{-# LANGUAGE MultiParamTypeClasses #-}

-- | Example Graphs
module Data.Graph.Inductive.Example(
    -- * Auxiliary Functions
    genUNodes, genLNodes, labUEdges, noEdges,
    -- * Small Dynamic Graphs
    a, b, c, e, loop, ab, abb, dag3, e3, cyc3, g3, g3b, dag4, d1, d3,
    -- * Small Static Graphs
    a', b', c', e', loop', ab', abb', dag3', e3', dag4', d1', d3',
    -- * Functions to Create (Regular) Graphs
    ucycle, star, ucycleM, starM,
    -- * More Graphs
    -- | clr : Cormen\/Leiserson\/Rivest

    -- | kin : Kingston

    -- ** Dynamic Versions
    clr479, clr489, clr486, clr508, clr528, clr595, gr1, kin248, vor,
    -- ** Static Versions
    clr479', clr489', clr486', clr508', clr528', kin248', vor'
)where

import Data.Graph.Inductive.Graph
import Data.Graph.Inductive.PatriciaTree

import Data.Graph.Inductive.Monad
import Data.Graph.Inductive.Monad.IOArray

-- | generate list of unlabeled nodes
genUNodes :: Int -> [UNode]
genUNodes n = zip [1..n] (repeat ())

-- | generate list of labeled nodes
genLNodes :: (Enum a) => a -> Int -> [LNode a]
genLNodes q i = take i (zip [1..] [q..])

-- | denote unlabeled edges
labUEdges :: [Edge] -> [UEdge]
labUEdges = map (\(i,j) -> (i,j,()))

-- | empty (unlabeled) edge list
noEdges :: [UEdge]
noEdges = []


a,b,c,e,loop,ab,abb,dag3   :: Gr Char ()
e3                         :: Gr () String
cyc3,g3,g3b                :: Gr Char String
dag4                       :: Gr Int ()
d1,d3                      :: Gr Int Int

a    = ([],1,'a',[]) & empty                  -- just a node
b    = mkGraph (zip [1..2] "ab") noEdges      -- just two nodes
c    = mkGraph (zip [1..3] "abc") noEdges     -- just three nodes
e    = ([((),1)],2,'b',[]) & a                -- just one edge a-->b
e3   = mkGraph (genUNodes 2)
       [(1,2,"a"),(1,2,"b"),(1,2,"a")]        -- three edges (two labels) a-->b
loop = ([],1,'a',[((),1)]) & empty            -- loop on single node
ab   = ([((),1)],2,'b',[((),1)]) & a          -- cycle of two nodes:  a<-->b
abb  = mkGraph (zip [1..2] "ab") (labUEdges [(2,2)]) -- a and loop on b

cyc3 = buildGr                                -- cycle of three nodes
       [([("ca",3)],1,'a',[("ab",2)]),
                ([],2,'b',[("bc",3)]),
                ([],3,'c',[])]

dag3 = mkGraph (zip [1..3] "abc") (labUEdges [(1,3)])
dag4 = mkGraph (genLNodes 1 4) (labUEdges [(1,2),(1,4),(2,3),(2,4),(4,3)])

d1   = mkGraph (genLNodes 1 2) [(1,2,1)]
d3   = mkGraph (genLNodes 1 3) [(1,2,1),(1,3,4),(2,3,2)]

g3 = ([("left",2),("up",3)],1,'a',[("right",2)]) & (
                        ([],2,'b',[("down",3)])  & (
                        ([],3,'c',[])            & empty ))
g3b = ([("down",2)], 3,'c',[("up",1)])   & (
      ([("right",1)],2,'b',[("left",1)]) & (
                 ([],1,'a',[])           & empty ))


a',b',c',e',loop',ab',abb',dag3' :: IO (SGr Char ())
e3'                              :: IO (SGr () String)
dag4'                            :: IO (SGr Int ())
d1',d3'                          :: IO (SGr Int Int)

a'    = mkGraphM [(1,'a')] noEdges              -- just a node
b'    = mkGraphM (zip [1..2] "ab") noEdges      -- just two nodes
c'    = mkGraphM (zip [1..3] "abc") noEdges     -- just three nodes
e'    = mkGraphM (zip [1..2] "ab") [(1,2,())]   -- just one edge a-->b
e3'   = mkGraphM (genUNodes 2)
          [(1,2,"a"),(1,2,"b"),(1,2,"a")]       -- three edges (two labels) a-->b
loop' = mkGraphM [(1,'a')] [(1,1,())]           -- loop on single node
ab'   = mkGraphM (zip [1..2] "ab")
          [(1,2,()),(2,1,())]                   -- cycle of two nodes:  a<-->b
abb'  = mkGraphM (zip [1..2] "ab") (labUEdges [(2,2)]) -- a and loop on b

dag3' = mkGraphM (zip [1..3] "abc") (labUEdges [(1,3)])
dag4' = mkGraphM (genLNodes 1 4) (labUEdges [(1,2),(1,4),(2,3),(2,4),(4,3)])

d1'   = mkGraphM (genLNodes 1 2) [(1,2,1)]
d3'   = mkGraphM (genLNodes 1 3) [(1,2,1),(1,3,4),(2,3,2)]

ucycle :: (Graph gr) => Int -> gr () ()
ucycle n = mkUGraph vs (map (\v->(v,v `mod` n+1)) vs)
           where vs = [1..n]

star :: (Graph gr) => Int -> gr () ()
star n = mkUGraph [1..n] (map (\v->(1,v)) [2..n])

ucycleM :: (GraphM m gr) => Int -> m (gr () ())
ucycleM n = mkUGraphM vs (map (\v->(v,v `mod` n+1)) vs)
            where vs = [1..n]

