如何生成给定长度和元素总和的所有元组的集合？ [英] How to generate a set of all tuples of given length and sum of elements?

问题描述

我想拥有一个函数，该函数生成具有给定长度和元素总和的所有可能元组的集合（或列表）。元组的元素不能为负整数。

I would like to have a function that generates a set (or a list) of all possible tuples with a given length and sum of their elements. The elements of tuples should be not negative integer.

例如，以下输入

get_tuple(length=3, total=2)

我想获得以下输出：

[(1, 0, 1), (2, 0, 0), (1, 1, 0), (0, 0, 2), (0, 1, 1), (0, 2, 0)]

是标准库在Python中可以做到这一点？如果没有，如何编写一个可以做到的函数？

Is the a standard library in Python that can do that? If not, how to write a function that can do it?

推荐答案

您可以创建一个递归函数，避免创建所有候选组合并检查它们的总和：

You can create a recursive function, avoiding creating all candidate combinations and checking their sums:

def get_tuples(length, total):
    if length == 1:
        yield (total,)
        return

    for i in xrange(total + 1):
        for t in get_tuples(length - 1, total - i):
            yield (i,) + t

如果我们测试：

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

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