wta: Swap algorithm if transition count is too large

The existing algorithm for generating unique transitions is inefficient if the
transition count is close to the maximal number of transitions. This now
switches to a different algorithm if the transition count is above 70% of the
maximum.

src/random-wta/Generator.hs

@@ -15,6 +15,7 @@ import           Control.Arrow                  ( (&&&) )
 import qualified Data.Map.Strict            as M
 import qualified Data.Set                   as S
 import           Data.Coerce
+import           Data.Ratio
 
 import           Types                   hiding ( spec )
 import           Probability
@@ -98,13 +99,28 @@ genTransitions = do
 
 -- TODO Implement (Random IndexedTransition)
 uniqueTransitions :: Int -> IndexedTransition -> IO [IndexedTransition]
-uniqueTransitions num (IndexedTransition.Index max) = helper S.empty num
+uniqueTransitions num idxMax@(IndexedTransition.Index max)
+  | fromIntegral num < fromIntegral max * (7%10) = uniqueTransitionsByGeneration num idxMax
+  | otherwise       = uniqueTransitionsByElimination num idxMax
+
+uniqueTransitionsByGeneration :: Int -> IndexedTransition -> IO [IndexedTransition]
+uniqueTransitionsByGeneration num (IndexedTransition.Index max) = helper S.empty num
   where
     helper m 0 = return $ coerce (S.toList m)
     helper m c = do
       x <- randomRIO (0, max-1)
       if x `S.member` m then helper m c else helper (S.insert x m) (c-1)
 
+uniqueTransitionsByElimination :: Int -> IndexedTransition -> IO [IndexedTransition]
+uniqueTransitionsByElimination num (IndexedTransition.Index max) = helper whole num
+  where
+    helper free 0 = return $ coerce (S.toList (S.difference whole free))
+    helper free c = do
+      idx <- randomRIO (0, S.size free - 1)
+      let x = S.elemAt idx free
+      helper (S.delete x free) (c-1)
+
+    whole = S.fromList [0..max-1]
 
 genTransitions' :: Int -> Generator m (Vector (Vector (Transition m)))
 genTransitions' numTransitions = do