Python3 - Permutations for 7 digit number that totals to a number

Question

I need to find a solution for the below problem in Python3. I tried itertools.combinations but not clear on how to do it.

Prepare a 7-digit number that sums to 5. Each digit can be between 0-4 only. Also, there can be repetitions. Valid example numbers are -

[ [2,1,1,0,0,1,0], [3,0,1,0,0,1,0], [0,0,0,4,0,0,1], [1,0,0,3,0,1,0], [1,1,1,1,0,1,0], ...... ]

As you can see, numbers may appear more than once in this list.

How can I create a list of all combinations meeting the criteria above?

Answer 1

This function will find every combination, with repeated combinations, that sum to N:

from itertools import product
from typing import List, Tuple
def perm_n_digit_total(n_digits, total, choices) -> List[Tuple]:
    return list(filter(
        lambda x: sum(x) == total,
        product(choices, repeat=n_digits)
    ))

Example:

perm_n_digit_total(3, 1, range(4))
Out[43]: [(0, 0, 1), (0, 1, 0), (1, 0, 0)]

perm_n_digit_total(7, 5, range(4))[::50]
Out[49]: 
[(0, 0, 0, 0, 0, 0, 5),
 (0, 0, 0, 3, 1, 1, 0),
 (0, 0, 2, 0, 3, 0, 0),
 (0, 1, 0, 1, 3, 0, 0),
 (0, 2, 0, 0, 1, 0, 2),
 (0, 4, 1, 0, 0, 0, 0),
 (1, 0, 1, 1, 1, 0, 1),
 (1, 1, 1, 1, 1, 0, 0),
 (2, 0, 1, 0, 0, 2, 0),
 (3, 1, 0, 0, 0, 1, 0)]