最短距离算法 Python

Question

我想创建一个简单的广度优先搜索算法，它返回最短路径。

演员信息字典将演员映射到该演员出现的电影列表：

actor_info = { "act1" : ["movieC", "movieA"], "act2" : ["movieA", "movieB"], 
     "act3" :["movieA", "movieB"], "act4" : ["movieC", "movieD"], 
     "act5" : ["movieD", "movieB"], "act6" : ["movieE"], 
     "act7" : ["movieG", "movieE"], "act8" : ["movieD", "movieF"], 
     "KevinBacon" : ["movieF"], "act10" : ["movieG"], "act11" : ["movieG"] }

与此相反，将电影映射到其中出现的演员列表：

movie_info = {'movieB': ['act2', 'act3', 'act5'], 'movieC': ['act1', 'act4'], 
      'movieA': ['act1', 'act2', 'act3'], 'movieF': ['KevinBacon', 'act8'], 
      'movieG': ['act7', 'act10', 'act11'], 'movieD': ['act8', 'act4', 'act5'], 
      'movieE': ['act6', 'act7']}

因此对于调用，

shortest_dictance("act1", "Kevin Bacon", actor_info, movie_info)

我应该得到 3 因为 act1 出现在 movieC 中，Act4 出现在 movieD 中，Act8 出现在 >电影F与凯文培根。所以最短距离是 3。

到目前为止，我有这样的情况：

def shotest_distance(actA, actB, actor_info, movie_info):
   '''Return the number of movies required to connect actA and actB. 
   If theres no connection return -1.'''

    # So we keep 2 lists of actors:
    #   1.The actors that we have already investigated.
    #   2.The actors that need to be investigated because we have found a 
    #      connection beginning at actA. This list must be 
    #      ordered, since we want to investigate actors in the order we 
    #      discover them.
    #      -- Each time we put an actor in this list, we also store
    #         her distance from actA.
    investigated = []
    to_investigate = [actA]
    distance = 0
    while actB not in to_investigate and to_investigate!= []:
        for actor in to_investigate:
            to_investigated.remove(actA)
            investigated.append(act)

            for movie in actor_info[actor]:
                for co_star in movie_info[movie]:
                    if co_star not in (investigated and to_investigate):
                        to_investigate.append(co_star)

 ....
 ....

 return d    

我无法找到适当的方法来跟踪代码每次迭代发现的距离。此外，该代码似乎在时间上效率很低。

Answer 1

首先创建一个图来连接所有节点，然后运行最短路径代码（可能有一个高效的图库来完成此操作，而不是下面提到的函数，尽管如此，这个库很优雅），然后找出所有节点的数量最短路径的电影名称。

for i in movie_info:
    actor_info[i] = movie_info[i]

def find_shortest_path(graph, start, end, path=[]):
    path = path + [start]
    if start == end:
        return path
    if not start in graph:
        return None
    shortest = None
    for node in graph[start]:
        if node not in path:
            newpath = find_shortest_path(graph, node, end, path)
            if newpath:
                if not shortest or len(newpath) < len(shortest):
                    shortest = newpath
    return shortest

L = find_shortest_path(actor_info, 'act1', 'act2')
print len([i for i in L if i in movie_info])

find_shortest_path 来源： http://www.python.org/doc/essays/graphs/

Answer 2

这看起来可行。它跟踪当前的一组电影。对于每一步，它都会查看所有尚未考虑（“看过”）的单步电影。

actor_info = { "act1" : ["movieC", "movieA"], "act2" : ["movieA", "movieB"], 
     "act3" :["movieA", "movieB"], "act4" : ["movieC", "movieD"], 
     "act5" : ["movieD", "movieB"], "act6" : ["movieE"], 
     "act7" : ["movieG", "movieE"], "act8" : ["movieD", "movieF"], 
     "KevinBacon" : ["movieF"], "act10" : ["movieG"], "act11" : ["movieG"] }

movie_info = {'movieB': ['act2', 'act3', 'act5'], 'movieC': ['act1', 'act4'], 
      'movieA': ['act1', 'act2', 'act3'], 'movieF': ['KevinBacon', 'act8'], 
      'movieG': ['act7', 'act10', 'act11'], 'movieD': ['act8', 'act4', 'act5'], 
      'movieE': ['act6', 'act7']}

def shortest_distance(actA, actB, actor_info, movie_info):
    if actA not in actor_info:
        return -1  # "infinity"
    if actB not in actor_info:
        return -1  # "infinity"
    if actA == actB:
        return 0

    dist = 1
    movies = set(actor_info[actA])
    end_movies = set(actor_info[actB])
    if movies & end_movies:
        return dist

    seen = movies.copy()
    print "All movies with", actA, seen
    while 1:
        dist += 1
        next_step = set()
        for movie in movies:
            for actor in movie_info[movie]:
                next_step.update(actor_info[actor])
        print "Movies with actors from those movies", next_step
        movies = next_step - seen 
        print "New movies with actors from those movies", movies
        if not movies:
            return -1 # "Infinity"

        # Has actorB been in any of those movies?
        if movies & end_movies:
            return dist

        # Update the set of seen movies, so I don't visit them again
        seen.update(movies)

if __name__ == "__main__":
    print shortest_distance("act1", "KevinBacon", actor_info, movie_info)

输出是

All movies with act1 set(['movieC', 'movieA'])
Movies with actors from those movies set(['movieB', 'movieC', 'movieA', 'movieD'])
New movies with actors from those movies set(['movieB', 'movieD'])
Movies with actors from those movies set(['movieB', 'movieC', 'movieA', 'movieF', 'movieD'])
New movies with actors from those movies set(['movieF'])
3

Here's a version，它返回构成最小连接的电影列表（无连接则为 None，如果 actA 和 actB 相同则返回空列表。）

def connect(links, movie):
    chain = []
    while movie is not None:
        chain.append(movie)
        movie = links[movie]
    return chain

def shortest_distance(actA, actB, actor_info, movie_info):
    if actA not in actor_info:
        return None  # "infinity"
    if actB not in actor_info:
        return None  # "infinity"
    if actA == actB:
        return []

    # {x: y} means that x is one link outwards from y
    links = {}

    # Start from the destination and work backward
    for movie in actor_info[actB]:
        links[movie] = None
    dist = 1
    movies = links.keys()

    while 1:
        new_movies = []
        for movie in movies:
            for actor in movie_info[movie]:
                if actor == actA:
                    return connect(links, movie)
                for other_movie in actor_info[actor]:
                    if other_movie not in links:
                        links[other_movie] = movie
                        new_movies.append(other_movie)
        if not new_movies:
            return None # Infinity
        movies = new_movies

if __name__ == "__main__":
    dist = shortest_distance("act1", "KevinBacon", actor_info, movie_info)
    if dist is None:
        print "Not connected"
    else:
        print "The Kevin Bacon Number for act1 is", len(dist)
        print "Movies are:", ", ".join(dist)

输出如下：

The Kevin Bacon Number for act1 is 3
Movies are: movieC, movieD, movieF