2018: d12: ex2: add solution

2018/d12/ex2/ex2.py

@@ -0,0 +1,51 @@
+#!/usr/bin/env python
+
+import sys
+
+
+def solve(input: str) -> int:
+    def parse_rules(input: list[str]) -> dict[str, str]:
+        return {key: val for key, val in map(lambda s: s.split(" => "), input)}
+
+    def parse(input: str) -> tuple[str, dict[str, str]]:
+        init, rules = input.split("\n\n")
+        return init.split(": ")[1], parse_rules(rules.splitlines())
+
+    def step(state: str, rules: dict[str, str]) -> str:
+        state = "...." + state + "...."
+        return "".join(
+            rules.get(state[i - 2 : i + 2 + 1], ".") for i in range(2, len(state) - 2)
+        )
+
+    def count_pots(state: str) -> int:
+        return sum(
+            i for i, c in enumerate(state, start=-(len(state) - 100) // 2) if c == "#"
+        )
+
+    def get_diffs(state: str, rules: dict[str, str], iterations: int) -> list[int]:
+        res: list[int] = [count_pots(state)]
+        prev_count = res[0]
+        for _ in range(iterations):
+            state = step(state, rules)
+            delta = count_pots(state) - prev_count
+            prev_count += delta
+            res.append(delta)
+        return res
+
+    state, rules = parse(input)
+    assert len(state) == 100  # Sanity check for `count_pots`
+
+    STEPS = 1000
+    deltas = get_diffs(state, rules, STEPS)
+    # Change in deltas gets into a steady state after some time
+    average_delta = sum(deltas[-100:]) // 100
+    return sum(deltas) + (50000000000 - STEPS) * average_delta
+
+
+def main() -> None:
+    input = sys.stdin.read()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()