python实现棋盘覆盖问题及可视化

import numpy as np
import matplotlib.pyplot as plt


class Board:
 def __init__(self, size, x, y):
  '''
  初始化棋盘

  :param size: 棋盘边长
  :param x: 特殊点横坐标
  :param y: 特殊点纵坐标
  '''
  self.special_block = (x, y)
  self.board = np.zeros((size, size), dtype=int)
  self.board[x][y] = (size * size - 1) / 3 + 1
  self.t = 1
  self.size = size

 def visualize(self):
  '''
  可视化函数

  :return: None
  '''
  plt.imshow(self.board, cmap=plt.cm.gray)
  plt.colorbar()
  plt.show()

 def fill_block(self, x, y):
  '''
  填充点(x, y)
  :param x: x
  :param y: y
  :return: None
  '''
  if self.board[x][y] == 0:
   self.board[x][y] = self.t
  else:
   raise Exception

 def fill(self, s_x, s_y, size, c_x, c_y):
  '''
  递归函数填充棋盘或子棋盘（下文称区块)

  :param s_x: 区块左上角x
  :param s_y: 区块左上角y
  :param size: 区块边长
  :param c_x: 区块特殊点坐标x
  :param c_y: 区块特殊点坐标x
  :return: None
  '''
  if size == 1:
   return
  pos = (round((c_x - s_x + 1) / size), round((c_y - s_y + 1) / size))
  center = (round(s_x + size / 2 - 1), round(s_y + size / 2 - 1))
  ls = [(0, 0), (0, 1), (1, 0), (1, 1)] # 代表四个子区块
  for i in ls:
   if i != pos: # 如果不是原有特殊点所在区块，则构造特殊点并填充
    x = center[0] + i[0]
    y = center[1] + i[1]
    self.fill_block(x, y)
  self.t += 1 # 标记号加一，标记下一骨牌
  for i in ls:
   if i != pos: # 如果不是原有特殊点所在区块
    # 所构造特殊点位置(x, y)
    x = center[0] + i[0]
    y = center[1] + i[1]
    x1 = s_x + i[0] * (size / 2)
    y1 = s_y + i[1] * (size / 2)
    self.fill(x1, y1, size / 2, x, y)
   else: # 如果是原有特殊点所在区块
    x1 = s_x + i[0] * (size / 2)
    y1 = s_y + i[1] * (size / 2)
    self.fill(x1, y1, size / 2, c_x, c_y)

if __name__ == '__main__':
 k = eval(input("请输入正整数K(棋盘大小2^2k,2^2k):\n"))
 loc_x = eval(input("请输入特殊点横坐标:\n"))
 loc_y = eval(input("请输入特殊点纵坐标:\n"))
 size = 2 ** (2 * k)
 b = Board(size, loc_x, loc_y)
 b.fill(0, 0, size, loc_x, loc_y)
 b.visualize()
 print(b.board)