After using combinations with replacement, how to remove tuples with combinations that I don't want

Question

I'm trying to get a list of lists (or tuples) which follows a pattern something like this:

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

Using itertools.combinations_with_replacement I've gotten close, but I end up with lists which jump values for example:

[1,1,1,3]
or
[2,2,2,3]

I don't want this. I always want to start at 1, and increase until the list is filled, and then increase to the next value.

If I'm using itertools, then is there a way to remove the lists that I don't want?

Answer 1

Instead of using combinations, I would generate the pattern directly.

Create a list of 1's with the desired length and iterate backward, changing the list accordingly.

def generate_increment(n):
    lst = [1] * n
    result = []
    for k in range(n-1):
        lst[-1] += 1
        result.append(lst[:])
        for i in range(len(lst)-2, k, -1):
            a, b = lst[i], lst[i+1]
            if a != b:
                lst[i] = b
                result.append(lst[:])
    return result

>>print(*generate_increment(4), sep='\n')

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