From 0326eafd5205b9e008f62ea237ff3cd1941e7658 Mon Sep 17 00:00:00 2001
From: xiaoxiae <tomas@slama.dev>
Date: Thu, 24 Apr 2025 00:42:21 +0200
Subject: [PATCH] =?UTF-8?q?Python=20=C5=99e=C5=A1en=C3=AD?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 asteracer-python-search/README.md          |     3 +
 asteracer-python-search/__main__.py        |   569 +
 asteracer-python-search/asteracer.py       |   429 +
 asteracer-python-search/marathon/14290.txt | 14291 +++++++++++++++++++
 asteracer-python-search/sprint/1151.txt    |  1152 ++
 asteracer-python-search/test/307.txt       |   308 +
 6 files changed, 16752 insertions(+)
 create mode 100644 asteracer-python-search/README.md
 create mode 100644 asteracer-python-search/__main__.py
 create mode 100644 asteracer-python-search/asteracer.py
 create mode 100644 asteracer-python-search/marathon/14290.txt
 create mode 100644 asteracer-python-search/sprint/1151.txt
 create mode 100644 asteracer-python-search/test/307.txt

diff --git a/asteracer-python-search/README.md b/asteracer-python-search/README.md
new file mode 100644
index 0000000..dc5e695
--- /dev/null
+++ b/asteracer-python-search/README.md
@@ -0,0 +1,3 @@
+# Asteracer v Pythonu
+
+Mělo by stačit spustit `__main__.py`.
diff --git a/asteracer-python-search/__main__.py b/asteracer-python-search/__main__.py
new file mode 100644
index 0000000..4b92259
--- /dev/null
+++ b/asteracer-python-search/__main__.py
@@ -0,0 +1,569 @@
+"""Tom's solution to Asteracer. Moves on the vertices of the asteroid graph by simulating all angles."""
+import os
+from typing import Optional
+
+import drawsvg as draw
+import networkx as nx
+import numpy as np
+
+from asteracer import *
+
+directional_instructions_cache = {}
+
+Vertex = tuple[int, int]
+
+
+def load_asteroid_graph(path: str):
+    with open(path) as file:
+        lines = [line.strip() for line in file.readlines()]
+
+    # Filter out comments and empty lines
+    contents = [line for line in lines if line and not line.startswith('#')]
+
+    iter_lines = iter(contents)
+    first_line = list(map(int, next(iter_lines).split()))
+    n_racer, n_asteroid, n_goal, m = first_line
+
+    vertices = []
+    edges = []
+    vertex_objects = []
+
+    # Load vertices
+    for i in range(n_racer + n_asteroid + n_goal):
+        line = list(map(int, next(iter_lines).split()))
+        vertices.append((line[0], line[1]))
+
+        if i < n_racer:
+            vertex_objects.append(('S', i))
+        elif i < (n_racer + n_asteroid):
+            vertex_objects.append(('A', line[2]))
+        else:
+            vertex_objects.append(('G', line[2]))
+
+    # Load edges
+    for _ in range(m):
+        line = list(map(int, next(iter_lines).split()))
+        edges.append((line[0], line[1]))
+
+    return vertices, edges, vertex_objects
+
+
+def _yield_points_at_distance(x: float, y: float, r: float, n: int):
+    """Generate n points uniformly at distance r from the coordinates (x, y)."""
+    for i in range(n):
+        t = (i / n) * np.pi * 2
+        yield x + np.cos(t) * r, y + np.sin(t) * r
+
+
+def _get_directional_instructions(
+        n: int = 1000,
+        sort_by_angle_to: tuple[float, float] = None,
+        limit_angle=None
+) -> list[Instruction]:
+    """Generate normalized instructions in at most n different angles with maximum velocity."""
+    instructions = []
+
+    if n in directional_instructions_cache:
+        instructions = directional_instructions_cache[n]
+
+    else:
+        for point in _yield_points_at_distance(0, 0, 127, n):
+            i1 = Instruction(*point)
+
+            if i1 in instructions:
+                continue
+
+            for i2 in instructions:
+                if np.sign(i1.vx) == np.sign(i2.vx) and abs(i1.vx) <= abs(i2.vx) \
+                        and np.sign(i1.vy) == np.sign(i2.vy) and abs(i1.vy) <= abs(i2.vy):
+                    break
+            else:
+                instructions.append(i1)
+
+        directional_instructions_cache[n] = instructions
+
+    def instr_vector_angle(i_from: Instruction, v_to: tuple[float, float]) -> float:
+        """The angle between an instruction and a vector."""
