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python的数据类型：1. 数字类型，包括int（整型）、long（长整型）和float（浮点型）。2.字符串，分别是str类型和unicode类型。3.布尔型，Python布尔类型也是用于逻辑运算，有两个值：True（真）和False（假）。4.列表，列表是Python中使用最频繁的数据类型，集合中可以放任何数据类型。5. 元组，元组用”()”标识，内部元素用逗号隔开。6. 字典，字典是一种键值对的集合。7. 集合，集合是一个无序的、不重复的数据组合。
# 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])
每一个面的 顺时针 和 逆时针 旋转由函数 clockwise() 和 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。
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
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