python - 带递归的循环变量

Question

想通过递归执行以下操作，以便我可以改变“for”循环的数量:

n = 5
out = []
for i in range(n):
    for j in range(i,n):
        for k in range(j,n):
            out.append([i,j,k])

返回

out =   [[0 0 0]
         [0 0 1]
         [0 0 2]
         [0 0 3]
         [0 0 4]
         [0 1 1]
         [0 1 2]
         [0 1 3]
         [0 1 4]
         [0 2 2]
         [0 2 3]
         [0 2 4]
         [0 3 3]
         [0 3 4]
         [0 4 4]
         [1 1 1]
         [1 1 2]
         [1 1 3]
         [1 1 4]
         [1 2 2]...]

例如

def Recurse(n, p):
  # where p is the number of for loops
  some magic recursion 
  return out

我看过其他一些递归问题，但很难找到解决方案。

Answer 1

不使用递归，而是使用 itertools.product() ，相当于生成器表达式中的嵌套 for 循环:

>>> import itertools
>>> list(itertools.product(range(3), repeat=2))
[(0, 0), (0, 1), (0, 2), (1, 0), (1, 1), (1, 2), (2, 0), (2, 1), (2, 2)]
>>> list(itertools.product(range(3), repeat=3))
[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 2, 0), (0, 2, 1), (0, 2, 2), (1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 2, 0), (1, 2, 1), (1, 2, 2), (2, 0, 0), (2, 0, 1), (2, 0, 2), (2, 1, 0), (2, 1, 1), (2, 1, 2), (2, 2, 0), (2, 2, 1), (2, 2, 2)]

编辑: 没有意识到这实际上不是笛卡尔积，因为内部循环使用外部变量来开始范围，这是一种可能性，但效率不如它可能是因为它会生成额外的值并需要检查每个值是否有效:

def nested_loops(n, num_loops):
    prod = itertools.product(range(n), repeat=num_loops)
    for item in prod:
        if all(item[i] <= item[i+1] for i in range(num_loops-1)):
            yield item

>>> list(nested_loops(3, 2))
[(0, 0), (0, 1), (0, 2), (1, 1), (1, 2), (2, 2)]
>>> list(nested_loops(3, 3))
[(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 1, 1), (0, 1, 2), (0, 2, 2), (1, 1, 1), (1, 1, 2), (1, 2, 2), (2, 2, 2)]