python实现三阶魔方还原的示例代码


Posted in Python onApril 28, 2021

思路

复原魔方困难问题的分解:

​ 1、用合适的数据结构表示出三阶魔方的六个面以及每一面的颜色

​ 2、每一次不同旋转操作的实现

​ 3、复原时如何判断当前魔方应该使用哪一种公式

本次实验实现了前两个操作,具体思路是:

用numpy库中的矩阵将六个面分别表示出来,按上下左右前后的顺序放入列表中。再依据流行公式里的方法编写对每一个面进行旋转操作的函数,调用函数实现魔方的旋转。最后输入指令可得到旋转之后的魔方,以及执行逆序指令后验证魔方还原。

预备知识

矩阵:使用numpy库中的矩阵结构

函数说明:

U: 上面顺时针旋转 90°

D: 底面顺时针旋转 90°

L: 左面顺时针旋转 90°

R: 右面顺时针旋转 90°

F: 正面顺时针旋转 90°

B: 背面顺时针旋转 90°

**注:**字母前加上下划线 ‘_' 表示逆时针

代码详解

本次实验将【上、下、左、右、前、后】六个面用数字【0、1、2、3、4、5】表示原本每个面的颜色,并依次存入列表faces【】里(即:faces[0]中存放的是最上面的数字全为0的三阶矩阵)

注:魔方视角始终固定,即在整个过程中正(左…)面始终是正(左…)面

# 创建六个面,放在faces列表里,顺序为上(0),下(1),左(2),右(3),前(4),后(5)
faces = [np.zeros((3, 3))]

for i in range(1, 6):
    faces.append(np.ones((3, 3)) + faces[i - 1])

python实现三阶魔方还原的示例代码

每一个面的 顺时针逆时针 旋转由函数 clockwise()antiClockwise() 实现

t = np.array([[0, 0, 1],
              [0, 1, 0],
              [1, 0, 0]])

# 该面顺时针旋转 90 度
def clockwise(face):
    face = face.transpose().dot(t)
    return face

# 该面逆时针旋转 90 度
def antiClockwise(face):
    face = face.dot(t).transpose()
    return face

A.transpose() 方法是实现 A 矩阵的转置

A.dot(B) 方法是实现 A乘以矩阵B

通过计算,上述方法可以实现矩阵顺时针或者逆时针旋转的效果

在这里以左面的顺时针旋转 90°为例,其它旋转方式可以类比

def L(FACES):
    FACES[2] = clockwise(FACES[2])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = clockwise(FACES_new[4]), clockwise(FACES_new[1]), antiClockwise(FACES_new[5]), clockwise(FACES_new[0])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    e[0], f[0], g[0], h[0] = d[0], a[0], b[0], c[0]
    FACES[4], FACES[1], FACES[5], FACES[0] = antiClockwise(e), antiClockwise(f), clockwise(g), antiClockwise(h)

1、直接调用函数将左面(第2面)顺时针旋转 90°

FACES[2] = clockwise(FACES[2])

2、这里采用深度复制,使用 cp.deepcopy() 的方法,避免直接使用等号 ‘=' 导致不同的变量指向同一个值。这时,【e、f、g、h】和【a、b、c、d】代表魔方的

【正面、底面顺时针旋转90°、背面逆时针旋转90°、上面顺时针旋转90°】

a, b, c, d = clockwise(FACES_new[4]), clockwise(FACES_new[1]), antiClockwise(FACES_new[5]), clockwise(FACES_new[0])

旋转的目的是:

在左面旋转的过程中,左面会影响到其它四个面,但对其它四个面的影响是不同的。例如正面、底面和上面被影响的是第一列,而背面被影响的是第三列。我们为了使各面统一起来,方便数值的改变,我们选择将正、底、上面顺时针旋转90°,将背面逆时针旋转90°。这时,我们只需按顺序交换每一面的第一行,最后再逆时针或顺时针转回来即可。

python实现三阶魔方还原的示例代码

3、按顺序交换:正面第一行传递到底面第一行

​ 上面第一行传递到正面第一行

​ 背面第一行传递到上面第一行

​ 底面第一行传递到背面第一行

e[0], f[0], g[0], h[0] = d[0], a[0], b[0], c[0]

最后再依次根据上述操作逆旋转回去:

FACES[4], FACES[1], FACES[5], FACES[0] = antiClockwise(e), antiClockwise(f), clockwise(g), antiClockwise(h)

