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doing the wheel
This commit is contained in:
maoake
@@ -0,0 +1,591 @@
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from abc import ABC, abstractmethod
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from typing import Generator, Any
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import numpy as np
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from numpy.typing import NDArray
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from .Cell import Cell
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import math
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import random
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class MazeGenerator(ABC):
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"""Define the common interface and helpers for maze generators."""
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def __init__(
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self, start: tuple[int, int], end: tuple[int, int], perfect: bool
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) -> None:
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"""Initialize the maze generator.
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Args:
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start: Starting cell coordinates, using 1-based indexing.
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end: Ending cell coordinates, using 1-based indexing.
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perfect: Whether to generate a perfect maze with no loops.
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"""
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self.start = (start[0] - 1, start[1] - 1)
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self.end = (end[0] - 1, end[1] - 1)
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self.perfect = perfect
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@abstractmethod
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def generator(
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self, height: int, width: int, seed: int | None = None
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) -> Generator[NDArray[Any], None, NDArray[Any]]:
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"""Generate a maze step by step.
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Args:
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height: Number of rows in the maze.
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width: Number of columns in the maze.
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seed: Optional random seed for reproducibility.
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Yields:
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Intermediate maze states during generation.
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Returns:
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The final generated maze.
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"""
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...
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@staticmethod
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def get_cell_ft(width: int, height: int) -> set[tuple[int, int]]:
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"""Return the coordinates used to reserve the '42' pattern.
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Args:
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width: Number of columns in the maze.
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height: Number of rows in the maze.
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Returns:
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A set of cell coordinates belonging to the reserved pattern.
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"""
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forty_two = set()
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y, x = (int(height / 2), int(width / 2))
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forty_two.add((y, x - 1))
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forty_two.add((y, x - 2))
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forty_two.add((y, x - 3))
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forty_two.add((y - 1, x - 3))
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forty_two.add((y - 2, x - 3))
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forty_two.add((y + 1, x - 1))
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forty_two.add((y + 2, x - 1))
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forty_two.add((y, x + 1))
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forty_two.add((y, x + 2))
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forty_two.add((y, x + 3))
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forty_two.add((y - 1, x + 3))
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forty_two.add((y - 2, x + 3))
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forty_two.add((y - 2, x + 2))
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forty_two.add((y - 2, x + 1))
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forty_two.add((y + 1, x + 1))
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forty_two.add((y + 2, x + 1))
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forty_two.add((y + 2, x + 2))
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forty_two.add((y + 2, x + 3))
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return forty_two
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@staticmethod
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def unperfect_maze(
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width: int,
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height: int,
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maze: NDArray[Any],
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forty_two: set[tuple[int, int]] | None,
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prob: float = 0.1,
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) -> Generator[NDArray[Any], None, NDArray[Any]]:
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"""Add extra openings to transform a perfect maze into an imperfect
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one.
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Random walls are removed while optionally preserving the reserved
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``forty_two`` area.
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Args:
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width: Number of columns in the maze.
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height: Number of rows in the maze.
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maze: The maze to modify.
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forty_two: Optional set of reserved coordinates that must not be
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altered.
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prob: Probability of breaking an eligible wall.
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Yields:
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Intermediate maze states after each wall removal.
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Returns:
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The modified maze.
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"""
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directions = {"N": (0, -1), "S": (0, 1), "W": (-1, 0), "E": (1, 0)}
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reverse = {"N": "S", "S": "N", "W": "E", "E": "W"}
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min_break = 2
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while True:
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count = 0
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for y in range(height):
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for x in range(width):
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if forty_two and (x, y) in forty_two:
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continue
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for direc, (dx, dy) in directions.items():
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nx, ny = x + dx, y + dy
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if forty_two and (
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(y, x) in forty_two or (ny, nx) in forty_two
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):
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continue
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if not (0 <= nx < width and 0 < ny < height):
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continue
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if direc in ["S", "E"]:
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continue
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if np.random.random() < prob:
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count += 1
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cell = maze[y][x]
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cell_n = maze[ny][nx]
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cell = DepthFirstSearch.broken_wall(cell, direc)
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cell_n = DepthFirstSearch.broken_wall(
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cell_n,
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reverse[direc],
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)
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maze[y][x] = cell
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maze[ny][nx] = cell_n
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yield maze
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if count > min_break:
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break
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return maze
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class Kruskal(MazeGenerator):
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"""Generate a maze using a Kruskal-based algorithm."""
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class KruskalSet:
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"""Represent a connected component of maze cells."""
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def __init__(self, cells: list[int]) -> None:
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"""Initialize a set of connected cells.
