 'Denver'))
        self.assertTrue(g.are_adjacent('Denver', 'Boston'))

    def test_add_edges_without_nodes(self):
        g = weighted_digraph()
        g.add_edges([('Denver', 'Boston', 1971.8), ('Boston', 'Denver', 1971.8)])
        self.assertEqual(str(g), \
            'Denver->Boston(1971.8)\nBoston->Denver(1971.8)\n')

    def test_dijkstra(self):
        # 
        #     2---1---4
        #    /|\      |\
        #   2 | \     | 6
        #  /  |  \    |  \
        # 1   1   2   3   6
        #  \  |    \  |  /
        #   1 |     \ | 1
        #    \|      \|/
        #     3---5---5
        # 
        
        g = weighted_digraph(False)
        g.add_edges([(1,2,2), (1,3,1), (2,3,1), (2,4,1), \
            (2,5,2), (3,5,5), (4,5,3), (4,6,6), (5,6,1)])
        if not track_previous:
            self.assertEqual(g.dijkstra(1), [[0, 1], [1, 3], [2, 2], \
                [3, 4], [4, 5], [5, 6]])
        else:
            # distance, path...
            self.assertEqual(g.dijkstra(1), [[0, 1], [1, 3, 1], [2, 2, 1], \
                [3, 4, 2, 1], [4, 5, 2, 1], [5, 6, 5, 2, 1]])

if '__main__' == __name__:
    g = weighted_digraph(False)
    file = open(argv[1], "r")
    for line in file:
        a = line.strip().split(" ")
        g.add_edge(a[0], a[1], int(a[2]))
    result = g.dijkstra("Denver")
    for city in result:
        print(city[1], "is", city[0], 'miles from Denver')
        if track_previous:
            for path in city[2:]:
                print("     ", path)

Add an edge between two values. If the nodes for those values             aren't already in the graph, add those. # I have no memory of this place. # #     2---1---4 #    /|\      |\ #   2 | \     | 6 #  /  |  \    |  \ # 1   1   2   3   6 #  \  |    \  |  / #   1 |     \ | 1 #    \|      \|/ #     3---5---5 # # distance, path...