+        i_vec = np.array([i_from.vx, i_from.vy])
+        o_vec = np.array(v_to)
+        return (1 - np.dot(i_vec, o_vec) / (np.linalg.norm(i_vec) * np.linalg.norm(o_vec))) / 2
+
+    # possibly sort by an angle to a given instruction
+    if sort_by_angle_to:
+        instructions = sorted(instructions, key=lambda x: instr_vector_angle(x, sort_by_angle_to))
+
+        if limit_angle:
+            return [i for i in instructions if abs(instr_vector_angle(i, sort_by_angle_to)) <= limit_angle]
+        else:
+            return instructions
+    else:
+        return instructions
+
+
+def instructions_to_position(
+        simulation: Simulation,
+        position: Vertex,
+        try_ticks=7,
+        max_distance=1.25,
+) -> Optional[list[Instruction]]:
+    """Return a sequence of instructions that brings us the closest to the provided coordinates.
+    Returns None if there is no such set that brings us at most max_distance * racer_radius away."""
+    x, y = position
+
+    best_distance = float('inf')
+    best_instructions = None
+
+    def is_safe(simulation: Simulation) -> bool:
+        """Returns True if the racer has a sequence of instructions to not crash at this stage of the simulation."""
+        simulation.push()
+        for instruction in _get_directional_instructions(10):
+            simulation.apply()
+
+            for _ in range(try_ticks):
+                result = simulation.tick(instruction)
+
+                if result & TickFlag.COLLIDED:
+                    break
+            else:
+                simulation.pop()
+                return True
+
+        simulation.pop()
+        return False
+
+    simulation.push()
+    for inst in _get_directional_instructions(
+            sort_by_angle_to=(x - int(simulation.racer.x), y - int(simulation.racer.y)),
+            limit_angle=0.5
+    ):
+        simulation.apply()
+        started_improving = False
+        prev_dist = 0
+
+        i = 0
+        while True:
+            result = simulation.tick(inst)
+
+            if result & TickFlag.COLLIDED:
+                break
+
+            distance = euclidean_distance(simulation.racer.x, simulation.racer.y, x, y)
+
+            # if we're closer than before, we started improving
+            if distance < prev_dist:
+                started_improving = True
+
+            # if we've started improving but are now getting worse, terminate this instruction
+            if started_improving and distance > prev_dist:
+                break
+
+            prev_dist = distance
+
+            # if we improved and are safe, save results
+            if distance < best_distance and is_safe(simulation):
+                best_distance = distance
+                best_instructions = [inst] * i
+
+            i += 1
+
+    simulation.pop()
+
+    if best_distance > max_distance * simulation.racer.radius:
+        return None
+
+    return best_instructions
+
+
+def get_preview(simulation: Simulation, size=1000):
+    """Generate preview of the simulation as an SVG."""
+    d = draw.Drawing(size, size, origin='center')
+
+    # background
+    d.append(
+        draw.Rectangle(
+            -size / 2, -size / 2,
+            size, size,
+            fill="White"
+        )
+    )
+
+    def draw_circles(circles: list[Asteroid | Goal | Racer], color: str):
+        """Draw a circle with a specific color on the SVG."""
+        s = simulation.bounding_box.width() / size
+
+        for i, circle in enumerate(circles):
+            d.append(draw.Circle(circle.x / s, circle.y / s, circle.radius / s, fill=color, stroke=color))
+
+    draw_circles(simulation.asteroids, "Black")
+    draw_circles([g for i, g in enumerate(simulation.goals) if simulation.reached_goals[i]], "LightGreen")
+    draw_circles([g for i, g in enumerate(simulation.goals) if not simulation.reached_goals[i]], "Red")
+    draw_circles([simulation.racer], "Gray")
+
+    return d
+
+
+def get_solution_preview(
+        simulation: Simulation,
+        simulation_path: Optional[list[Vertex]],
+        color: str = "Green"
+) -> draw.Drawing:
+    """Return an SVG object with the solution graph, possibly with the simulation too."""
+    d = get_preview(simulation)
+    s = simulation.bounding_box.width() / d.width
+
+    def draw_path(path, color, stroke_width, stroke_opacity) -> draw.Path:
+        p = draw.Path(stroke_width=stroke_width, stroke=color, opacity=stroke_opacity, fill_opacity=0)
+
+        p.M(path[0][0] / s, path[0][1] / s)
+        for i in range(1, len(path)):
+            p.L(path[i][0] / s, path[i][1] / s)
+        d.append(p)
+
+    if simulation_path:
+        d.append(draw_path(simulation_path, color, simulation.racer.radius / (s * 2), 1))
+
+    return d
+
+
+def get_checkpoints_path(
+        simulation, vertices, edges, goal_vertices,
+        longest_edges,
+):
+    """Get a path that the rocket should follow to obtain all goals."""