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Args:
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cells: List of cell indices belonging to the set.
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"""
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self.cells: list[int] = cells
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class Sets:
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"""Store all connected components used during generation."""
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def __init__(self, sets: list["Kruskal.KruskalSet"]) -> None:
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"""Initialize the collection of connected components.
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Args:
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sets: List of disjoint cell sets.
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"""
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self.sets = sets
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@staticmethod
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def walls_to_maze(
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walls: list[tuple[int, int]], height: int, width: int
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) -> NDArray[Any]:
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"""Convert a list of remaining walls into a maze grid.
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Args:
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walls: Collection of wall pairs between adjacent cells.
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height: Number of rows in the maze.
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width: Number of columns in the maze.
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Returns:
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A two-dimensional array of :class:`Cell` instances representing the
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maze.
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"""
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maze: NDArray[Any] = np.array(
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[[Cell(value=0) for _ in range(width)] for _ in range(height)]
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)
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for wall in walls:
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x, y = wall
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match y - x:
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case 1:
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maze[math.trunc((x / width))][x % width].set_est(True)
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maze[math.trunc((y / width))][y % width].set_west(True)
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case width:
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maze[math.trunc((x / width))][x % width].set_south(True)
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maze[math.trunc((y / width))][y % width].set_north(True)
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for x in range(height):
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for y in range(width):
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if x == 0:
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maze[x][y].set_north(True)
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if x == height - 1:
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maze[x][y].set_south(True)
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if y == 0:
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maze[x][y].set_west(True)
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if y == width - 1:
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maze[x][y].set_est(True)
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return maze
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@staticmethod
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def is_in_same_set(sets: Sets, wall: tuple[int, int]) -> bool:
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"""Check whether both cells connected by a wall are in the same set.
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Args:
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sets: Current collection of connected components.
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wall: Pair of adjacent cell indices.
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Returns:
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``True`` if both cells belong to the same set, otherwise ``False``.
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"""
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a, b = wall
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for set in sets.sets:
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if a in set.cells and b in set.cells:
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return True
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elif a in set.cells or b in set.cells:
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return False
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return False
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@staticmethod
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def merge_sets(sets: Sets, wall: tuple[int, int]) -> None:
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"""Merge the two sets connected by the given wall.
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Args:
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sets: Current collection of connected components.
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wall: Pair of adjacent cell indices.
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Raises:
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Exception: If the two corresponding sets cannot be found.
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"""
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a, b = wall
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base_set = None
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for i in range(len(sets.sets)):
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if base_set is None and (
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a in sets.sets[i].cells or b in sets.sets[i].cells
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):
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base_set = sets.sets[i]
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elif base_set and (
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a in sets.sets[i].cells or b in sets.sets[i].cells
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):
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base_set.cells += sets.sets[i].cells
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sets.sets.pop(i)
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return
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raise Exception("two sets not found")
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@staticmethod
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def touch_ft(
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width: int,
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wall: tuple[int, int],
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cells_ft: None | set[tuple[int, int]],
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) -> bool:
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"""Check whether a wall touches the reserved '42' pattern.
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Args:
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width: Number of columns in the maze.
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wall: Pair of adjacent cell indices.
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cells_ft: Reserved coordinates, or ``None``.
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Returns:
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``True`` if either endpoint of the wall belongs to the reserved
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pattern, otherwise ``False``.
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"""
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if cells_ft is None:
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return False
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s1 = (math.trunc(wall[0] / width), wall[0] % width)
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s2 = (math.trunc(wall[1] / width), wall[1] % width)
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return s1 in cells_ft or s2 in cells_ft
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def generator(
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self, height: int, width: int, seed: int | None = None
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) -> Generator[NDArray[Any], None, NDArray[Any]]:
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"""Generate a maze using a Kruskal-based approach.
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Args:
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height: Number of rows in the maze.
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width: Number of columns in the maze.
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seed: Optional random seed for reproducibility.
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Yields:
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Intermediate maze states during generation.
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Returns:
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The final generated maze.
