如何在Python中生成所有不同的3x3拉丁方的列表

Question

拉丁方是一个nxn数组，填充了n个不同的符号，每一个符号在每行和每列中分别出现一次(就像数独一样(。拉丁方块的一个例子：

1 2 3
2 3 1
3 1 2

这是我尝试过的，但它仍然不是完全不同的

grid = []
temp = []
block = [[1,2,3],
[2,3,1],
[3,1,2]]
perm = permutations(block)
for i in perm:  #row permutations
temp.extend(i)
if len(temp)==3:
grid.extend([temp])
temp = []
for perm in zip(permutations(block[0]), permutations(block[1]), permutations(block[2])): #column permutations
temp.extend([perm])
for i in range(len(temp)):  #convert to list
temp[i] = list(temp[i])
for j in range(len(temp[0])):
temp[i][j] = list(temp[i][j])
grid.extend(temp)
for i in grid:
for j in i:
print(j)
print()

输出为：

[1, 2, 3]
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[2, 3, 1]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
[3, 1, 2]
[1, 2, 3]
[2, 3, 1]
[3, 1, 2]
[2, 3, 1]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[1, 2, 3]
[3, 2, 1]
[2, 1, 3]
[1, 3, 2]
[1, 3, 2]
[3, 2, 1]
[2, 1, 3]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[2, 3, 1]
[1, 2, 3]
[3, 1, 2]
[2, 1, 3]
[1, 3, 2]
[3, 2, 1]

结果应该是这样的(顺序无关紧要(：拉丁方

[1, 2, 3]
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[1, 3, 2]
[2, 1, 3]
[3, 2, 1]
[1, 3, 2]
[3, 2, 1]
[2, 1, 3]
[2, 1, 3]
[1, 3, 2]
[3, 2, 1]
[2, 1, 3]
[3, 2, 1]
[1, 3, 2]
[2, 3, 1]
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
[3, 2, 1]
[1, 3, 2]
[2, 1, 3]
[3, 2, 1]
[2, 1, 3]
[1, 3, 2]
[3, 1, 2]
[1, 2, 3]
[2, 3, 1]
[3, 1, 2]
[2, 3, 1]
[1, 2, 3]

Answer 1

您可以将递归与生成器一起使用：

def row(n, r, c = []):
if len(c) == n:
yield c
for i in range(1, n+1):
if i not in c and i not in r[len(c)]:
yield from row(n, r, c+[i])
def to_latin(n, c = []):
if len(c) == n:
yield c
else:
for i in row(n, [[]]*n if not c else list(zip(*c))):
yield from to_latin(n, c+[i])

for i in to_latin(3):
for b in i:
print(b)
print('-'*9)

输出：

[1, 2, 3]
[2, 3, 1]
[3, 1, 2]
---------
[1, 2, 3]
[3, 1, 2]
[2, 3, 1]
---------
[1, 3, 2]
[2, 1, 3]
[3, 2, 1]
---------
[1, 3, 2]
[3, 2, 1]
[2, 1, 3]
---------
[2, 1, 3]
[1, 3, 2]
[3, 2, 1]
---------
[2, 1, 3]
[3, 2, 1]
[1, 3, 2]
---------
[2, 3, 1]
[1, 2, 3]
[3, 1, 2]
---------
[2, 3, 1]
[3, 1, 2]
[1, 2, 3]
---------
[3, 1, 2]
[1, 2, 3]
[2, 3, 1]
---------
[3, 1, 2]
[2, 3, 1]
[1, 2, 3]
---------
[3, 2, 1]
[1, 3, 2]
[2, 1, 3]
---------
[3, 2, 1]
[2, 1, 3]
[1, 3, 2]
---------