python function for list of lists n long, with each element 0-m

Question

I need to make a function so that I can put in two parameters, an order, and a max, and return a list of all of the lists 'order' long and with each element ranging from 0 to 'max'. I suspect I may need to use recursion, but I am getting lost in this.

so order = 2 max = 3 should return

[[0,0], [0,1], [0,2], [0,3], [1,0], [1,1], ... ,[3,3]]

and order=4, max=5 should return

[[0,0,0,0], [0,0,0,1], [0,0,0,2], ...  [3,3,3,3]]

Thanks for the help

Answer 1

Note that in general, @Prune's answer is the weapon of choice, here.

As for recursion: The requested list can be constructed recursively as

1. The list of length 1 is the list of all 1 -element lists with elements from the initial set:

[1] -> [[1]]

[1, 2] -> [[1], [2]]

[1, 2, 3] -> [[1], [2], [3]]

In Python:

l1 = [[item] for item in range(0, max + 1)]

2. The list ln1 of length n + 1 consists of the cartesian product of ln of length n with l1 with the elements joined by list concatenation.

In Python:

ln1 = [a + b for a in combine(base, n - 1) for b in combine(base, 1)]

def combinations(base, n):
    if n == 0:
        return []
    elif n == 1:
        return [[item] for item in base]
    else:
        return [a + b for a in combine(base, n - 1) for b in combine(base, 1)]

itertools.combinations_with_replacements() is both faster and more memory efficient. It's also an existing wheel rather than a new one.

Answer 2

You don't need recursion; all you need is the Python itertools package:

import itertools
num_list = [x for x in range(max+1)]

for one_combo in itertools.combinations_with_replacement(num_list, order):
    ...

Of course, you can combine the two computational lines; it's just easier to see this way.

Answer 3

Here's a function that uses recursion to solve the problem. When you are dealing with recursion, make sure you have a base case and a general case.

def recurseNumbers(order, mx):
    if order == 1:
        return [[n] for n in range(mx + 1)]
    else:
        total_array = []
        for num in range(mx + 1):
            numbers = recurseNumbers(order - 1, mx)
            for number in numbers:
                total_array.append([num] + number)
        return total_array

Also note that Python list addition makes this relatively simple. ["a"] + ["b"] = ["a", "b"]