canonicalize tableaus

The solver was wasting incredible amounts of time shuffling cards around
between equivalent states. Picture two long runs with an empty column: it
would try every permutation of runs on columns, then break up the runs to try
every permutation of cards in runs or the empty column. Then it would slightly
move some other card in another column and do it all again.

Sorting the cells and columns makes for an incredible reduction in the number
of states enumerated during a solving. Putting Dragon before Suited puts them
on the left because freeing them up for collection is a very positive move and
possibleMoves generates Pack commands from left-to-right.

src/Main.hs

@@ -44,7 +44,7 @@ instance Show Rank where
   show Nine  = "9"
 
 
-data Card = Flower | Suited Suit Rank | Dragon Suit
+data Card = Flower | Dragon Suit | Suited Suit Rank
   deriving (Eq, Ord)
 
 instance Show Card where
@@ -368,9 +368,12 @@ takeCardFromCol cols i = (card, newCols)
     newCol = drop 1 fromCol
     newCols = replaceIndex i newCol cols
 
+canonicalize :: Tableau -> Tableau
+canonicalize (Tableau cells fl fo cols) = Tableau (sort cells) fl fo (sort cols)
+
 -- applys a player's move and automatically builds if possible
 applyT :: Tableau -> Move -> Tableau
-applyT t m = automaticBuild (applied t m)
+applyT t m = canonicalize $ automaticBuild (applied t m)
   where
     applied (Tableau cells fl fo cols) (MoveFromColumnToCell coli celli) = Tableau newCells fl fo newCols
       where
@@ -509,7 +512,7 @@ outcomes ls g
   where
     seen = previous g -- [Tableau]
     now = last seen
-    moves = possibleMoves (trace (show (moveCount g) ++ " " ++ show now) now)
+    moves = possibleMoves (trace (show (moveCount g) ++ " " show (length ls) ++ " " ++ show now) now)
     foo :: Losses -> Tableau -> Bool
     foo ls' tab = tab `Set.notMember` ls' && tab `notElem` seen
     bar :: Losses -> [Move] -> Either Losses (Game, Losses)