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"""
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cells_ft = None
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if height > 10 and width > 10:
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cells_ft = self.get_cell_ft(width, height)
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if cells_ft and (self.start in cells_ft or self.end in cells_ft):
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cells_ft = None
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if seed is not None:
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np.random.seed(seed)
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sets = self.Sets([self.KruskalSet([i]) for i in range(height * width)])
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walls = []
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for h in range(height):
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for w in range(width - 1):
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walls += [(w + (width * h), w + (width * h) + 1)]
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for h in range(height - 1):
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for w in range(width):
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walls += [(w + (width * h), w + (width * (h + 1)))]
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np.random.shuffle(walls)
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yield self.walls_to_maze(walls, height, width)
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while (len(sets.sets) != 1 and cells_ft is None) or (
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len(sets.sets) != 19 and cells_ft is not None
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):
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for wall in walls:
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if not self.is_in_same_set(sets, wall) and not self.touch_ft(
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width, wall, cells_ft
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):
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self.merge_sets(sets, wall)
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walls.remove(wall)
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yield self.walls_to_maze(walls, height, width)
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if (len(sets.sets) == 1 and cells_ft is None) or (
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len(sets.sets) == 19 and cells_ft is not None
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):
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break
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print(f"nb sets: {len(sets.sets)}")
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maze = self.walls_to_maze(walls, height, width)
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if self.perfect is False:
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gen = Kruskal.unperfect_maze(width, height, maze, cells_ft)
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for res in gen:
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maze = res
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yield maze
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return maze
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class DepthFirstSearch(MazeGenerator):
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"""Generate a maze using a depth-first search backtracking algorithm."""
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def __init__(
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self, start: tuple[int, int], end: tuple[int, int], perfect: bool
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) -> None:
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"""Initialize the depth-first search generator.
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Args:
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start: Starting cell coordinates, using 1-based indexing.
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end: Ending cell coordinates, using 1-based indexing.
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perfect: Whether to generate a perfect maze with no loops.
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"""
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self.start = (start[0] - 1, start[1] - 1)
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self.end = (end[0] - 1, end[1] - 1)
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self.perfect = perfect
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self.forty_two: set[tuple[int, int]] | None = None
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def generator(
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self, height: int, width: int, seed: int | None = None
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) -> Generator[NDArray[Any], None, NDArray[Any]]:
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"""Generate a maze using depth-first search.
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Args:
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height: Number of rows in the maze.
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width: Number of columns in the maze.
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seed: Optional random seed for reproducibility.
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Yields:
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Intermediate maze states during generation.
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Returns:
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The final generated maze.
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"""
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if seed is not None:
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np.random.seed(seed)
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maze = self.init_maze(width, height)
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if width > 9 and height > 9:
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self.forty_two = self.get_cell_ft(width, height)
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visited: NDArray[np.object_] = np.zeros((height, width), dtype=bool)
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if (
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self.forty_two
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and self.start not in self.forty_two
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and self.end not in self.forty_two
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):
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visited = self.lock_cell_ft(visited, self.forty_two)
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path: list[tuple[int, int]] = list()
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w_h = (width, height)
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coord = (0, 0)
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x, y = coord
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first_iteration = True
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while path or first_iteration:
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first_iteration = False
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visited[y, x] = True
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path = self.add_cell_visited(coord, path)
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random_c = self.random_cells(visited, coord, w_h)
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if not random_c:
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path = self.back_on_step(path, w_h, visited)
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if not path:
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break
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coord = path[-1]
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random_c = self.random_cells(visited, coord, w_h)
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x, y = coord
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wall = self.next_step(random_c)
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maze[y][x] = self.broken_wall(maze[y][x], wall)
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coord = self.next_cell(x, y, wall)
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wall_r = self.reverse_path(wall)
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x, y = coord
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maze[y][x] = self.broken_wall(maze[y][x], wall_r)
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yield maze
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if self.perfect is False:
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gen = DepthFirstSearch.unperfect_maze(
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width,
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height,
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maze,
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self.forty_two,
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)
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for res in gen:
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maze = res
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yield maze
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return maze
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@staticmethod
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def init_maze(width: int, height: int) -> NDArray[Any]:
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"""Create a fully walled maze grid.
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Args:
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width: Number of columns in the maze.
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height: Number of rows in the maze.
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||||
|
||||
Returns:
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A two-dimensional array of cells initialized with all
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walls present.
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"""
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maze = np.array(
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[[Cell(value=15) for _ in range(width)] for _ in range(height)]
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)
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return maze
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@staticmethod
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||||
def add_cell_visited(
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coord: tuple[int, int], path: list[tuple[int, int]]
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) -> list[tuple[int, int]]:
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"""Append a visited coordinate to the current traversal path.
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||||
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||||
Args:
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coord: Coordinate of the visited cell.
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path: Current traversal path.
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Returns:
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The updated path.
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"""
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path.append(coord)
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return path
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@staticmethod
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||||
def random_cells(
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visited: NDArray[Any], coord: tuple[int, int], w_h: tuple[int, int]
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||||
) -> list[str]:
|
||||
"""Return the list of unvisited neighboring directions.
|
||||
|
||||
Args:
|
||||
visited: Boolean array marking visited cells.
|
||||
coord: Current cell coordinate.
|
||||
w_h: Tuple containing maze width and height.
|
||||
|
||||
Returns:
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||||
A list of direction strings among ``"N"``, ``"S"``, ``"W"``, and
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||||
``"E"``.
