-----------------------------------------------------------------------------
-- |
-- Module    : Documentation.SBV.Examples.Puzzles.U2Bridge
-- Copyright : (c) Levent Erkok
-- License   : BSD3
-- Maintainer: erkokl@gmail.com
-- Stability : experimental
--
-- The famous U2 bridge crossing puzzle: <http://www.braingle.com/brainteasers/515/u2.html>
-----------------------------------------------------------------------------

{-# LANGUAGE DeriveAnyClass       #-}
{-# LANGUAGE DeriveDataTypeable   #-}
{-# LANGUAGE DeriveGeneric        #-}
{-# LANGUAGE FlexibleInstances    #-}
{-# LANGUAGE StandaloneDeriving   #-}
{-# LANGUAGE TemplateHaskell      #-}

{-# OPTIONS_GHC -Wall -Werror -Wno-incomplete-uni-patterns #-}

module Documentation.SBV.Examples.Puzzles.U2Bridge where

import Control.Monad       (unless)
import Control.Monad.State (State, runState, put, get, gets, modify, evalState)

import Data.List(sortOn)

import GHC.Generics (Generic)

import Data.SBV

-------------------------------------------------------------
-- * Modeling the puzzle
-------------------------------------------------------------

-- | U2 band members. We want to translate this to SMT-Lib as a data-type, and hence the
-- call to mkSymbolicEnumeration.
data U2Member = Bono | Edge | Adam | Larry

-- | Make 'U2Member' a symbolic value.
mkSymbolicEnumeration ''U2Member

-- | Model time using 32 bits
type Time  = Word32

-- | Symbolic variant for time
type STime = SBV Time

-- | Crossing times for each member of the band
crossTime :: U2Member -> Time
crossTime :: U2Member -> Time
crossTime U2Member
Bono  = Time
1
crossTime U2Member
Edge  = Time
2
crossTime U2Member
Adam  = Time
5
crossTime U2Member
Larry = Time
10

-- | The symbolic variant.. The duplication is unfortunate.
sCrossTime :: SU2Member -> STime
sCrossTime :: SU2Member -> STime
sCrossTime SU2Member
m =   SBool -> STime -> STime -> STime
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
m SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sBono) (Time -> STime
forall a. SymVal a => a -> SBV a
literal (U2Member -> Time
crossTime U2Member
Bono))
               (STime -> STime) -> STime -> STime
forall a b. (a -> b) -> a -> b
$ SBool -> STime -> STime -> STime
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
m SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sEdge) (Time -> STime
forall a. SymVal a => a -> SBV a
literal (U2Member -> Time
crossTime U2Member
Edge))
               (STime -> STime) -> STime -> STime
forall a b. (a -> b) -> a -> b
$ SBool -> STime -> STime -> STime
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
m SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sAdam) (Time -> STime
forall a. SymVal a => a -> SBV a
literal (U2Member -> Time
crossTime U2Member
Adam))
                                   (Time -> STime
forall a. SymVal a => a -> SBV a
literal (U2Member -> Time
crossTime U2Member
Larry)) -- Must be Larry