+
+    def astar_heuristic(p1, p2):
+        return np.linalg.norm(np.array(p1) - np.array(p2))
+
+    def perturb_shortest_path(G, best_path, penalty_factor=2.0):
+        """ Perturbs the shortest path by increasing the weight of a random edge. """
+        if len(best_path) < 2:
+            return best_path  # No modification possible
+        
+        # Randomly choose an edge along the best path
+        idx = random.randint(2, len(best_path) - 3)
+        u, v = best_path[idx], best_path[idx + 1]
+
+        if G.has_edge(u, v):
+            original_weight = G[u][v].get("weight", 1.0)
+            G[u][v]["weight"] = original_weight * penalty_factor
+            if G.has_edge(v, u):  # If the graph is undirected
+                G[v][u]["weight"] = original_weight * penalty_factor
+
+        perturbed_path = nx.astar_path(G, best_path[0], best_path[-1], heuristic=astar_heuristic)
+
+        return perturbed_path
+
+    # convert vertices, edges to nx.Graph
+    G = nx.Graph()
+    for v in vertices:
+        G.add_node(v)
+    for u, v in edges:
+        G.add_edge(u, v, weight=np.linalg.norm(np.array(u) - np.array(v)))
+
+    # for more than 1 goal, we have to solve TSP (at least approximately)
+    if len(simulation.goals) > 1:
+        G_tsp = nx.DiGraph()
+
+        tsp_vertices = [(simulation.racer.x, simulation.racer.y)]
+
+        for g in simulation.goals:
+            tsp_vertices.append((g.x, g.y))
+            G_tsp.add_node(tsp_vertices[-1])
+
+        count = 0
+        for i, u in enumerate(tsp_vertices):
+            for v in tsp_vertices[i + 1:]:
+                print(f"TSP: building graph {count + 1}/{len(tsp_vertices) * (len(tsp_vertices) - 1) // 2}")
+                w = nx.astar_path_length(G, u, v, heuristic=astar_heuristic)
+                G_tsp.add_edge(u, v, weight=w)
+                G_tsp.add_edge(v, u, weight=w)
+
+                count += 1
+
+        print(f"TSP: graph built")
+
+        # nx doesn't play nice with infinite values, but this might as well be
+        INF = 100000000000
+
+        # we solve TSP by adding a hack vertex to force us to try all possible ending vertices
+        # this means that we have to solve #number_of_vertices instances of TSP
+        G_tsp.add_node("hack")
+        G_tsp.add_edge(vertices[0], "hack", weight=0)
+        G_tsp.add_edge("hack", vertices[0], weight=INF)
+
+        best_cost = float('inf')
+        best_path = None
+
+        for i, g in enumerate(simulation.goals):
+            print(f"TSP: solving {i + 1}/{len(simulation.goals)}")
+
+            for g_hack in simulation.goals:
+                v = (g_hack.x, g_hack.y)
+                G_tsp.add_edge("hack", v, weight=0 if g is g_hack else INF)
+                G_tsp.add_edge(v, "hack", weight=INF)
+
+            path = nx.approximation.simulated_annealing_tsp(G_tsp, init_cycle="greedy")
+            path.pop()
+
+            cost = 0
+            for j in range(len(path)):
+                cost += G_tsp[path[j - 1]][path[j]]["weight"]
+
+            for g_hack in simulation.goals:
+                v = (g_hack.x, g_hack.y)
+                G_tsp.remove_edge("hack", v)
+                G_tsp.remove_edge(v, "hack")
+
+            path = list(reversed(path))
+            j = path.index("hack")
+            path.remove("hack")
+            path = path[j:] + path[:j]
+
+            assert len(path) == len(simulation.goals) + 1, "Not all goals visited!"
