import sys
import random
import string
from bigfloat import *

factor = BigFloat(1)/BigFloat(26)

def encode(encode_str, N):
    count = dict.fromkeys(string.ascii_lowercase, 1)                                        # probability table
    cdf_range = dict.fromkeys(string.ascii_lowercase, 0)
    pdf = dict.fromkeys(string.ascii_lowercase, 0)

    with precision(200) + RoundTowardZero:
        low = 0
        high = factor

        for key, value in sorted(cdf_range.iteritems()):
            cdf_range[key] = [low, high]
            low = high
            high += factor

        for key, value in sorted(pdf.iteritems()):
            pdf[key] = factor

        # for key, value in sorted(cdf_range.iteritems()):
        #   print key, value

        # for key, value in sorted(pdf.iteritems()):
        #   print key, value

        i = 26

        lower_bound = 0                         # upper bound
        upper_bound = 1                         # lower bound

        u = 0

        # go thru every symbol in the string
        for sym in encode_str:
            i += 1
            u += 1
            count[sym] += 1

            curr_range = upper_bound - lower_bound                                          # current range
            upper_bound = lower_bound + (curr_range * cdf_range[sym][1])                    # upper_bound
            lower_bound = lower_bound + (curr_range * cdf_range[sym][0])                    # lower bound

            # update cdf_range after N symbols have been read
            if (u == N):
                u = 0

                for key, value in sorted(pdf.iteritems()):
                    pdf[key] = BigFloat(count[key])/BigFloat(i)

                low = 0
                for key, value in sorted(cdf_range.iteritems()):
                    high = pdf[key] + low
                    cdf_range[key] = [low, high]
                    low = high

    return lower_bound

def decode(encoded, strlen, every):
    decoded_str = ""

    count = dict.fromkeys(string.ascii_lowercase, 1)                                        # probability table
    cdf_range = dict.fromkeys(string.ascii_lowercase, 0)
    pdf = dict.fromkeys(string.ascii_lowercase, 0)


    with precision(200) + RoundTowardZero:
        low = 0
        high = factor

        for key, value in sorted(cdf_range.iteritems()):
            cdf_range[key] = [low, high]
            low = high
            high += factor

        for key, value in sorted(pdf.iteritems()):
            pdf[key] = factor


        lower_bound = BigFloat(0)                           # upper bound
        upper_bound = BigFloat(1)                           # lower bound

        k = 0

        while (strlen != len(decoded_str)):
            for key, value in sorted(pdf.iteritems()):

                curr_range = upper_bound - lower_bound                                      # current range
                upper_cand = lower_bound + (curr_range * cdf_range[key][1])                 # upper_bound
                lower_cand = lower_bound + (curr_range * cdf_range[key][0])                 # lower bound

                if (lower_cand <= encoded < upper_cand):
                    k += 1
                    decoded_str += key

                    if (strlen == len(decoded_str)):
                        break

                    upper_bound = upper_cand
                    lower_bound = lower_cand

                    count[key] += 1

                    if (k == every):
                        k = 0
                        for key, value in sorted(pdf.iteritems()):
                            pdf[key] = BigFloat(count[key])/BigFloat(26+len(decoded_str))

                        low = 0
                        for key, value in sorted(cdf_range.iteritems()):
                            high = pdf[key] + low
                            cdf_range[key] = [low, high]
                            low = high

        print decoded_str

def main():
    count = 10
    encode_str = "heloworldheloworld"
    strlen = len(encode_str)
    every = 3
    encoded = encode(encode_str, every)
    decoded = decode(encoded, strlen, every)

if __name__ == '__main__':
    main()