https://www.codewars.com/kata/how-many-numbers-iii/train/python

Task

We want to generate all the numbers of three digits that:

• the value of adding their corresponding ones(digits) is equal to 10.

• their digits are in increasing order (the numbers may have two or more equal contiguous digits)

The numbers that fulfill the two above constraints are: 118, 127, 136, 145, 226, 235, 244, 334

Make a function that receives two arguments:

• the sum of digits value

• the amount of desired digits for the numbers

The function should output an array with three values: [1,2,3]

1 - the total amount of all these possible numbers

2 - the minimum number

3 - the maximum numberwith

The example given above should be:

find_all(10, 3) == [8, 118, 334]

If we have only one possible number as a solution, it should output a result like the one below:

find_all(27, 3) == [1, 999, 999]

If there are no possible numbers, the function should output the empty array.

find_all(84, 4) == []

The number of solutions climbs up when the number of digits increases.

find_all(35, 6) == [123, 116999, 566666]

Features of the random tests:

Numbers of tests: 111
Sum of digits value between 20 and 65
Amount of digits between 2 and 15

Best Practices

Py First:

def find_all(s, d):
    xs = [x for x in digs(d) if sum(x) == s]
    if not xs:
        return []
    else:
        reduce_int = lambda xs: int(''.join(map(str, xs)))
        min = reduce_int(xs[0])
        max = reduce_int(xs[-1])    
        return [len(xs), min, max]

def digs(d, start=1):
    """
    >>> list(digs(3, start=9))
    [[9, 9, 9]]
    >>> list(digs(2, start=8))
    [[8, 8], [8, 9], [9, 9]]
    """
    if d == 1:
        for x in range(start, 10):
            yield [x]
    else:
        for x in range(start, 10):
            for y in digs(d - 1, x):
                yield [x] + y

Py Second:

from itertools import combinations_with_replacement

def find_all(sum_dig, digs):
    combs = combinations_with_replacement(list(range(1, 10)), digs)
    target = [''.join(str (x) for x in list(comb)) for comb in combs if sum(comb) == sum_dig]
    if not target:
        return []
    return [len(target), int(target[0]), int(target[-1])]