+
+            if cost < best_cost:
+                best_path = path
+                best_cost = cost
+                print(f"TSP: new optimum of length {best_cost}")
+
+        path = [(int(simulation.racer.x), int(simulation.racer.y))]
+        for i in range(len(best_path) - 1):
+            path += nx.astar_path(G, best_path[i], best_path[i + 1], heuristic=astar_heuristic)[1:]
+
+        # last vertex is a center of some goal
+        path = path[:-1]
+
+        # shorten the path by cutting out vertices
+        while True:
+            # try to remove vertices for goals
+            for i in range(len(path) - 2):
+                if not G.has_edge(path[i], path[i + 2]):
+                    continue
+
+                # if it's not a part of a goal, we can remove for free
+                if path[i + 1] not in goal_vertices:
+                    path.pop(i + 1)
+                    break
+
+                # if it is and is not the only one, we can remove it too
+                goal_vertices_count = 0
+                for v in path:
+                    if v in goal_vertices and goal_vertices[v] == goal_vertices[path[i + 1]]:
+                        goal_vertices_count += 1
+
+                if goal_vertices_count != 1:
+                    path.pop(i + 1)
+                    break
+            else:
+                break
+
+        # rotate goal vertices (we can take an arbitrary one to get the goal)
+        while True:
+            improved = False
+
+            for i in range(len(path) - 2):
+                u = path[i + 1]
+
+                if u not in goal_vertices:
+                    continue
+
+                for v in vertices:
+                    if v not in goal_vertices:
+                        continue
+
+                    if goal_vertices[u] != goal_vertices[v]:
+                        continue
+
+                    if not G.has_edge(path[i], v) or not G.has_edge(v, path[i + 2]):
+                        continue
+
+                    u_dist = G[path[i]][u]["weight"] + G[u][path[i + 2]]["weight"]
+                    v_dist = G[path[i]][v]["weight"] + G[v][path[i + 2]]["weight"]
+
+                    if u_dist > v_dist:
+                        path = path[:i + 1] + [v] + path[i + 2:]
+                        improved = True
+                        break
+
+            if not improved:
+                break
+
+        # TODO: remove goal vertices entirely if the edge exists and intersects it
+        # TODO: for each goal, attempt to remove vertex and connect astar to next and to previous
+
+        print("Solved with TSP.")
+    else:
+        path = nx.astar_path(
+            G,
+            (simulation.racer.x, simulation.racer.y),
+            (simulation.goals[0].x, simulation.goals[0].y),
+            heuristic=astar_heuristic,
+        )
+
+        path = perturb_shortest_path(G, path, penalty_factor=1000)
+
+        print("Solved with A*.")
+
+    # split long edges
+    while True:
+        split = False
+
+        i = 0
+        while i < len(path) - 1:
+            if euclidean_distance(*path[i], *path[i + 1]) > longest_edges:
+                x = path[i][0] + path[i + 1][0]
+                y = path[i][1] + path[i + 1][1]
+                path.insert(i + 1, (x / 2, y / 2))
+                split = True
+            i += 1
+
+        if not split:
+            break
+
+    return path
+
+
+def finalize_instructions(simulation, instructions):
+    """Finalize the instructions (cut useless ones + extend if the simulation isn't finished)."""
+    simulation.restart()
+    for i, instruction in enumerate(instructions):
+        simulation.tick(instruction)
+
+        # there might be some redundant instructions at the very end
+        if simulation.finished():
+            break
+
+    instructions = instructions[:i + 1]
+
+    # if we ended just before the goal, repeat last instruction
+    simulation.simulate(instructions)
+    i = 0
+    while not simulation.finished():
+        simulation.tick(instruction)
+        instructions.append(instruction)
+        i += 1
+
+        if i > 1000:
+            break
+
+    return instructions
+
+
+def get_solution_path(simulation, instructions):
+    """Generate the path the racer took using the instructions."""
+    simulation.restart()
+    solution_path = [(simulation.racer.x, simulation.racer.y)]
+    for i, instruction in enumerate(instructions):
+        simulation.tick(instruction)
+        solution_path.append((simulation.racer.x, simulation.racer.y))
+
+    return solution_path
+
+
+def solve(simulation, path):
+    """Solve the simulation by following the path."""
