stairway.py

from pprint import pprint as pp


def reached_top_of_stairs(stairway_height, step_tuple):
    return sum(step_tuple) == stairway_height

def compute_max_steps(stairway_height, step_options):
    non_zero = [f for f in step_options if f != 0]
    min_step = min(non_zero)
    return int(stairway_height / min_step)

def smallest_possible_steps(stairway_height, step_options):
    max_steps = compute_max_steps(stairway_height, step_options)
    min_value = min(step_options)
    return [min_value,] * max_steps


def largest_possible_steps(stairway_height, step_options):
    max_steps = compute_max_steps(stairway_height, step_options)
    max_value = max(step_options)
    return [max_value,] * max_steps


def inc_digit(step_options, d):
    cur_index = step_options.index(d)
    next_index = 1 + cur_index
    try:
        return step_options[next_index]
    except IndexError:
        return None

def inc_tuple(stairway_height, step_options, v):
    v_len = len(v)
    inc_value = inc_digit(step_options, v[-1])
    min_digit = min(step_options)
    largest_steps = largest_possible_steps(stairway_height, step_options)
    if v == largest_steps:
        return None
    if inc_value:
        v[v_len -1] = inc_value
        return v
    else:
        drop_last = v[:-1]
        ret = inc_tuple(stairway_height, step_options, drop_last )
        ret.append(min_digit)
        return ret

def generate_all_possibilities(stairway_height, step_options):
    cur_tuple         = smallest_possible_steps(stairway_height, step_options)
    largest_steps     = largest_possible_steps(stairway_height, step_options)
    all_possibilities = []
    while True:
        all_possibilities.append(cur_tuple)
        if cur_tuple == largest_steps:
            break
        else:
            cur_tuple = inc_tuple(stairway_height, step_options, cur_tuple)
    return all_possibilities


step_options = [0, 1, 2]
stairway_height = 3


pp(generate_all_possibilities(stairway_height, step_options))

# ???? horray python.

# In [6]: [[0, 0, 2],
#  [0, 0, 2],
#  [0, 0, 2],
#  [0, 1, 2],
#  [0, 1, 2],
#  [0, 1, 2],
#  [0, 2, 2],
#  [0, 2, 2],
#  [0, 2, 2],
#  [1, 0, 2],
#  [1, 0, 2],
#  [1, 0, 2],
#  [1, 1, 2],
#  [1, 1, 2],
#  [1, 1, 2],
#  [1, 2, 2],
#  [1, 2, 2],
#  [1, 2, 2],
#  [2, 0, 2],
#  [2, 0, 2],
#  [2, 0, 2],
#  [2, 1, 2],
#  [2, 1, 2],
#  [2, 1, 2],
#  [2, 2, 2],
#  [2, 2, 2],
#  [2, 2, 2]]
#