-- | Location of the flash
data Location = Here | There

-- | Make 'Location' a symbolic value.
mkSymbolicEnumeration ''Location

-- | The status of the puzzle after each move
--
-- This type is equipped with an automatically derived 'Mergeable' instance
-- because each field is 'Mergeable'. A 'Generic' instance must also be derived
-- for this to work, and the @DeriveAnyClass@ language extension must be
-- enabled. The derived 'Mergeable' instance simply walks down the structure
-- field by field and merges each one. An equivalent hand-written 'Mergeable'
-- instance is provided in a comment below.
data Status = Status { Status -> STime
time   :: STime       -- ^ elapsed time
                     , Status -> SLocation
flash  :: SLocation   -- ^ location of the flash
                     , Status -> SLocation
lBono  :: SLocation   -- ^ location of Bono
                     , Status -> SLocation
lEdge  :: SLocation   -- ^ location of Edge
                     , Status -> SLocation
lAdam  :: SLocation   -- ^ location of Adam
                     , Status -> SLocation
lLarry :: SLocation   -- ^ location of Larry
                     } deriving ((forall x. Status -> Rep Status x)
-> (forall x. Rep Status x -> Status) -> Generic Status
forall x. Rep Status x -> Status
forall x. Status -> Rep Status x
forall a.
(forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a
$cfrom :: forall x. Status -> Rep Status x
from :: forall x. Status -> Rep Status x
$cto :: forall x. Rep Status x -> Status
to :: forall x. Rep Status x -> Status
Generic, Bool -> SBool -> Status -> Status -> Status
(Bool -> SBool -> Status -> Status -> Status)
-> (forall b.
    (Ord b, SymVal b, Num b, Num (SBV b)) =>
    [Status] -> Status -> SBV b -> Status)
-> Mergeable Status
forall b.
(Ord b, SymVal b, Num b, Num (SBV b)) =>
[Status] -> Status -> SBV b -> Status
forall a.
(Bool -> SBool -> a -> a -> a)
-> (forall b.
    (Ord b, SymVal b, Num b, Num (SBV b)) =>
    [a] -> a -> SBV b -> a)
-> Mergeable a
$csymbolicMerge :: Bool -> SBool -> Status -> Status -> Status
symbolicMerge :: Bool -> SBool -> Status -> Status -> Status
$cselect :: forall b.
(Ord b, SymVal b, Num b, Num (SBV b)) =>
[Status] -> Status -> SBV b -> Status
select :: forall b.
(Ord b, SymVal b, Num b, Num (SBV b)) =>
[Status] -> Status -> SBV b -> Status
Mergeable)

-- The derived Mergeable instance is equivalent to the following:
--
-- instance Mergeable Status where
--   symbolicMerge f t s1 s2 = Status { time   = symbolicMerge f t (time   s1) (time   s2)
--                                    , flash  = symbolicMerge f t (flash  s1) (flash  s2)
--                                    , lBono  = symbolicMerge f t (lBono  s1) (lBono  s2)
--                                    , lEdge  = symbolicMerge f t (lEdge  s1) (lEdge  s2)
--                                    , lAdam  = symbolicMerge f t (lAdam  s1) (lAdam  s2)
--                                    , lLarry = symbolicMerge f t (lLarry s1) (lLarry s2)
--                                    }

-- | Start configuration, time elapsed is 0 and everybody is here
start :: Status
start :: Status
start = Status { time :: STime
time   = STime
0
               , flash :: SLocation
flash  = SLocation
sHere
               , lBono :: SLocation
lBono  = SLocation
sHere
               , lEdge :: SLocation
lEdge  = SLocation
sHere
               , lAdam :: SLocation
lAdam  = SLocation
sHere
               , lLarry :: SLocation
lLarry = SLocation
sHere
               }

-- | A puzzle move is modeled as a state-transformer
type Move a = State Status a

-- | Mergeable instance for 'Move' simply pushes the merging the data after run of each branch
-- starting from the same state.
instance Mergeable a => Mergeable (Move a) where
  symbolicMerge :: Bool -> SBool -> Move a -> Move a -> Move a
symbolicMerge Bool
f SBool
t Move a
a Move a
b
    = do s <- StateT Status Identity Status
forall s (m :: * -> *). MonadState s m => m s
get
         let (ar, s1) = runState a s
             (br, s2) = runState b s
         put $ symbolicMerge f t s1 s2
         return $ symbolicMerge f t ar br

-- | Read the state via an accessor function
peek :: (Status -> a) -> Move a
peek :: forall a. (Status -> a) -> Move a
peek = (Status -> a) -> StateT Status Identity a
forall s (m :: * -> *) a. MonadState s m => (s -> a) -> m a
gets

-- | Given an arbitrary member, return his location
whereIs :: SU2Member -> Move SLocation
whereIs :: SU2Member -> Move SLocation
whereIs SU2Member
p =  SBool -> Move SLocation -> Move SLocation -> Move SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sBono) ((Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
lBono)
           (Move SLocation -> Move SLocation)
-> Move SLocation -> Move SLocation
forall a b. (a -> b) -> a -> b
$ SBool -> Move SLocation -> Move SLocation -> Move SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sEdge) ((Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
lEdge)
           (Move SLocation -> Move SLocation)
-> Move SLocation -> Move SLocation
forall a b. (a -> b) -> a -> b
$ SBool -> Move SLocation -> Move SLocation -> Move SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sAdam) ((Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
lAdam)
                               ((Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
lLarry)