+    steps_instructions = []
+    randomize_step_counter = 0
+    i = 1
+    while i < len(path):
+        v = path[i]
+
+        for goal in simulation.goals:
+            if euclidean_distance(goal.x, goal.y, v[0], v[1]) < goal.radius + simulation.racer.radius:
+                is_goal_position = True
+                break
+        else:
+            is_goal_position = False
+
+        print(f"Simulating {i}/{len(path) - 1}{'' if not is_goal_position else ' to goal'}", end=": ", flush=True)
+
+        if randomize_step_counter:
+            print("randomized, ", end="")
+
+            # only move towards the goal
+            if is_goal_position:
+                p2g_vector = np.array([goal.x, goal.y]) - np.array(v)
+                v = (p2g_vector / np.linalg.norm(p2g_vector)) * np.random.normal(0, simulation.racer.radius, 1)
+            else:
+                v = np.array(v) + np.random.normal(0, simulation.racer.radius, 2)
+
+        new_instructions = instructions_to_position(simulation, v, max_distance=2 if not is_goal_position else 0.75)
+
+        if new_instructions is None:
+            if len(steps_instructions) != 0:
+                randomize_step_counter += 1
+
+                i -= randomize_step_counter
+                for _ in range(randomize_step_counter):
+                    steps_instructions.pop()
+
+            print(f"(- backtrack {randomize_step_counter}x)")
+
+            if len(steps_instructions) != 0:
+                simulation.simulate(list(np.hstack(steps_instructions)))
+            else:
+                simulation.restart()
+
+            continue
+        else:
+            randomize_step_counter = max(randomize_step_counter - 1, 0)
+
+        steps_instructions.append(new_instructions)
+        simulation.simulate(list(np.hstack(steps_instructions)))
+
+        print(f"(+ {len(new_instructions)})")
+
+        i += 1
+
+    return finalize_instructions(simulation, list(np.hstack(steps_instructions)))
+
+
+if __name__ == "__main__":
+    iterations = 5000
+
+    for task in ["sprint"]:
+        print(f"Solving {task} ({iterations} attempts):")
+
+        os.makedirs(task, exist_ok=True)
+
+        simulation = Simulation.load(f"../mapy/{task}.txt")
+        print("Simulation loaded.")
+
+        vertices, edges, object_types = load_asteroid_graph(f"../grafy/{task}.txt")
+        edges = [(vertices[u], vertices[v]) for u, v in edges]
+
+        print("Graph loaded.")
+
+        average_asteroid_radius = sum([asteroid.radius for asteroid in simulation.asteroids]) / len(simulation.asteroids)
+        goal_vertices = {
+            vertices[i]: (simulation.goals[j].x, simulation.goals[j].y)
+            for (i, (c, j)) in enumerate(object_types)
+            if c == "G"
+        }
+
+        best_instructions = None
+        best_instructions_length = float('inf')
+
+        i = 0
+        while i < iterations:
+            simulation.restart()
+            path = get_checkpoints_path(
+                simulation,
+                vertices, edges, goal_vertices,
+                longest_edges=average_asteroid_radius * np.random.uniform(0.5, 5),
+            )
+
+            instructions = solve(simulation, path)
+            i += 1
+
+            if len(instructions) < best_instructions_length:
+                best_instructions = instructions
+                best_instructions_length = len(instructions)
+                print(f"Solved with {len(instructions)} instructions.")
+
+                solution_path = get_solution_path(simulation, best_instructions)
+                d = get_solution_preview(simulation, solution_path, "Green")
+                d.save_svg(f"{task}/solution.svg")
+                save_instructions(f"{task}/solution.txt", best_instructions)
+
+        print(f"Best solution: {len(best_instructions)} instructions.")
diff --git a/asteracer-python-search/asteracer.py b/asteracer-python-search/asteracer.py
new file mode 100644
index 0000000..8968a89
--- /dev/null
+++ b/asteracer-python-search/asteracer.py
@@ -0,0 +1,429 @@
+"""The Asteracer game implementation. Includes the base movement code + couple of QOL additions (eg. save states)."""
+from __future__ import annotations
+
+import dataclasses
+import random
+from collections import defaultdict
+from dataclasses import dataclass
+from math import isqrt
+
+
+class TickFlag:
+    """Flags returned by simulation.tick() for various events that can occur during a tick."""
+    COLLIDED = 1
+    GOAL_REACHED = 2
+
+
+@dataclass
+class Racer:
+    x: int = 0
+    y: int = 0
+    vx: int = 0
+    vy: int = 0
+    radius: int = 1
+
+
+@dataclass(frozen=True)
+class Asteroid:
+    x: int = 0
+    y: int = 0
+    radius: int = 1
+
+Goal = Asteroid
+
+
+class Instruction:
+    MAX_ACCELERATION = 127
+
+    def __init__(self, vx: int | float = 0, vy: int | float = 0):
+        """Whatever values we get, normalize them."""
