Creating an array of numbers that sum to a given number

Question

I\'ve been working on some quick and dirty scripts for doing some of my chemistry homework, and one of them iterates through lists of a constant length where all the element

Answer 1

Here's a recursive generator that yields the lists in lexicographic order. Leaving exact as True gives the requested result where every sum==limit; setting exact to False gives all lists with 0 <= sum <= limit. The recursion takes advantage of this option to produce the intermediate results.

def lists_with_sum(length, limit, exact=True):
    if length:
        for l in lists_with_sum(length-1, limit, False):
            gap = limit-sum(l)
            for i in range(gap if exact else 0, gap+1):
                yield l + [i]
    else:
        yield []