代码

import numpy as np
import copy as cp

# 创建六个面,放在faces列表里,顺序为上(0),下(1),左(2),右(3),前(4),后(5)
faces = [np.zeros((3, 3))]

for i in range(1, 6):
    faces.append(np.ones((3, 3)) + faces[i - 1])

t = np.array([[0, 0, 1],
              [0, 1, 0],
              [1, 0, 0]])

# 该面顺时针旋转 90 度
def clockwise(face):
    face = face.transpose().dot(t)
    return face

# 该面逆时针旋转 90 度
def antiClockwise(face):
    face = face.dot(t).transpose()
    return face


def U(FACES):
    FACES[0] = clockwise(FACES[0])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][0], FACES[2][0], FACES[5][0], FACES[3][0] = d[0], a[0], b[0], c[0]


def _U(FACES):
    FACES[0] = antiClockwise(FACES[0])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][0], FACES[2][0], FACES[5][0], FACES[3][0] = b[0], c[0], d[0], a[0]


def U2(FACES):
    for i in range(2):
        U(FACES)
    '''
    FACES[0] = clockwise(clockwise(FACES[0]))
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][0], FACES[2][0], FACES[5][0], FACES[3][0] = c[0], d[0], a[0], b[0]
    '''


def D(FACES):
    FACES[1] = clockwise(FACES[1])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][2], FACES[2][2], FACES[5][2], FACES[3][2] = b[2], c[2], d[2], a[2]


def _D(FACES):
    FACES[1] = antiClockwise(FACES[1])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][2], FACES[2][2], FACES[5][2], FACES[3][2] = d[2], a[2], b[2], c[2]


def D2(FACES):
    for i in range(2):
        D(FACES)
    '''
    FACES[1] = clockwise(clockwise(FACES[1]))
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[4], FACES_new[2], FACES_new[5], FACES_new[3]
    FACES[4][2], FACES[2][2], FACES[5][2], FACES[3][2] = c[2], d[2], a[2], b[2]
    '''


def L(FACES):
    FACES[2] = clockwise(FACES[2])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = clockwise(FACES_new[4]), clockwise(FACES_new[1]), antiClockwise(FACES_new[5]), clockwise(FACES_new[0])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    e[0], f[0], g[0], h[0] = d[0], a[0], b[0], c[0]
    FACES[4], FACES[1], FACES[5], FACES[0] = antiClockwise(e), antiClockwise(f), clockwise(g), antiClockwise(h)


def _L(FACES):
    FACES[2] = antiClockwise(FACES[2])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = clockwise(FACES_new[4]), clockwise(FACES_new[1]), antiClockwise(FACES_new[5]), clockwise(FACES_new[0])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    e[0], f[0], g[0], h[0] = b[0], c[0], d[0], a[0]
    FACES[4], FACES[1], FACES[5], FACES[0] = antiClockwise(e), antiClockwise(f), clockwise(g), antiClockwise(h)


def L2(FACES):
    for i in range(2):
        L(FACES)


# 上(0),下(1),左(2),右(3),前(4),后(5)
def R(FACES):
    FACES[3] = clockwise(FACES[3])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = antiClockwise(FACES_new[4]), antiClockwise(FACES_new[1]), clockwise(FACES_new[5]), antiClockwise(
        FACES_new[0])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    g[0], f[0], e[0], h[0] = d[0], c[0], b[0], a[0]
    FACES[4], FACES[1], FACES[5], FACES[0] = clockwise(e), clockwise(f), antiClockwise(g), clockwise(h)


def _R(FACES):
    FACES[3] = antiClockwise(FACES[3])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = antiClockwise(FACES_new[4]), antiClockwise(FACES_new[1]), clockwise(FACES_new[5]), antiClockwise(
        FACES_new[0])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    f[0], g[0], h[0], e[0] = a[0], b[0], c[0], d[0]
    FACES[4], FACES[1], FACES[5], FACES[0] = clockwise(e), clockwise(f), antiClockwise(g), clockwise(h)


def R2(FACES):
    for i in range(2):
        R(FACES)


def F(FACES):
    FACES[4] = clockwise(FACES[4])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = clockwise(clockwise(FACES_new[0])), FACES_new[1], antiClockwise(FACES_new[2]), clockwise(FACES_new[3])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    e[0], g[0], f[0], h[0] = c[0], b[0], d[0], a[0]
    FACES[0], FACES[1], FACES[2], FACES[3] = clockwise(clockwise(e)), f, clockwise(g), antiClockwise(h)


def _F(FACES):
    FACES[4] = antiClockwise(FACES[4])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = clockwise(clockwise(FACES_new[0])), FACES_new[1], antiClockwise(FACES_new[2]), clockwise(FACES_new[3])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    g[0], f[0], h[0], e[0] = a[0], c[0], b[0], d[0]
    FACES[0], FACES[1], FACES[2], FACES[3] = clockwise(clockwise(e)), f, clockwise(g), antiClockwise(h)


def F2(FACES):
    for _ in range(2):
        F(FACES)