+        vx = int(vx)
+        vy = int(vy)
+
+        if distance_squared(vx, vy) > Instruction.MAX_ACCELERATION ** 2:
+            vx = float(vx)
+            vy = float(vy)
+
+            # use float to properly normalize here
+            distance = (vx ** 2 + vy ** 2) ** (1/2)
+
+            vx = int(vx / distance * Instruction.MAX_ACCELERATION)
+            vy = int(vy / distance * Instruction.MAX_ACCELERATION)
+
+            # if we're still over, decrement both values
+            if distance_squared(vx, vy) > Instruction.MAX_ACCELERATION ** 2:
+                vx -= signum(vx)
+                vy -= signum(vy)
+
+        assert distance_squared(vx, vy) <= Instruction.MAX_ACCELERATION ** 2
+
+        self.vx = vx
+        self.vy = vy
+
+    def __hash__(self):
+        return hash((self.vx, self.vy))
+
+    def __eq__(self, other):
+        return self.vx == other.vx and self.vy == other.vy
+
+    def __str__(self):
+        return f"Instruction({self.vx}, {self.vy})"
+
+    @classmethod
+    def random(cls):
+        return cls(
+            random.randint(
+                -cls.MAX_ACCELERATION,
+                cls.MAX_ACCELERATION
+            ),
+            random.randint(
+                -cls.MAX_ACCELERATION,
+                cls.MAX_ACCELERATION
+            ),
+        )
+
+
+@dataclass
+class BoundingBox:
+    min_x: int
+    min_y: int
+    max_x: int
+    max_y: int
+
+    def width(self) -> int:
+        return int(self.max_x - self.min_x)
+
+    def height(self) -> int:
+        return int(self.max_y - self.min_y)
+
+
+def distance_squared(x1, y1, x2=0, y2=0) -> int:
+    """Squared Euclidean distance between two points."""
+    return (int(x1) - int(x2)) ** 2 + (int(y1) - int(y2)) ** 2
+
+
+def euclidean_distance(x1, y1, x2=0, y2=0):
+    """Integer Euclidean distance between two points. Uses integer square root."""
+    return int(isqrt(distance_squared(x1, y1, x2, y2)))
+
+
+def signum(x):
+    return -1 if x < 0 else 0 if x == 0 else 1
+
+
+def division(a, b):
+    """Correctly implemented division, removing the fractional component."""
+    return (abs(int(a)) // int(b)) * signum(a)
+
+
+
+class Simulation:
+    DRAG_FRACTION = (9, 10)  # slowdown of the racer's velocity after each tick
+    COLLISION_FRACTION = (1, 2)  # slowdown of the racer's velocity after a tick where a collision occurred
+    MAX_COLLISION_RESOLUTIONS = 5  # at most how many collision iterations to perform
+
+    CELL_SIZE = 10_000
+
+    def __init__(
+            self,
+            racer: Racer = Racer(),
+            asteroids: list[Asteroid] = None,
+            goals: list[Goal] = None,
+            bounding_box: BoundingBox = None,
+    ):
+        # the initial racer state (used when resetting the simulation)
+        self.initial_racer = dataclasses.replace(racer)
+
+        self.racer = racer
+        self.asteroids = asteroids or []
+        self.goals = goals or []
+        self.bounding_box = bounding_box
+
+        # to speed up the computation, we divide the bounding box (if we have one) into a grid
+        # we do this so we don't need to check all asteroids at each tick, only those that could collide with the racer
+        self._grid: dict[tuple[int, int], list[Asteroid]] = defaultdict(list)
+
+        for asteroid in asteroids:
+            min_x, min_y = self._coordinate_to_grid(
+                asteroid.x - asteroid.radius - racer.radius,
+                asteroid.y - asteroid.radius - racer.radius,
+            )
+
+            max_x, max_y = self._coordinate_to_grid(
+                asteroid.x + asteroid.radius + racer.radius,
+                asteroid.y + asteroid.radius + racer.radius,
+            )
+
+            for grid_x in range(min_x, max_x + 1):
+                for grid_y in range(min_y, max_y + 1):
+                    self._grid[(grid_x, grid_y)].append(asteroid)
+
+        self.reached_goals: list[bool] = [False] * len(self.goals)
+
+        # a list of simulation states that can be popped (restored to)
+        self._pushed_states = []
+
+    def _coordinate_to_grid(self, x: float, y: float) -> tuple[int, int]:
+        """Translate an (x,y) coordinate into a coordinate of the grid."""
+        return (x // self.CELL_SIZE, y // self.CELL_SIZE)
+
+    def _move_racer(self, instruction: Instruction):
+        """Move the racer in the given direction."""
+        vx, vy = instruction.vx, instruction.vy
+
+        # drag
+        self.racer.vx = division(self.racer.vx * self.DRAG_FRACTION[0], self.DRAG_FRACTION[1])
+        self.racer.vy = division(self.racer.vy * self.DRAG_FRACTION[0], self.DRAG_FRACTION[1])
+
+        # velocity
+        self.racer.vx += int(vx)
+        self.racer.vy += int(vy)
+
+        # movement
+        self.racer.x += self.racer.vx
+        self.racer.y += self.racer.vy
+
+    def _push_out(self, obj: Asteroid | BoundingBox) -> bool:
+        """Attempt to push the racer out of the object (if he's colliding), adjusting
+        his velocity accordingly (based on the angle of collision). Returns True if the
+        racer was pushed out, otherwise returns False."""
