From d85baf2a6d39a327ec6c002aa67cfef7865af7c0 Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Tue, 21 Dec 2021 15:04:56 +0100
Subject: [PATCH] 2021: d21: ex2: add solution

---
 2021/d21/ex2/ex2.py | 79 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 79 insertions(+)
 create mode 100755 2021/d21/ex2/ex2.py

diff --git a/2021/d21/ex2/ex2.py b/2021/d21/ex2/ex2.py
new file mode 100755
index 0000000..5184285
--- /dev/null
+++ b/2021/d21/ex2/ex2.py
@@ -0,0 +1,79 @@
+#!/usr/bin/env python
+
+import functools
+import itertools
+import sys
+from typing import Iterable, Iterator, List, NamedTuple, Tuple, TypeVar
+
+T = TypeVar("T")
+
+
+def grouper(iterable: Iterable[T], n: int) -> Iterator[Tuple[T, ...]]:
+    args = [iter(iterable)] * n
+    return itertools.zip_longest(*args)
+
+
+def take(n: int, iterable: Iterable[T]) -> List[T]:
+    return list(itertools.islice(iterable, n))
+
+
+class PlayerStats(NamedTuple):
+    position: int
+    score: int
+
+
+ROLL_TO_UNIVERSES = {
+    3: 1,
+    4: 3,
+    5: 6,
+    6: 7,
+    7: 6,
+    8: 3,
+    9: 1,
+}
+
+WINNING_SCORE = 21
+
+
+def solve(input: List[str]) -> int:
+    def parse() -> Tuple[int, int]:
+        p1, p2 = input[0].split(" ")[-1], input[1].split(" ")[-1]
+        return int(p1), int(p2)
+
+    def do_turn(stats: PlayerStats, roll: int) -> PlayerStats:
+        position, score = stats
+        position = ((position - 1 + roll) % 10) + 1
+        score += position
+        return PlayerStats(position, score)
+
+    @functools.cache
+    def play_universes(p1: PlayerStats, p2: PlayerStats) -> Tuple[int, int]:
+        p1_wins, p2_wins = 0, 0
+
+        # Only 9 different outcomes from a 3d3 roll, with differing probabilities
+        for roll, roll_probability in ROLL_TO_UNIVERSES.items():
+            new_p1 = do_turn(p1, roll)
+            if new_p1.score >= WINNING_SCORE:
+                # Account for differing number of split universes when counting a win
+                p1_wins += roll_probability
+                continue
+
+            # Exchange p1 and p2 roles, count their wins, and account for number of splits
+            new_p2_wins, new_p1_wins = play_universes(p2, new_p1)
+            p1_wins += new_p1_wins * roll_probability
+            p2_wins += new_p2_wins * roll_probability
+
+        return p1_wins, p2_wins
+
+    p1, p2 = parse()
+    p1_wins, p2_wins = play_universes(PlayerStats(p1, 0), PlayerStats(p2, 0))
+    return max(p1_wins, p2_wins)
+
+
+def main() -> None:
+    input = [line.strip() for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()