starM :: (GraphM m gr) => Int -> m (gr () ())
starM n = mkUGraphM [1..n] (map (\v->(1,v)) [2..n])


clr479,clr489    :: Gr Char ()
clr486           :: Gr String ()
clr508,clr528    :: Gr Char Int
clr595,gr1       :: Gr Int Int
kin248           :: Gr Int ()
vor              :: Gr String Int

clr479 = mkGraph (genLNodes 'u' 6)
         (labUEdges [(1,2),(1,4),(2,5),(3,5),(3,6),(4,2),(5,4),(6,6)])
clr486 = mkGraph (zip [1..9] ["shorts","socks","watch","pants","shoes",
                              "shirt","belt","tie","jacket"])
                 (labUEdges [(1,4),(1,5),(2,5),(4,5),(4,7),(6,7),(6,8),(7,9),(8,9)])
clr489 = mkGraph (genLNodes 'a' 8)
                 (labUEdges [(1,2),(2,3),(2,5),(2,6),(3,4),(3,7),(4,3),(4,8),
                         (5,1),(5,6),(6,7),(7,6),(7,8),(8,8)])
clr508 = mkGraph (genLNodes 'a' 9)
                 [(1,2,4),(1,8,8),(2,3,8),(2,8,11),(3,4,7),(3,6,4),(3,9,2),
                  (4,5,9),(4,6,14),(5,6,10),(6,7,2),(7,8,1),(7,9,6),(8,9,7)]
clr528 = mkGraph [(1,'s'),(2,'u'),(3,'v'),(4,'x'),(5,'y')]
                 [(1,2,10),(1,4,5),(2,3,1),(2,4,2),(3,5,4),
                  (4,2,3),(4,3,9),(4,5,2),(5,1,7),(5,3,6)]
clr595 = mkGraph (zip [1..6] [1..6])
                 [(1,2,16),(1,3,13),(2,3,10),(2,4,12),(3,2,4),
                  (3,5,14),(4,3,9),(4,6,20),(5,4,7),(5,6,4)]
gr1    = mkGraph (zip [1..10] [1..10])
                 [(1,2,12),(1,3,1),(1,4,2),(2,3,1),(2,5,7),(2,6,5),(3,6,1),
                  (3,7,7),(4,3,3),(4,6,2),(4,7,5),(5,3,2),(5,6,3),(5,8,3),
                  (6,7,2),(6,8,3),(6,9,1),(7,9,9),(8,9,1),(8,10,4),(9,10,11)]
kin248 = mkGraph (genLNodes 1 10)
                 (labUEdges [(1,2),(1,4),(1,7),(2,4),(2,5),(3,4),(3,10),
                         (4,5),(4,8),(5,2),(5,3),(6,7),(7,6),(7,8),
                         (8,10),(9,9),(9,10),(10,8),(10,9)])
         -- this is the inverse graph shown on the bottom of the page

vor = mkGraph (zip [1..8] ["A","B","C","H1","H2","D","E","F"])
              [(1,4,3),(2,3,3),(2,4,3),(4,2,4),(4,6,2),
               (5,2,5),(5,3,6),(5,7,5),(5,8,6),
               (6,5,3),(6,7,2),(7,8,3),(8,7,3)]


clr479',clr489'  :: IO (SGr Char ())
clr486'          :: IO (SGr String ())
clr508',clr528'  :: IO (SGr Char Int)
kin248'          :: IO (SGr Int ())
vor'             :: IO (SGr String Int)

clr479' = mkGraphM (genLNodes 'u' 6)
          (labUEdges [(1,2),(1,4),(2,5),(3,5),(3,6),(4,2),(5,4),(6,6)])
clr486' = mkGraphM (zip [1..9] ["shorts","socks","watch","pants","shoes",
                                "shirt","belt","tie","jacket"])
                   (labUEdges [(1,4),(1,5),(2,5),(4,5),(4,7),(6,7),(6,8),(7,9),(8,9)])
clr489' = mkGraphM (genLNodes 'a' 8)
                   (labUEdges [(1,2),(2,3),(2,5),(2,6),(3,4),(3,7),(4,3),(4,8),
                           (5,1),(5,6),(6,7),(7,6),(7,8),(8,8)])
clr508' = mkGraphM (genLNodes 'a' 9)
                   [(1,2,4),(1,8,8),(2,3,8),(2,8,11),(3,4,7),(3,6,4),(3,9,2),
                   (4,5,9),(4,6,14),(5,6,10),(6,7,2),(7,8,1),(7,9,6),(8,9,7)]
clr528' = mkGraphM [(1,'s'),(2,'u'),(3,'v'),(4,'x'),(5,'y')]
                   [(1,2,10),(1,4,5),(2,3,1),(2,4,2),(3,5,4),
                    (4,2,3),(4,3,9),(4,5,2),(5,1,7),(5,3,6)]
kin248' = mkGraphM (genLNodes 1 10)
                   (labUEdges [(1,2),(1,4),(1,7),(2,4),(2,5),(3,4),(3,10),
                           (4,5),(4,8),(5,2),(5,3),(6,7),(7,6),(7,8),
                           (8,10),(9,9),(9,10),(10,8),(10,9)])
         -- this is the inverse graph shown on the bottom of the page

vor' = mkGraphM (zip [1..8] ["A","B","C","H1","H2","D","E","F"])
                [(1,4,3),(2,3,3),(2,4,3),(4,2,4),(4,6,2),
                 (5,2,5),(5,3,6),(5,7,5),(5,8,6),
                 (6,5,3),(6,7,2),(7,8,3),(8,7,3)]