-- | Transferring the flash to the other side
xferFlash :: Move ()
xferFlash :: Move ()
xferFlash = (Status -> Status) -> Move ()
forall s (m :: * -> *). MonadState s m => (s -> s) -> m ()
modify ((Status -> Status) -> Move ()) -> (Status -> Status) -> Move ()
forall a b. (a -> b) -> a -> b
$ \Status
s -> Status
s{flash = ite (flash s .== sHere) sThere sHere}

-- | Transferring a person to the other side
xferPerson :: SU2Member -> Move ()
xferPerson :: SU2Member -> Move ()
xferPerson SU2Member
p =  do ~[lb, le, la, ll] <- ((Status -> SLocation) -> Move SLocation)
-> [Status -> SLocation] -> StateT Status Identity [SLocation]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM (Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek [Status -> SLocation
lBono, Status -> SLocation
lEdge, Status -> SLocation
lAdam, Status -> SLocation
lLarry]
                   let move SLocation
l = SBool -> SLocation -> SLocation -> SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SLocation
l SLocation -> SLocation -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SLocation
sHere) SLocation
sThere SLocation
sHere
                       lb' = SBool -> SLocation -> SLocation -> SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sBono)  (SLocation -> SLocation
move SLocation
lb) SLocation
lb
                       le' = SBool -> SLocation -> SLocation -> SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sEdge)  (SLocation -> SLocation
move SLocation
le) SLocation
le
                       la' = SBool -> SLocation -> SLocation -> SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sAdam)  (SLocation -> SLocation
move SLocation
la) SLocation
la
                       ll' = SBool -> SLocation -> SLocation -> SLocation
forall a. Mergeable a => SBool -> a -> a -> a
ite (SU2Member
p SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sLarry) (SLocation -> SLocation
move SLocation
ll) SLocation
ll
                   modify $ \Status
s -> Status
s{lBono = lb', lEdge = le', lAdam = la', lLarry = ll'}

-- | Increment the time, when only one person crosses
bumpTime1 :: SU2Member -> Move ()
bumpTime1 :: SU2Member -> Move ()
bumpTime1 SU2Member
p = (Status -> Status) -> Move ()
forall s (m :: * -> *). MonadState s m => (s -> s) -> m ()
modify ((Status -> Status) -> Move ()) -> (Status -> Status) -> Move ()
forall a b. (a -> b) -> a -> b
$ \Status
s -> Status
s{time = time s + sCrossTime p}

-- | Increment the time, when two people cross together
bumpTime2 :: SU2Member -> SU2Member -> Move ()
bumpTime2 :: SU2Member -> SU2Member -> Move ()
bumpTime2 SU2Member
p1 SU2Member
p2 = (Status -> Status) -> Move ()
forall s (m :: * -> *). MonadState s m => (s -> s) -> m ()
modify ((Status -> Status) -> Move ()) -> (Status -> Status) -> Move ()
forall a b. (a -> b) -> a -> b
$ \Status
s -> Status
s{time = time s + sCrossTime p1 `smax` sCrossTime p2}

-- | Symbolic version of 'Control.Monad.when'
whenS :: SBool -> Move () -> Move ()
whenS :: SBool -> Move () -> Move ()
whenS SBool
t Move ()
a = SBool -> Move () -> Move () -> Move ()
forall a. Mergeable a => SBool -> a -> a -> a
ite SBool
t Move ()
a (() -> Move ()
forall a. a -> StateT Status Identity a
forall (m :: * -> *) a. Monad m => a -> m a
return ())

-- | Move one member, remembering to take the flash
move1 :: SU2Member -> Move ()
move1 :: SU2Member -> Move ()
move1 SU2Member
p = do f <- (Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
flash
             l <- whereIs p
             -- only do the move if the person and the flash are at the same side
             whenS (f .== l) $ do bumpTime1 p
                                  xferFlash
                                  xferPerson p

