Haskell中抽象图的DFS实现

Question

我正在尝试在 Haskell 中实现 DFS 算法，该算法将无法访问 Graph 内部和构造函数，但只能使用提供的函数来检索图中的所有图顶点和所有节点的邻居：

vertices :: Eq a => Graph a -> [a]
neighbors :: Eq a => Graph a -> a -> [a]

作为输入，该函数得到一个Graph a 和一个对象a。

作为输出，我正在尝试提供一个连接组件Graph a，它将具有可从对象访问的所有顶点。

为了检索一个空图并添加我已经实现的函数的顶点

empty :: Graph a
addVertex :: Eq a => Graph a -> a -> Graph a

对于dfs，到目前为止，我已经实现了一个功能，它看起来更像是一个一般的想法，但还没有接近工作。 我觉得有点卡住了，所以非常感谢任何建议或提示

最后，我需要从输入中获取包含节点的图的连接组件。 （非强连接）

所以dfs 本身可能应该返回一个节点列表，然后可以使用neighbours 函数将其用于形成图形..？

到目前为止我有这个，但它仍然不能正常工作。

我剩下的唯一问题是将边缘保留在子图中

connectedComponent :: Eq a => Graph a -> a -> Graph a
connectedComponent g vrtx | vrtx `notElem`  vertices g = empty
                            --adds all the points to the created graph   
                          | otherwise = foldl (\graph x -> addVertex graph x) initialGraph points 
                                --gets all neighbors of the nodes retrieved in dfs
                                where 
                                    points = concatMap (neighbors g) (dfs g vrtx) 
                                    initialGraph = addVertex empty vrtx

-- Getting the Graph and a vertex to start from
dfs :: Eq a => Graph a -> a -> [a]
dfs graph node | graph == empty = []
               | [x|x<-(vertices graph),x==node] == [] = []
               | otherwise = dfs' (vertices graph) graph [node]

dfs' [] _ _ = []
dfs' _ _ [] = []
dfs' v graph (top:stack) | [x|x<-v,x==top] == [] = dfs' nextv graph stack
                     | otherwise = top : dfs' nextv graph (adjacent ++ stack)
                     where 
                        adjacent = neighbors graph top
                        --adjacent = [x | (x,y)<-e,y==top] ++ [x | (y,x)<-e,y==top]
                        nextv = [x|x<-v,x/=top]

Answer 1

这是我最后所做的，对我来说是正确的。

connectedComponent :: Eq a => Graph a -> a -> Graph a
connectedComponent g vrtx | vrtx `notElem`  vertices g = empty
                            --adds all the nodes and edges to the created graph   
                          | otherwise = foldl addEdge (foldl (\graph x -> addVertex graph x) initialGraph nodes) edges
                                --gets all neighbors of the nodes retrieved in dfs
                                where 
                                    nodes = concatMap (neighbors g) (dfs g vrtx) 
                                    -- init the graph with the start node
                                    initialGraph = addVertex empty vrtx
                                    edges = removeDub [(x,y) | x <- (vertices g), y <- (neighbors g x), x `elem` dfs g vrtx]

-- removes dublicates from the edges if (a,b) and (b,a) exist
removeDub ::Eq a => [(a,a)] -> [(a,a)]
removeDub [] = []
removeDub ((x,y):xs) | (y,x) `elem` xs = removeDub xs
                     | otherwise = (x,y) : removeDub xs


-- Getting the Graph and a vertex to start from
dfs :: Eq a => Graph a -> a -> [a]
dfs graph node | graph == empty = []
                 -- stop if this is the node
               | [x | x<-(vertices graph), x==node] == [] = []
               | otherwise = dfs' (vertices graph) graph [node]

-- help function for dfs
dfs' [] _ _ = []
dfs' _ _ [] = []
dfs' vs graph (top:stack) | [x | x <- vs, x==top] == [] = dfs' nextv graph stack
                        -- append the current one and go to the next node
                     | otherwise = top : dfs' nextv graph (adjacent ++ stack)
                     where
                        -- getting all neibourhs for currently viewed node 
                        adjacent = neighbors graph top
                        -- getting the next node
                        nextv = [x|x<-vs,x/=top]