From 8ce97fe1fffb331d0286754a45192a4f60c653de Mon Sep 17 00:00:00 2001
From: Bruno BELANYI <bruno@belanyi.fr>
Date: Sat, 14 Dec 2024 11:22:58 -0500
Subject: [PATCH] 2024: d14: ex2: add solution

---
 2024/d14/ex2/ex2.py | 80 +++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 80 insertions(+)
 create mode 100755 2024/d14/ex2/ex2.py

diff --git a/2024/d14/ex2/ex2.py b/2024/d14/ex2/ex2.py
new file mode 100755
index 0000000..65fc259
--- /dev/null
+++ b/2024/d14/ex2/ex2.py
@@ -0,0 +1,80 @@
+#!/usr/bin/env python
+
+import dataclasses
+import functools
+import itertools
+import sys
+from typing import Literal, NamedTuple
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+
+
+@dataclasses.dataclass
+class Robot:
+    pos: Point
+    vel: Point
+
+    def step(self, dims: Point, delta: int = 1) -> "Robot":
+        x, y = self.pos.x + self.vel.x * delta, self.pos.y + self.vel.y * delta
+        return Robot(
+            Point(x % dims.x, y % dims.y),
+            self.vel,
+        )
+
+
+def solve(input: str) -> int:
+    def parse_robot(input: str) -> Robot:
+        pos, vel = map(lambda s: s.split("=")[1], input.split(" "))
+        return Robot(
+            Point(*map(int, pos.split(","))),
+            Point(*map(int, vel.split(","))),
+        )
+
+    def parse(input: list[str]) -> list[Robot]:
+        return [parse_robot(line) for line in input]
+
+    def find_tree(robots: list[Robot], dims: Point) -> int:
+        def compute_positions(step: int) -> list[Point]:
+            return [robot.step(dims, step).pos for robot in robots]
+
+        def compute_variance(values: list[int]) -> float:
+            avg = sum(values) / len(values)
+            variance = sum((n - avg) ** 2 for n in values) / len(values)
+            return variance
+
+        def cluster_variance(step: int, dimension: Literal["x", "y"]) -> float:
+            return compute_variance(
+                [getattr(p, dimension) for p in compute_positions(step)]
+            )
+
+        # The tree should have robots clustered together in X and Y
+        cluster_x = min(
+            range(dims.x),
+            key=functools.partial(cluster_variance, dimension="x"),
+        )
+        cluster_y = min(
+            range(dims.y),
+            key=functools.partial(cluster_variance, dimension="y"),
+        )
+
+        # And those clusers should repeat modulo each dimension
+        for i in itertools.count(cluster_x, step=dims.x):
+            if i % dims.y == cluster_y:
+                return i
+        assert False  # Sanity check
+
+    robots = parse(input.splitlines())
+    dims = Point(101, 103)
+    return find_tree(robots, dims)
+
+
+def main() -> None:
+    input = sys.stdin.read()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()