Implement day 22 part 2

2019/aoc2019/day22.py

@@ -32,7 +32,7 @@ def shuffle(instructions: List[str], deck_size: int) -> List[int]:
     return deck
 
 
-def part1(data: TextIO):
+def part1(data: TextIO) -> int:
     instructions = [line.strip() for line in data]
 
     result = shuffle(instructions, 10007)
@@ -42,3 +42,49 @@ def part1(data: TextIO):
             return i
 
     raise Exception("Did not find card")
+
+
+def modpow(a: int, b: int, m: int) -> int:
+    assert b >= 0
+
+    result = 1
+    n = a
+
+    while b > 0:
+        if b % 2:
+            result = (result * n) % m
+
+        b //= 2
+        n = (n * n) % m
+
+    return result
+
+
+def inverse(a: int, m: int) -> int:
+    """ Computes the modulo multiplicative inverse """
+    return modpow(a, m - 2, m)
+
+
+def part2(data: TextIO) -> int:
+    deck_size = 119315717514047
+    shuffles = 101741582076661
+
+    a, b = 1, 0
+
+    for line in data:
+        parts = line.split(' ')
+        if 'new stack' in line:
+            la, lb = -1, -1
+        elif parts[0] == 'deal':
+            la, lb = int(parts[-1]), 0
+        else:
+            la, lb = 1, -int(parts[-1])
+
+        a = (la * a) % deck_size
+        b = (la * b + lb) % deck_size
+
+    final_a = modpow(a, shuffles, deck_size)
+    final_b = ((b * (final_a - 1)) * inverse(a - 1, deck_size)) % deck_size
+
+    return ((2020 - final_b) * inverse(final_a, deck_size)) % deck_size
+