+        if isinstance(obj, Asteroid):
+            # not colliding, nothing to be done
+            if euclidean_distance(self.racer.x, self.racer.y, obj.x, obj.y) > (self.racer.radius + obj.radius):
+                return False
+
+            # the vector to push the racer out by
+            nx = self.racer.x - obj.x
+            ny = self.racer.y - obj.y
+
+            # how much to push by
+            distance = euclidean_distance(self.racer.x, self.racer.y, obj.x, obj.y)
+            push_by = distance - (self.racer.radius + obj.radius)
+
+            # the actual push
+            self.racer.x -= division(nx * push_by, distance)
+            self.racer.y -= division(ny * push_by, distance)
+
+            return True
+
+        elif isinstance(obj, BoundingBox):
+            # not pretty but easy to read :)
+            collided = False
+
+            if self.racer.x - self.racer.radius < obj.min_x:
+                self.racer.x = obj.min_x + self.racer.radius
+                collided = True
+            if self.racer.x + self.racer.radius > obj.max_x:
+                self.racer.x = obj.max_x - self.racer.radius
+                collided = True
+            if self.racer.y - self.racer.radius < obj.min_y:
+                self.racer.y = obj.min_y + self.racer.radius
+                collided = True
+            if self.racer.y + self.racer.radius > obj.max_y:
+                self.racer.y = obj.max_y - self.racer.radius
+                collided = True
+
+            return collided
+
+        else:
+            raise Exception("Attempted to collide with something other than asteroid / bounding box!")
+
+    def _check_goal(self) -> bool:
+        """Sets the _reached_goals variable to True according to if the racer is intersecting them, returning True if
+        a new one was reached."""
+        new_goal_reached = False
+
+        for i, goal in enumerate(self.goals):
+            if euclidean_distance(self.racer.x, self.racer.y, goal.x, goal.y) <= (self.racer.radius + goal.radius):
+                if not self.reached_goals[i]:
+                    new_goal_reached = True
+
+                self.reached_goals[i] = True
+
+        return new_goal_reached
+
+    def _resolve_collisions(self) -> bool:
+        """Resolve all collisions of the racer and asteroids, returning True if a collison occurred."""
+        collided = False
+        for _ in range(self.MAX_COLLISION_RESOLUTIONS):
+            collided_this_iteration = False
+
+            for asteroid in self._grid[self._coordinate_to_grid(self.racer.x, self.racer.y)]:
+                if self._push_out(asteroid):
+                    collided_this_iteration = collided = True
+                    break
+
+            if self.bounding_box is not None and self._push_out(self.bounding_box):
+                collided_this_iteration = collided = True
+
+            if not collided_this_iteration:
+                break
+
+        if collided:
+            self.racer.vx = division(self.racer.vx * self.COLLISION_FRACTION[0], self.COLLISION_FRACTION[1])
+            self.racer.vy = division(self.racer.vy * self.COLLISION_FRACTION[0], self.COLLISION_FRACTION[1])
+
+        return collided
+
+    def finished(self) -> bool:
+        """Returns True if the racer reached all goals."""
+        return all(self.reached_goals)
+
+    def restart(self):
+        """Restart the simulation to its initial state."""
+        self.racer.x = self.initial_racer.x
+        self.racer.y = self.initial_racer.y
+        self.racer.vx = 0
+        self.racer.vy = 0
+
+        for i in range(len(self.reached_goals)):
+            self.reached_goals[i] = False
+
+    def tick(self, instruction: Instruction):
+        """Simulate a single tick of the simulation."""
+        self._move_racer(instruction)
+        collided = self._resolve_collisions()
+        goal = self._check_goal()
+
+        return (TickFlag.COLLIDED if collided else 0) | (TickFlag.GOAL_REACHED if goal else 0)
+
+    def simulate(self, instructions: list[Instruction]):
+        """Simulate a number of instructions for the simulation (from the start)."""
