find_num_steps.py

from math import log, floor, ceil

is_odd = lambda n: n % 2
is_even = lambda n: not is_odd(n)
log2 = lambda n: log(n, 2)
is_power_of_2 = lambda n: log2(n) == int(log2(n))


def find_number_of_steps(n):
	if is_power_of_2(n):
		return log2(n)
	if is_even(n):
		return min(steps_from_closest_power_of_2(n), 1 + find_number_of_steps(n / 2))
	if is_odd(n):
		return 1 + min(find_number_of_steps(n + 1), find_number_of_steps(n - 1))

def steps_from_closest_power_of_2(n):
	m = log2(n)
	m_up = ceil(m)
	m_down = floor(m)
	return min(abs(n - m_up) + m_up, abs(n - m_down) + m_down)