# 上(0),下(1),左(2),右(3),前(4),后(5)
def B(FACES):
    FACES[5] = clockwise(FACES[5])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[0], clockwise(clockwise(FACES_new[1])), clockwise(FACES_new[2]), antiClockwise(FACES_new[3])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    g[0], f[0], h[0], e[0] = a[0], c[0], b[0], d[0]
    FACES[0], FACES[1], FACES[2], FACES[3] = e, clockwise(clockwise(f)), antiClockwise(g), clockwise(h)


def _B(FACES):
    FACES[5] = antiClockwise(FACES[5])
    FACES_new = cp.deepcopy(FACES)
    a, b, c, d = FACES_new[0], clockwise(clockwise(FACES_new[1])), clockwise(FACES_new[2]), antiClockwise(FACES_new[3])
    e, f, g, h = cp.deepcopy(a), cp.deepcopy(b), cp.deepcopy(c), cp.deepcopy(d)
    e[0], g[0], f[0], h[0] = c[0], b[0], d[0], a[0]
    FACES[0], FACES[1], FACES[2], FACES[3] = e, clockwise(clockwise(f)), antiClockwise(g), clockwise(h)


def B2(FACES):
    for i in range(2):
        B(FACES)


'''
                          |************|
                          |*U1**U2**U3*|
                          |************|
                          |*U4**U5**U6*|
                          |************|
                          |*U7**U8**U9*|
                          |************|
              ************|************|************|************|
              *L1**L2**L3*|*F1**F2**F3*|*R1**R2**R3*|*B1**B2**B3*|
              ************|************|************|************|
              *L4**L5**L6*|*F4**F5**F6*|*R4**R5**R6*|*B4**B5**B6*|
              ************|************|************|************|
              *L7**L8**L9*|*F7**F8**F9*|*R7**R8**R9*|*B7**B8**B9*|
              ************|************|************|************|
                          |************|
                          |*D1**D2**D3*|
                          |************|
                          |*D4**D5**D6*|
                          |************|
                          |*D7**D8**D9*|
                          |************|
'''


def toString(FACES):
    print()
    for i in range(3):
        print("     ", int(FACES[0][i][0]), int(FACES[0][i][1]), int(FACES[0][i][2]))
    for i in range(3):
        print(int(FACES[2][i][0]), int(FACES[2][i][1]), int(FACES[2][i][2]), end=" ")
        print(int(FACES[4][i][0]), int(FACES[4][i][1]), int(FACES[4][i][2]), end=" ")
        print(int(FACES[3][i][0]), int(FACES[3][i][1]), int(FACES[3][i][2]), end=" ")
        print(int(FACES[5][i][0]), int(FACES[5][i][1]), int(FACES[5][i][2]))
    for i in range(3):
        print("     ", int(FACES[1][i][0]), int(FACES[1][i][1]), int(FACES[1][i][2]))
    print()


def moves(FACES, lst):
    for x in lst:
        if x == 'U':
            U(faces)
        elif x == 'u':
            _U(faces)
        elif x == 'D':
            D(faces)
        elif x == 'd':
            _D(faces)
        elif x == 'L':
            L(faces)
        elif x == 'l':
            _L(faces)
        elif x == 'R':
            R(faces)
        elif x == 'r':
            _R(faces)
        elif x == 'F':
            F(faces)
        elif x == 'f':
            _F(faces)
        elif x == 'B':
            B(faces)
        elif x == 'b':
            _B(faces)


lst = input("请输入步骤:")
moves(faces, lst)
print("执行后的魔方为")
toString(faces)
reverse = ''.join(map(chr, map(lambda x: ord(x) ^ 32, lst)))[::-1]
moves(faces, reverse)
print("魔方恢复步骤:", reverse)
toString(faces)

示例

请输入步骤:UBLDFRULFDRULBGBVFDRLLBFLLDSSDBVDJFRUDLRFBDLFBbdj
执行后的魔方为

      2 5 3
      5 0 2
      5 0 5
5 2 3 1 2 1 2 4 0 4 0 0
1 2 3 1 4 5 1 3 1 4 5 2
2 5 2 4 4 3 1 0 5 3 4 4
      1 0 4
      3 1 3
      0 3 0

魔方恢复步骤: JDBbfldbfrldurfjdvbdssdllfbllrdfvbgblurdflurfdlbu

      0 0 0
      0 0 0
      0 0 0
2 2 2 4 4 4 3 3 3 5 5 5
2 2 2 4 4 4 3 3 3 5 5 5
2 2 2 4 4 4 3 3 3 5 5 5
      1 1 1
      1 1 1
      1 1 1


Process finished with exit code 0

注:大写为顺时针,小写为逆时针

到此这篇关于python实现三阶魔方还原的示例代码的文章就介绍到这了,更多相关python 三阶魔方还原内容请搜索三水点靠木以前的文章或继续浏览下面的相关文章希望大家以后多多支持三水点靠木!