-- | Move two members, again with the flash
move2 :: SU2Member -> SU2Member -> Move ()
move2 :: SU2Member -> SU2Member -> Move ()
move2 SU2Member
p1 SU2Member
p2 = do f  <- (Status -> SLocation) -> Move SLocation
forall a. (Status -> a) -> Move a
peek Status -> SLocation
flash
                 l1 <- whereIs p1
                 l2 <- whereIs p2
                 -- only do the move if both people and the flash are at the same side
                 whenS (f .== l1 .&& f .== l2) $ do bumpTime2 p1 p2
                                                    xferFlash
                                                    xferPerson p1
                                                    xferPerson p2

-------------------------------------------------------------
-- * Actions
-------------------------------------------------------------

-- | A move action is a sequence of triples. The first component is symbolically
-- True if only one member crosses. (In this case the third element of the triple
-- is irrelevant.) If the first component is (symbolically) False, then both members
-- move together
type Actions = [(SBool, SU2Member, SU2Member)]

-- | Run a sequence of given actions.
run :: Actions -> Move [Status]
run :: Actions -> Move [Status]
run = ((SBool, SU2Member, SU2Member) -> StateT Status Identity Status)
-> Actions -> Move [Status]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM (SBool, SU2Member, SU2Member) -> StateT Status Identity Status
step
 where step :: (SBool, SU2Member, SU2Member) -> StateT Status Identity Status
step (SBool
b, SU2Member
p1, SU2Member
p2) = SBool -> Move () -> Move () -> Move ()
forall a. Mergeable a => SBool -> a -> a -> a
ite SBool
b (SU2Member -> Move ()
move1 SU2Member
p1) (SU2Member -> SU2Member -> Move ()
move2 SU2Member
p1 SU2Member
p2) Move ()
-> StateT Status Identity Status -> StateT Status Identity Status
forall a b.
StateT Status Identity a
-> StateT Status Identity b -> StateT Status Identity b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> StateT Status Identity Status
forall s (m :: * -> *). MonadState s m => m s
get

-------------------------------------------------------------
-- * Recognizing valid solutions
-------------------------------------------------------------

-- | Check if a given sequence of actions is valid, i.e., they must all
-- cross the bridge according to the rules and in less than 17 seconds
isValid :: Actions -> SBool
isValid :: Actions -> SBool
isValid Actions
as = Status -> STime
time Status
end STime -> STime -> SBool
forall a. OrdSymbolic a => a -> a -> SBool
.<= STime
17 SBool -> SBool -> SBool
.&& ((SBool, SU2Member, SU2Member) -> SBool) -> Actions -> SBool
forall a. (a -> SBool) -> [a] -> SBool
sAll (SBool, SU2Member, SU2Member) -> SBool
check Actions
as SBool -> SBool -> SBool
.&& [SLocation] -> [SLocation] -> SBool
forall {b}. EqSymbolic b => [b] -> [b] -> SBool
zigZag ([SLocation] -> [SLocation]
forall a. HasCallStack => [a] -> [a]
cycle [SLocation
sThere, SLocation
sHere]) ((Status -> SLocation) -> [Status] -> [SLocation]
forall a b. (a -> b) -> [a] -> [b]
map Status -> SLocation
flash [Status]
states) SBool -> SBool -> SBool
.&& (SLocation -> SBool) -> [SLocation] -> SBool
forall a. (a -> SBool) -> [a] -> SBool
sAll (SLocation -> SLocation -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SLocation
sThere) [Status -> SLocation
lBono Status
end, Status -> SLocation
lEdge Status
end, Status -> SLocation
lAdam Status
end, Status -> SLocation
lLarry Status
end]
  where check :: (SBool, SU2Member, SU2Member) -> SBool
check (SBool
s, SU2Member
p1, SU2Member
p2) =   (SBool -> SBool
sNot SBool
s SBool -> SBool -> SBool
.=> SU2Member
p1 SU2Member -> SU2Member -> SBool
forall a. OrdSymbolic a => a -> a -> SBool
.> SU2Member
p2)       -- for two person moves, ensure first person is "larger"
                          SBool -> SBool -> SBool
.&& (SBool
s      SBool -> SBool -> SBool
.=> SU2Member
p2 SU2Member -> SU2Member -> SBool
forall a. EqSymbolic a => a -> a -> SBool
.== SU2Member
sBono)   -- for one person moves, ensure second person is always "bono"
        states :: [Status]
states = Move [Status] -> Status -> [Status]
forall s a. State s a -> s -> a
evalState (Actions -> Move [Status]
run Actions
as) Status
start
        end :: Status
end = [Status] -> Status
forall a. HasCallStack => [a] -> a
last [Status]
states
        zigZag :: [b] -> [b] -> SBool
zigZag [b]
reqs [b]
locs = [SBool] -> SBool
sAnd ([SBool] -> SBool) -> [SBool] -> SBool
forall a b. (a -> b) -> a -> b
$ (b -> b -> SBool) -> [b] -> [b] -> [SBool]
forall a b c. (a -> b -> c) -> [a] -> [b] -> [c]
zipWith b -> b -> SBool
forall a. EqSymbolic a => a -> a -> SBool
(.==) [b]
locs [b]
reqs