+        self.restart()
+
+        results = []
+
+        for instruction in instructions:
+            results.append(self.tick(instruction))
+
+        return results
+
+    def save(self, path: str):
+        """Save the simulation to a file:
+        | 0 0 5
+        | -100 -100 100 100  // bounding box (min_x/min_y/max_x/max_y)
+        | 5                  // number of asteroids
+        | 10 -10 10          // asteroid 1 x/y/radius
+        | 20 20 50           // asteroid 2 x/y/radius
+        | -10 10 30          // asteroid 3 x/y/radius
+        | 10 10 70           // asteroid 4 x/y/radius
+        | -10 -10 10         // asteroid 5 x/y/radius
+        | 1                  // number of goals
+        | 100 100 10         // goal 1 x/y/radius
+        """
+        with open(path, "w") as f:
+            f.write(f"{self.racer.x} {self.racer.y} {self.racer.radius}\n")
+
+            bbox = self.bounding_box
+            f.write(f"{bbox.min_x} {bbox.min_y} {bbox.max_x} {bbox.max_y}\n")
+
+            f.write(f"{len(self.asteroids)}\n")
+            for asteroid in self.asteroids:
+                f.write(f"{asteroid.x} {asteroid.y} {asteroid.radius}\n")
+
+            f.write(f"{len(self.goals)}\n")
+            for goal in self.goals:
+                f.write(f"{goal.x} {goal.y} {goal.radius}\n")
+
+    @classmethod
+    def load(cls, path: str) -> Simulation:
+        """Load the simulation from a file (see self.save for the format description)."""
+        with open(path) as f:
+            lines = f.read().splitlines()
+
+        racer_parts = lines[0].split()
+        racer = Racer(x=int(racer_parts[0]), y=int(racer_parts[1]), radius=int(racer_parts[2]))
+
+        bb_parts = lines[1].split()
+        bb = BoundingBox(int(bb_parts[0]), int(bb_parts[1]), int(bb_parts[2]), int(bb_parts[2]))
+
+        asteroid_count = int(lines[2])
+
+        asteroids = []
+        for i in range(3, 3 + asteroid_count):
+            asteroid_parts = lines[i].split()
+            asteroids.append(
+                Asteroid(
+                    x=int(asteroid_parts[0]),
+                    y=int(asteroid_parts[1]),
+                    radius=int(asteroid_parts[2]),
+                )
+            )
+
+        goal_count = int(lines[3 + asteroid_count])
+
+        goals = []
+        for i in range(4 + asteroid_count, 4 + asteroid_count + goal_count):
+            goal_parts = lines[i].split()
+            goals.append(
+                Asteroid(
+                    x=int(goal_parts[0]),
+                    y=int(goal_parts[1]),
+                    radius=int(goal_parts[2]),
+                )
+            )
+
+        return Simulation(racer=racer, bounding_box=bb, asteroids=asteroids, goals=goals)
+
+    def push(self):
+        """Push (save) the current state of the simulation. Can be popped (restored) later."""
+        self._pushed_states.append(
+            (
+                dataclasses.replace(self.racer),
+                list(self.reached_goals),
+            )
+        )
+
+    def pop(self):
+        """Pop (restore) the previously pushed state."""
+        assert len(self._pushed_states) != 0, "No states to pop!"
+        self.racer, self.reached_goals = self._pushed_states.pop()
+
+    def apply(self):
+        """Apply the previously pushed state without popping it."""
+        self.racer = dataclasses.replace(self._pushed_states[-1][0])
+        self.reached_goals = list(self._pushed_states[-1][1])
+
+
+def save_instructions(path: str, instructions: list[Instruction]):
+    """Save a list of instructions to a file:
+    | 4         // number if instructions
+    | -16 -127  // instructions...
+    | -16 -127
+    | -26 -125
+    | -30 -124
+    """
+    with open(path, "w") as f:
+        f.write(f"{len(instructions)}\n")
+
+        for instruction in instructions:
+            f.write(f"{instruction.vx} {instruction.vy}\n")
+
+
+def load_instructions(path: str) -> list[Instruction]:
+    """Load a list of instructions from a file (see save_instructions for the format description)."""
+    instructions = []
+
+    with open(path) as f:
+        for line in f.read().splitlines()[1:]:
+            instruction_parts = list(map(int, line.split()))
+            instructions.append(Instruction(*instruction_parts))
+
+    return instructions
+
+
+if __name__ == "__main__":
+    map_path = "../../maps/test.txt"
+
+    simulation = Simulation.load(map_path)
+
+    tick_result = 0
+
+    print("Running simulation until collision...")
+
+    while tick_result & TickFlag.COLLIDED == 0:
+        tick_result = simulation.tick(Instruction(0, Instruction.MAX_ACCELERATION))
+
+        print(simulation.racer)
+
+    print("Bam!")
diff --git a/asteracer-python-search/marathon/14290.txt b/asteracer-python-search/marathon/14290.txt
new file mode 100644
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