KenKen puzzle addends: REDUX A (corrected) non-recursive algorithm

Question

This question relates to those parts of the KenKen Latin Square puzzles which ask you to find all possible combinations of ncells numbers with values x such that 1 <= x &

Answer 1

Sorry to say, your code is kind of long and not particularly readable. If you can try to summarize it somehow, maybe someone can help you write it more clearly.

As for the problem itself, my first thought would be to use recursion. (For all I know, you're already doing that. Sorry again for my inability to read your code.) Think of a way that you can reduce the problem to a smaller easier version of the same problem, repeatedly, until you have a trivial case with a very simple answer.

To be a bit more concrete, you have these three parameters, max_val, target_sum, and n_cells. Can you set one of those numbers to some particular value, in order to give you an extremely simple problem requiring no thought at all? Once you have that, can you reduce the slightly harder version of the problem to the already solved one?

EDIT: Here is my code. I don't like the way it does de-duplication. I'm sure there's a more Pythonic way. Also, it disallows using the same number twice in one combination. To undo this behavior, just take out the line if n not in numlist:. I'm not sure if this is completely correct, but it seems to work and is (IMHO) more readable. You could easily add memoization and that would probably speed it up quite a bit.

def get_combos(max_val, target, n_cells):
    if target <= 0:
        return []
    if n_cells is 1:
        if target > max_val:
            return []
        else:
            return [[target]]
    else:
        combos = []
        for n in range(1, max_val+1, 1):
            for numlist in get_combos(max_val, target-n, n_cells-1):
                if n not in numlist:
                    combos.append(numlist + [n])
        return combos

def deduplicate(combos):
    for numlist in combos:
        numlist.sort()
    answer = [tuple(numlist) for numlist in combos]
    return set(answer)

def kenken(max_val, target, n_cells):
    return deduplicate(get_combos(max_val, target, n_cells))