-------------------------------------------------------------
-- * Solving the puzzle
-------------------------------------------------------------

-- | See if there is a solution that has precisely @n@ steps
solveN :: Int -> IO Bool
solveN :: Int -> IO Bool
solveN Int
n = do String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"Checking for solutions with " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show Int
n String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
" move" String -> ShowS
forall a. [a] -> [a] -> [a]
++ Int -> String
forall {a}. (Eq a, Num a) => a -> String
plu Int
n String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
"."
              let genAct :: SymbolicT IO (SBool, SU2Member, SU2Member)
genAct = do b  <- SymbolicT IO SBool
forall a. SymVal a => Symbolic (SBV a)
free_
                              p1 <- free_
                              p2 <- free_
                              return (b, p1, p2)
              res <- SymbolicT IO SBool -> IO AllSatResult
forall a. Satisfiable a => a -> IO AllSatResult
allSat (SymbolicT IO SBool -> IO AllSatResult)
-> SymbolicT IO SBool -> IO AllSatResult
forall a b. (a -> b) -> a -> b
$ Actions -> SBool
isValid (Actions -> SBool) -> SymbolicT IO Actions -> SymbolicT IO SBool
forall a b. (a -> b) -> SymbolicT IO a -> SymbolicT IO b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
`fmap` (Int -> SymbolicT IO (SBool, SU2Member, SU2Member))
-> [Int] -> SymbolicT IO Actions
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
forall (m :: * -> *) a b. Monad m => (a -> m b) -> [a] -> m [b]
mapM (SymbolicT IO (SBool, SU2Member, SU2Member)
-> Int -> SymbolicT IO (SBool, SU2Member, SU2Member)
forall a b. a -> b -> a
const SymbolicT IO (SBool, SU2Member, SU2Member)
genAct) [Int
1..Int
n]
              cnt <- displayModels (sortOn show) disp res
              if cnt == 0 then return False
                          else do putStrLn $ "Found: " ++ show cnt ++ " solution" ++ plu cnt ++ " with " ++ show n ++ " move" ++ plu n ++ "."
                                  return True
  where plu :: a -> String
plu a
v = if a
v a -> a -> Bool
forall a. Eq a => a -> a -> Bool
== a
1 then String
"" else String
"s"
        disp :: Int -> (Bool, [(Bool, U2Member, U2Member)]) -> IO ()
        disp :: Int -> (Bool, [(Bool, U2Member, U2Member)]) -> IO ()
disp Int
i (Bool
_, [(Bool, U2Member, U2Member)]
ss)
         | Int
lss Int -> Int -> Bool
forall a. Eq a => a -> a -> Bool
/= Int
n = String -> IO ()
forall a. HasCallStack => String -> a
error (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"Expected " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show Int
n String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
" results; got: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show Int
lss
         | Bool
True     = do String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"Solution #" String -> ShowS
forall a. [a] -> [a] -> [a]
++ Int -> String
forall a. Show a => a -> String
show Int
i String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
":"
                         Bool -> Time -> [(Bool, U2Member, U2Member)] -> IO ()
go Bool
False Time
0 [(Bool, U2Member, U2Member)]
ss
                         () -> IO ()
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return ()
         where lss :: Int
lss  = [(Bool, U2Member, U2Member)] -> Int
