random_generator.py

import random
import math

def random_number_generator(base, power, base_num):
    if power == 1:
        return base()
    return int((base_num ** (power-1)) * base() + random_number_generator(base, power-1, base_num))

def generate_given(rand_num, target_rand_range):
    if target_rand_range < rand_num:
        while True:
            n = random_number_generator(lambda: random.randint(0, rand_num-1), 1, rand_num)
            if target_rand_range < n:
                return target_rand_range % n
    power = math.ceil(math.log(target_rand_range, rand_num))
    while True:
        n = random_number_generator(lambda: random.randint(0, rand_num-1), power, rand_num)
        if n < target_rand_range:
            return n % target_rand_range

from collections import Counter
c = Counter((generate_given(12, 200) for _ in xrange(20000)))
import ipdb; ipdb.set_trace()
#print Counter((random_number_generator(lambda: random.randint(0, 3), 3, 4) for _ in xrange(200000)))