Question

我想帮助实现Haskell的最长路径算法。我只使用了Haskell大约两个星期，之前没有用函数式语言做过任何事情。当您仅限于不可变数据和递归时，我在尝试用函数式语言实现算法时真的迷失了。

我一直在尝试实施此算法：http://www.geeksforgeeks.org/find-longest-path-directed-acyclic-graph/

我的图表构造如下：

data = Graph w = Graph {vertices :: [(Char, w)],
                        edges :: [(Char, Char, w)]} deriving Show

所以我在顶点和边上都有权重，权重可以是任何数据类型。因此，在计算最长路径时，我还需要使用两个函数f和g。从顶点a到b的最长路径将是路径中所有权重的f(w)和g(w)的总和。

我试过实现这个但是我总是发现自己试图编写“命令式”的方式，这真的很难实现......

请指出正确的方向。

weight_of_longest_path :: (Ord w) => Graph w -> Char -> Char 
                                             -> (w -> w) -> (w -> w) -> w
weight_of_longest_path  (Graph v w) startVert endVert f g =
  let 
    topSort = dropWhile (/= startVert) $ topological_ordering (Graph v w)
    distList = zip topSort $ 
                 (snd $ head $ filter (\(a,b) -> a == startVert) v) 
                 : (repeat (-999999999))
    finalList = getFinalList (Graph v w) topSort distList f g
  in 
    snd $ head $ filter (\(a,b) -> b == endVert) finalList

getFinalList :: (Ord w) => Graph w -> [Char] -> [(Char, w)] 
                                   -> (w -> w) -> (w -> w) -> [(Char, w)]
getFinalList _  [] finalList _ _ = finalList
getFinalList (Graph v w) (firstVert:rest) distList f g =
  let 
    neighbours = secondNodes $ filter (\(a,b,w) -> a == firstVert) w
    finalList = updateList firstVert neighbours distList (Graph v w) f g
  in  
    getFinalList (Graph v w) rest finalList f g

updateList :: (Ord w) => Char -> [Char] -> [(Char, w)] -> Graph w 
                              -> (w -> w) -> (w -> w) -> [(Char, w)]
updateList _ [] updatedList _ _ _ = updatedList
updateList firstVert (neighbour:rest) distList (Graph vertices weights) f g =
  let 
    edgeWeight = selectThird $ head 
          $ filter (\(a,b,w) -> a == firstVert && b == neighbour) weights
    verticeWeight = snd $ head 
          $ filter (\(a,b) -> a == neighbour) vertices
    newDist = calcDist firstVert neighbour verticeWeight edgeWeight 
                       distList f g
    updatedList = replace distList neighbour newDist
  in  
    updateList firstVert rest updatedList (Graph vertices weights) f g


calcDist :: (Ord w) => Char -> Char -> w -> w -> [(Char, w)] 
                            -> (w -> w) -> (w -> w) -> w
calcDist firstVert neighbour verticeWeight edgeWeight distList f g =
  if (compareTo f g 
         (snd $ head $ filter (\(a,b) -> a == neighbour) distList) 
         (snd $ head $ filter (\(a,b) -> a == firstVert) distList) 
         edgeWeight verticeWeight) == True
  then 
     (f (snd $ head $ filter (\(a,b) -> a == firstVert) distList))
     + (g edgeWeight) + (f verticeWeight)
  else 
     (f (snd $ head $ filter (\(a,b) -> a == neighbour) distList))

replace :: [(Char, w)] -> Char -> w -> [(Char, w)]
replace distList vertice value = 
    map (\p@(f, _) -> if f == vertice then (vertice, value) else p) 
        distList

正如你所看到的，对于这样一个简单的算法来说，这是一个很乱的代码，而且我确信它可以用更干净的方式实现。

Answer 1

这是一种采用更“功能”的思维方式的方法。它围绕两个功能：

longestPath :: Graph -> Node -> Node -> [Edge]
pathCost :: Graph -> [Edges] -> Int

longestPath将路径作为最长路径的边缘列表返回。 pathCost返回路径的费用。

longestPath的定义是这样的：

longestPath g start end
  | start == end = []
  | otherwise    = 
    maximumBy (comparing (pathCost g))
              [ e : path | e <- edges of the node start
                           let start' = the other vertex of e,
                           let g' = graph g with node start deleted,
                           let path = longestPath g' start' end ]

（maximumBy来自Data.List和来自comparing的{{1}}

N.B。边缘将以相反的顺序生成。

有许多实现细节需要弄清楚，特别是，当没有从Data.Ord到start的路径时，您必须稍微修改它以处理这种情况（这可以在你开始删除节点时发生），但这是我开始的方法。

在Haskell中实现最长路径算法

1 个答案: