可变数量的相关嵌套循环

问题描述：

给出两个整数n和d，我想构造一个长度为d的所有非负元组的列表，这些元组的总和为n，包括所有排列.这类似于整数分区问题，但解决方案要简单得多.例如 d==3:

Given two integers n and d, I would like to construct a list of all nonnegative tuples of length d that sum up to n, including all permutations. This is similar to the integer partitioning problem, but the solution is much simpler. For example for d==3:

[
    [n-i-j, j, i]
    for i in range(n+1)
    for j in range(n-i+1)
]

可以很容易地将其扩展到更多维度，例如d==5:

This can be extended to more dimensions quite easily, e.g., d==5:

[
    [n-i-j-k-l, l, k, j, i]
    for i in range(n+1)
    for j in range(n-i+1)
    for k in range(n-i-j+1)
    for l in range(n-i-j-l+1)
]

我现在想制作d，即嵌套循环的数量，一个变量，但是我不确定当时如何嵌套循环.

I would now like to make d, i.e., the number of nested loops, a variable, but I'm not sure how to nest the loops then.

有任何提示吗?

答

递归:首先创建一个长度为d-1的元组列表，该元组遍历所有ijk，然后用另一列.

Recursion to the rescue: First create a list of tuples of length d-1 which runs through all ijk, then complete the list with another column n-sum(ijk).

def partition(n, d, depth=0):
    if d == depth:
        return [[]]
    return [
        item + [i]
        for i in range(n+1)
        for item in partition(n-i, d, depth=depth+1)
        ]


# extend with n-sum(entries)
n = 5
d = 3
lst = [[n-sum(p)] + p for p in partition(n, d-1)]

print(lst)

可变数量的相关嵌套循环

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