Hello

.gitignore

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+/ve

pyproject.toml

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+[tool.ruff]
+
+line-length = 88
+
+[tool.pylsp]
+
+line-length = 88

requirements.txt

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+numpy == 2.*

sim.py

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+# This program assumes a tick interval of 1 minute. That is, the events are
+# made to evolve on a one dimensional time grid of 1 minute resolution.
+
+import os
+import multiprocessing as mp
+import typing as T
+
+import numpy as np
+
+
+DEFAULT_SEED = 1312
+DEFAULT_PARALLELISM = mp.cpu_count()
+DEFAULT_RUNS = 1000
+
+
+class Simulation(object):
+    def __init__(
+        self,
+        queue: mp.Queue,
+        runs: int,
+        generator: np.random.Generator,
+        snail_len: float,
+        wheel_len: float,
+        wheel_dist: float,
+        road_len: float,
+        snail_speed: float,
+    ) -> None:
+        self.queue = queue
+        self.runs = runs
+        self.generator = generator
+        self.snail_len = snail_len / road_len
+        self.wheel_len = wheel_len / road_len
+        self.wheel_dist = wheel_dist / road_len
+        self.starting_wheel_pos_mul = (road_len - 2 * wheel_len - wheel_dist) / road_len
+        self.snail_speed = snail_speed / road_len
+
+    def is_car_passing(self) -> bool:
+        """
+        The probability a car is passing every minute is assumed to be
+        uniformly distributed in the hour. Having 10 cars/hour, and a tick
+        interval of 1 minute we have:
+
+        P_car = 10/60 ~ 0.1666666
+        """
+        return self.generator.random() <= 1 / 6
+
+    def is_dead(self, x: float) -> bool:
+        """
+        The probability of the car hitting the snail being at x is the
+        probability of any of the pieces of the two wheels to be in the
+        interval [x-snail_len, x].
+
+        |                                                       |
+        |-------------------------------------------------------| road_len
+        |------- x                                              |
+        |    @@@                                                |
+        |----    x-snail_len                                    |
+        |                                                       |
+        |                                                       |
+        |---------- x_wheel_pos                                 |
+        |          XXXXXXX--(wheel_dist)--XXXXXXX               |
+        |          -------   wheel_len    -------               |
+        |                                                       |
+        """
+
+        x_wheel_pos = self.generator.random() * self.starting_wheel_pos_mul
+        first_wheel_hit = self.intersect(x, x_wheel_pos)
+        second_wheel_hit = self.intersect(x, x_wheel_pos + self.wheel_dist)
+
+        return first_wheel_hit or second_wheel_hit
+
+    def intersect(self, x_snail: float, x_wheel: float) -> bool:
+        return (x_wheel > x_snail - self.snail_len) and (x_wheel < x_snail)
+
+    def _run(self) -> bool:
+        """
+        This is the entrypoint of the single run of a simulation. The result is
+        a boolean indicating whether the snail did survive the road crossing.
+
+        The simulation ends if the snail manages to run all the
+        road_len+snail_len distance.
+        """
+
+        win_dist = 1 + self.snail_len
+        x = 0
+        while x < win_dist:
+            if self.is_car_passing() and self.is_dead(x):
+                return False
+
+            x += self.snail_speed
+
+        return True
+
+    def run(self) -> None:
+        for i in range(self.runs):
+            self.queue.put(self._run())
+        self.queue.close()
+
+
+def clear():
+    os.system("cls" if os.name == "nt" else "clear")
+
+
+def print_result(runs: int, survived: int) -> None:
+    print(f"total runs: {runs}")
+    print(f"result: {survived/runs}")
+
+
+def gather(q: mp.Queue()) -> None:
+    runs = 0
+    survived = 0
+    while True:
+        data = q.get()
+        if data is None:
+            break
+        runs += 1
+        if data:
+            survived += 1
+
+    print("============= FINAL RESULT ============")
+    print_result(runs, survived)
+
+
+if __name__ == "__main__":
+    seed = int(os.getenv("SEED") or DEFAULT_SEED)
+    procs = int(os.getenv("PARALLELISM") or DEFAULT_PARALLELISM)
+    runs = int(os.getenv("RUNS") or DEFAULT_RUNS)
+
+    q = mp.Queue()
+
+    seq = np.random.default_rng(int(seed))
+    rng_stream = seq.spawn(int(procs))
+
+    snail_len = 5  # 5 cm
+    wheel_len = 20  # 20 cm
+    wheel_dist = 150  # 1.5 m
+    road_len = 500  # 5 m
+    snail_speed = 1  # 1 cm/min
+
+    sims = [
+        Simulation(
+            q,
+            runs,
+            rng,
+            snail_len,
+            wheel_len,
+            wheel_dist,
+            road_len,
+            snail_speed,
+        )
+        for rng in rng_stream
+    ]
+
+    processes: T.List[mp.Process] = [mp.Process(target=s.run, args=()) for s in sims]
+
+    collector = mp.Process(target=gather, args=(q,))
+    collector.start()
+
+    for p in processes:
+        p.start()
+
+    for p in processes:
+        p.join()
+        print(f"process finished: {p}")
+
+    q.put(None)
+    collector.join()