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||||
"""
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||||
rand_cell: list[str] = []
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||||
x, y = coord
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width, height = w_h
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||||
|
||||
if y - 1 >= 0 and not visited[y - 1][x]:
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||||
rand_cell.append("N")
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||||
|
||||
if y + 1 < height and not visited[y + 1][x]:
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||||
rand_cell.append("S")
|
||||
|
||||
if x - 1 >= 0 and not visited[y][x - 1]:
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||||
rand_cell.append("W")
|
||||
|
||||
if x + 1 < width and not visited[y][x + 1]:
|
||||
rand_cell.append("E")
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||||
return rand_cell
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||||
|
||||
@staticmethod
|
||||
def next_step(rand_cell: list[str]) -> str:
|
||||
"""Select the next direction at random.
|
||||
|
||||
Args:
|
||||
rand_cell: List of candidate directions.
|
||||
|
||||
Returns:
|
||||
A randomly selected direction.
|
||||
"""
|
||||
return random.choice(rand_cell)
|
||||
|
||||
@staticmethod
|
||||
def broken_wall(cell: Cell, wall: str) -> Cell:
|
||||
"""Remove the specified wall from a cell.
|
||||
|
||||
Args:
|
||||
cell: The cell to modify.
|
||||
wall: Direction of the wall to remove.
|
||||
|
||||
Returns:
|
||||
The modified cell.
|
||||
"""
|
||||
if wall == "N":
|
||||
cell.set_north(False)
|
||||
elif wall == "S":
|
||||
cell.set_south(False)
|
||||
elif wall == "W":
|
||||
cell.set_west(False)
|
||||
elif wall == "E":
|
||||
cell.set_est(False)
|
||||
return cell
|
||||
|
||||
@staticmethod
|
||||
def next_cell(x: int, y: int, next: str) -> tuple[int, int]:
|
||||
"""Return the coordinates of the adjacent cell in the given direction.
|
||||
|
||||
Args:
|
||||
x: Current column index.
|
||||
y: Current row index.
|
||||
next: Direction to move.
|
||||
|
||||
Returns:
|
||||
The coordinates of the next cell.
|
||||
"""
|
||||
next_step = {"N": (0, -1), "S": (0, 1), "W": (-1, 0), "E": (1, 0)}
|
||||
add_x, add_y = next_step[next]
|
||||
return (x + add_x, y + add_y)
|
||||
|
||||
@staticmethod
|
||||
def reverse_path(direction: str) -> str:
|
||||
"""Return the opposite cardinal direction.
|
||||
|
||||
Args:
|
||||
direction: Input direction.
|
||||
|
||||
Returns:
|
||||
The opposite direction.
|
||||
"""
|
||||
return {"N": "S", "S": "N", "W": "E", "E": "W"}[direction]
|
||||
|
||||
@staticmethod
|
||||
def back_on_step(
|
||||
path: list[tuple[int, int]],
|
||||
w_h: tuple[int, int],
|
||||
visited: NDArray[Any],
|
||||
) -> list[tuple[int, int]]:
|
||||
"""Backtrack through the path until a cell with unvisited neighbors
|
||||
is found.
|
||||
|
||||
Args:
|
||||
path: Current traversal path.
|
||||
w_h: Tuple containing maze width and height.
|
||||
visited: Boolean array marking visited cells.
|
||||
|
||||
Returns:
|
||||
The truncated path after backtracking.
|
||||
"""
|
||||
while path:
|
||||
last = path[-1]
|
||||
if DepthFirstSearch.random_cells(visited, last, w_h):
|
||||
break
|
||||
path.pop()
|
||||
return path
|
||||
|
||||
@staticmethod
|
||||
def lock_cell_ft(
|
||||
visited: NDArray[Any], forty_two: set[tuple[int, int]]
|
||||
) -> NDArray[Any]:
|
||||
"""Mark the reserved '42' pattern cells as already visited.
|
||||
|
||||
Args:
|
||||
visited: Boolean array marking visited cells.
|
||||
forty_two: Set of reserved cell coordinates.
|
||||
|
||||
Returns:
|
||||
The updated visited array.
|
||||
"""
|
||||
tab = [cell for cell in forty_two]
|
||||
for cell in tab:
|
||||
visited[cell] = True
|
||||
return visited
|
||||
Reference in New Issue
Block a user