fix: use average instead of max as evaluation function as it gives a slightly more efficient algorithm

Proj2.hs

@@ -40,7 +40,7 @@
 --
 -- To pick the best next guess, we filter the game state to contain only
 -- targets that are consistent with the received feedback from the previous
--- guess. We then calculate, for each candidate, the maximum number of guesses
+-- guess. We then calculate, for each candidate, the average number of guesses
 -- that would remain if we chose it as the next guess. We can then choose the
 -- candidate that has the smallest of this number as the next guess.
 
@@ -54,8 +54,9 @@ module Proj2
   )
 where
 
+import Data.Function (on)
 import Data.List
-import Data.Map qualified as M
+import Data.Map qualified as Map
 import Data.Ord (comparing)
 import Data.Set qualified as S
 
@@ -178,8 +179,8 @@ initialGuess = (bestFirstGuess, allChords)
 -- strategy:
 --  1. reduce the size of the search space by removing all guesses inconsistent
 --     with the answer received for the previous guess.
---  2. for each candidate, calculate the worst case number of remaining target
---  3. choose the candidate with the smallest of this number
+--  2. for each candidate, calculate the average number of remaining targets
+--  3. choose the candidate with the smallest average
 --
 nextGuess :: ([Pitch], GameState) -> (Int, Int, Int) -> ([Pitch], GameState)
 nextGuess (prevGuess, state) prevFeedback = (chosen, newState)
@@ -190,11 +191,12 @@ nextGuess (prevGuess, state) prevFeedback = (chosen, newState)
     scored = map (\x -> (x, score x candidates)) candidates
     candidates = filter (\x -> prevFeedback == feedback prevGuess x) state
 
-    -- maximum number of possible targets per candidate
-    score candidate candidates =
-      maximum $
-        M.elems $
-          M.fromListWith
+    -- average number of possible targets per candidate
+    score candidate candidates = ((/) `on` fromIntegral) (sum l) (length l)
+      where
+        l =
+          Map.elems $
+            Map.fromListWith
               (+)
               [(feedback candidate target, 1) | target <- candidates]