python - Get all numbers that add up to a number

Question

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

Or for 3 integers that make 6:

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

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.

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

Answer 1

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

You can use it like this.

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

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