# note: I added Anaheim to the sample graph here. The solution should work
# appropriately with either graph.

sample_graph = {
    'Santa Ana': {
        'Los Angeles': 5,
        'Anaheim': 3,
        'Palm Springs': 50
    },
    'Anaheim': {
        'Los Angeles': 2,
        'Santa Ana': 3
    },
    'Los Angeles': {
        'Anaheim': 2,
        'San Francisco': 25,
        'Santa Ana': 5
    },
    'Palm Springs': {
        'San Francisco': 30,
        'Santa Ana': 50
    },
    'San Francisco': {
        'Los Angeles': 25,
        'Palm Springs': 30
    }
}


def possible_paths(graph: dict[str, dict[str, int]],
                   start: str,
                   end: str):
    # (path, total distance represented by path)
    queue = [([start], 0)]
    valid_paths = []

    # appending to queue:
    # append the new vertex to the path, add the distance to the total distance
    # do not append to queue if in visited

    while queue:
        path, distance = queue.pop(0)
        if path[-1] == end:
            valid_paths.append((path, distance))
        else:
            for vertex, weight in graph[path[-1]].items():
                # question: what can we do to improve time efficiency here?
                if vertex not in path:
                    new_path = path.copy()
                    new_path.append(vertex)
                    queue.append((new_path, distance + weight))

    return valid_paths

print(possible_paths(sample_graph, 'Santa Ana', 'San Francisco'))