Python 相关文章推荐
Python Mysql自动备份脚本
Jul 14 Python
Python内置函数bin() oct()等实现进制转换
Dec 30 Python
python异步任务队列示例
Apr 01 Python
Python RuntimeError: thread.__init__() not called解决方法
Apr 28 Python
通过mod_python配置运行在Apache上的Django框架
Jul 22 Python
举例讲解如何在Python编程中进行迭代和遍历
Jan 19 Python
TensorFlow Session使用的两种方法小结
Jul 30 Python
python实现顺序表的简单代码
Sep 28 Python
Python中xml和json格式相互转换操作示例
Dec 05 Python
wxPython窗体拆分布局基础组件
Nov 19 Python
Python中SQLite如何使用
May 27 Python
卸载tensorflow-cpu重装tensorflow-gpu操作
Jun 23 Python
python基于opencv批量生成验证码的示例
python基于tkinter制作下班倒计时工具
Apr 28 #Python
Python爬虫之爬取哔哩哔哩热门视频排行榜
k-means & DBSCAN 总结
秀!学妹看见都惊呆的Python小招数!【详细语言特性使用技巧】
Apr 27 #Python
Python代码,能玩30多款童年游戏!这些有几个是你玩过的
python实现腾讯滑块验证码识别
Apr 27 #Python
You might like
php中数据的批量导入(csv文件)
2006/10/09 PHP
php中session退出登陆问题
2014/02/27 PHP
Dwz与thinkphp整合下的数据导出到Excel实例
2014/12/04 PHP
详解php命令注入攻击
2019/04/06 PHP
Linux下安装Memcached服务器和客户端与PHP使用示例
2019/04/15 PHP
JS的数组的扩展实例代码
2008/07/09 Javascript
JavaScript 入门基础知识 想学习js的朋友可以参考下
2009/12/26 Javascript
基于Jquery的回车成tab焦点切换效果代码(Enter To Tab )
2010/11/14 Javascript
JS中Iframe之间传值及子页面与父页面应用
2013/03/11 Javascript
打印json对象的内容及JSON.stringify函数应用
2013/03/29 Javascript
JS定时器用法分析【时钟与菜单中的应用】
2016/12/21 Javascript
详解使用angularjs的ng-options时如何设置默认值(初始值)
2017/07/18 Javascript
vue中本地静态图片路径写法
2018/03/06 Javascript
vue组件实现可搜索下拉框扩展
2020/10/23 Javascript
vue中typescript装饰器的使用方法超实用教程
2019/06/17 Javascript
vue中input的v-model清空操作
2019/09/06 Javascript
vue点击自增和求和的实例代码
2019/11/06 Javascript
JavaScript计算正方形面积
2019/11/26 Javascript
解决vue里a标签值解析变量,跳转页面,前面加默认域名端口的问题
2020/07/22 Javascript
JavaScript实现网页tab栏效果制作
2020/11/20 Javascript
代码块高亮可复制显示js插件highlight.js+clipboard.js整合
2021/02/15 Javascript
使用70行Python代码实现一个递归下降解析器的教程
2015/04/17 Python
python读取二进制mnist实例详解
2017/05/31 Python
Python实现购物程序思路及代码
2017/07/24 Python
Django高级编程之自定义Field实现多语言
2019/07/02 Python
Django实现发送邮件功能
2019/07/18 Python
Python3+Django get/post请求实现教程详解
2021/02/16 Python
法国家具及室内配件店:home24
2017/01/21 全球购物
LEGO玩具英国官方商店:LEGO Shop GB
2018/03/27 全球购物
STP协议的主要用途是什么?为什么要用STP
2012/12/20 面试题
几个Linux面试题笔试题
2016/08/01 面试题
课改先进个人汇报材料
2014/01/26 职场文书
优秀大学生自荐信
2014/06/09 职场文书
自主招生自荐信怎么写
2015/03/24 职场文书
2016年入党心得体会范文
2016/01/23 职场文书
工作计划范文之财务管理
2019/08/09 职场文书