forall a. [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [(Bool, U2Member, U2Member)]
ss
               go :: Bool -> Time -> [(Bool, U2Member, U2Member)] -> IO ()
go Bool
_ Time
t []                   = String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ String
"Total time: " String -> ShowS
forall a. [a] -> [a] -> [a]
++ Time -> String
forall a. Show a => a -> String
show Time
t
               go Bool
l Time
t ((Bool
True,  U2Member
a, U2Member
_):[(Bool, U2Member, U2Member)]
rest) = do String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Time -> String
forall a. Show a => a -> String
sh2 Time
t String -> ShowS
forall a. [a] -> [a] -> [a]
++ Bool -> String
shL Bool
l String -> ShowS
forall a. [a] -> [a] -> [a]
++ U2Member -> String
forall a. Show a => a -> String
show U2Member
a
                                                Bool -> Time -> [(Bool, U2Member, U2Member)] -> IO ()
go (Bool -> Bool
not Bool
l) (Time
t Time -> Time -> Time
forall a. Num a => a -> a -> a
+ U2Member -> Time
crossTime U2Member
a) [(Bool, U2Member, U2Member)]
rest
               go Bool
l Time
t ((Bool
False, U2Member
a, U2Member
b):[(Bool, U2Member, U2Member)]
rest) = do String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Time -> String
forall a. Show a => a -> String
sh2 Time
t String -> ShowS
forall a. [a] -> [a] -> [a]
++ Bool -> String
shL Bool
l String -> ShowS
forall a. [a] -> [a] -> [a]
++ U2Member -> String
forall a. Show a => a -> String
show U2Member
a String -> ShowS
forall a. [a] -> [a] -> [a]
++ String
", " String -> ShowS
forall a. [a] -> [a] -> [a]
++ U2Member -> String
forall a. Show a => a -> String
show U2Member
b
                                                Bool -> Time -> [(Bool, U2Member, U2Member)] -> IO ()
go (Bool -> Bool
not Bool
l) (Time
t Time -> Time -> Time
forall a. Num a => a -> a -> a
+ U2Member -> Time
crossTime U2Member
a Time -> Time -> Time
forall a. Ord a => a -> a -> a
`max` U2Member -> Time
crossTime U2Member
b) [(Bool, U2Member, U2Member)]
rest
               sh2 :: p -> String
sh2 p
t = let s :: String
s = p -> String
forall a. Show a => a -> String
show p
t in if String -> Int
forall a. [a] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length String
s Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
< Int
2 then Char
' ' Char -> ShowS
forall a. a -> [a] -> [a]
: String
s else String
s
               shL :: Bool -> String
shL Bool
False = String
" --> "
               shL Bool
True  = String
" <-- "

-- | Solve the U2-bridge crossing puzzle, starting by testing solutions with
-- increasing number of steps, until we find one. We have:
--
-- >>> solveU2
-- Checking for solutions with 1 move.
-- Checking for solutions with 2 moves.
-- Checking for solutions with 3 moves.
-- Checking for solutions with 4 moves.
-- Checking for solutions with 5 moves.
-- Solution #1:
--  0 --> Edge, Bono
--  2 <-- Bono
--  3 --> Larry, Adam
-- 13 <-- Edge
-- 15 --> Edge, Bono
-- Total time: 17
-- Solution #2:
--  0 --> Edge, Bono
--  2 <-- Edge
--  4 --> Larry, Adam
-- 14 <-- Bono
-- 15 --> Edge, Bono
-- Total time: 17
-- Found: 2 solutions with 5 moves.
--
-- Finding all possible solutions to the puzzle.
solveU2 :: IO ()
solveU2 :: IO ()
solveU2 = Int -> IO ()
go Int
1
 where go :: Int -> IO ()
go Int
i = do p <- Int -> IO Bool
solveN Int
i
                 unless p $ go (i+1)