1 files changed, 64 insertions, 0 deletions
diff --git a/bot/exts/evergreen/duck_game.py b/bot/exts/evergreen/duck_game.py
index 561d8a10..b455cc34 100644
--- a/bot/exts/evergreen/duck_game.py
+++ b/bot/exts/evergreen/duck_game.py
@@ -1,8 +1,72 @@
+import random
+from itertools import product
 
 from discord.ext import commands
 
 from bot.bot import Bot
 
+DECK = list(product(*[(0, 1, 2)]*4))
+
+
+class DuckGame:
+    """A class for a single game."""
+
+    def __init__(self,
+                 rows: int = 4,
+                 columns: int = 3,
+                 minimum_solutions: int = 1,
+                 ) -> None:
+        """
+        Take samples from the deck to generate a board.
+
+        Args:
+            rows (int, optional): Rows in the game board. Defaults to 4.
+            columns (int, optional): Columns in the game board. Defaults to 3.
+            minimum_solutions (int, optional): Minimum acceptable number of solutions in the board. Defaults to 1.
+        """
+        self._solutions = None
+        size = rows * columns
+        self.board = random.sample(DECK, size)
+        while len(self.solutions) < minimum_solutions:
+            self.board = random.sample(DECK, size)
+
+    @property
+    def board(self) -> list[tuple[int]]:
+        """Accesses board property."""
+        return self._board
+
+    @board.setter
+    def board(self, val: list[tuple[int]]) -> None:
+        """Erases calculated solutions if the board changes."""
+        self._solution = None
+        self._board = val
+
+    @property
+    def solutions(self) -> None:
+        """Calculate valid solutions and cache to avoid redoing work."""
+        if self._solutions is None:
+            self._solutions = set()
+            for idx_a, card_a in enumerate(self.board):
+                for idx_b, card_b in enumerate(self.board[idx_a+1:], start=idx_a+1):
+                    """
+                        Two points determine a line, and there are exactly 3 points per line in {0,1,2}^4.
+                        The completion of a line will only be a duplicate point if the other two points are the same,
+                        which is prevented by the triangle iteration.
+                    """
+                    completion = tuple(feat_a if feat_a == feat_b else 3-feat_a-feat_b
+                                       for feat_a, feat_b in zip(card_a, card_b)
+                                       )
+                    try:
+                        idx_c = self.board.index(completion)
+                    except ValueError:
+                        continue
+
+                    # Indices within the solution are sorted to detect duplicate solutions modulo order.
+                    solution = tuple(sorted((idx_a, idx_b, idx_c)))
+                    self._solutions.add(solution)
+
+        return self._solutions
+
 
 class DuckGamesDirector(commands.Cog):
     """A cog for running Duck Duck Duck Goose games."""