获取所有加起来为数字的数字 [英] Get all numbers that add up to a number

问题描述

我试图找到一种方法来显示所有可能的X整数集，这些X整数加起来等于一个给定的整数.例如，要获得所有2个整数集，使我得到5个:

I'm trying to find a way to display all the possible sets of X integers that add up to a given integer. for example to get all 2 integer sets that make 5 I would have:

1, 4
2, 3

或为3个整数组成6:

1, 1, 4
1, 2, 3
2, 2, 2

我只需要不包括0的整数，并且最多只需要处理一组中的15个和最大30个.数字.

I only need whole numbers not including 0 and it only needs to work on up to about 15 in a set and 30 max. number.

我什至不确定数学上是否有这个术语.我猜这类似于分解因子吗?

I'm not even sure if this has a term mathematically. It's similar to factorisation I guess?

推荐答案

这是解决此问题的一种方法:

Here is one way to solve this problem:

def sum_to_n(n, size, limit=None):
    """Produce all lists of `size` positive integers in decreasing order
    that add up to `n`."""
    if size == 1:
        yield [n]
        return
    if limit is None:
        limit = n
    start = (n + size - 1) // size
    stop = min(limit, n - size + 1) + 1
    for i in range(start, stop):
        for tail in sum_to_n(n - i, size - 1, i):
            yield [i] + tail

您可以像这样使用它.

for partition in sum_to_n(6, 3):
    print partition

[2, 2, 2]
[3, 2, 1]
[4, 1, 1]

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