棋盘覆盖问题可视化动图——python

棋盘覆盖问题是一个经典的分治法解决的问题，具体内容可以参照以下博主的解析

为了更好的理解该算法分治的过程

利用了python中的matplotlib库进行了该算法的可视化

具体动画可复制代码在本地运行查看

import matplotlib.pyplot as plt

import numpy as np

count=0

color=['yellow','green','blue','red','purple'] #颜色数组

def fill(x,y,t):

xx=np.linspace(x,x+1,10)

yy=np.linspace(y,y,10)

yy1=np.linspace(y+1,y+1,10)

plt.fill_between(xx,yy,yy1,facecolor=color[t%(len(color))]) #填充

plt.text(x+0.5,y+0.5,t) #添加文字

plt.pause(1) #动态画图 参数为变化的时间

pass

def ChessBoard(tr,tc,dr,dc,size):

if size==1: #算法实现

return

global count

global Board

count+=1

t=count

s=size//2

if dr

ChessBoard(tr,tc,dr,dc,s)

else:

Board[tr+s-1][tc+s-1]=t

fill(tr+s-1,tc+s-1,t)

ChessBoard(tr,tc,tr+s-1,tc+s-1,s)

if dr

=tc+s:

ChessBoard(tr,tc+s,dr,dc,s)

else:

Board[tr+s-1][tc+s]=t

fill(tr+s-1,tc+s,t)

ChessBoard(tr,tc+s,tr+s-1,tc+s,s)

if dr>=tr+s and dc

ChessBoard(tr+s,tc,dr,dc,s)

else:

Board[tr+s][tc+s-1]=t

fill(tr+s,tc+s-1,t)

ChessBoard(tr+s,tc,tr+s,tc+s-1,s)

if dr>=tr+s and dc>=tc+s:

ChessBoard(tr+s,tc+s,dr,dc,s)

else:

Board[tr+s][tc+s]=t

fill(tr+s,tc+s,t)

ChessBoard(tr+s,tc+s,tr+s,tc+s,s)

def pre():

x=2**n

y=2**n

xx=np.linspace(x,x+1,10)

yy=np.linspace(y,y,10)

yy1=np.linspace(y+1,y+1,10)

plt.fill_between(xx,yy,yy1,facecolor='white')

plt.pause(1)

pass

n=int(input())

Board=[[0 for i in range(2**n)] for j in range(2**n)]

x,y=map(int,input().split())

pre() #图像预处理

Board[x][y]=-1

ChessBoard(0,0,x,y,2**n)

for i in range(2**n):

for j in range(2**n):

print(Board[i][j],end=' ')

print()

plt.show()

# n为正方形的阶数 x y为方格点的坐标