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#!/usr/bin/env python3

"""

Implementation of entropy of information

https://en.wikipedia.org/wiki/Entropy_(information_theory)

"""

import math

from collections import Counter

from string import ascii_lowercase

from typing import Tuple

def calculate_prob(text: str) -> None:

"""

This method takes path and two dict as argument

and than calculates entropy of them.

:param dict:

:return: Prints

1) Entropy of information based on 1 alphabet

2) Entropy of information based on couples of 2 alphabet

3) print Entropy of H(X n∣Xn−1)

Text from random books. Also, random quotes.

>>> text = ("Behind Winston’s back the voice "

... "from the telescreen was still "

... "babbling and the overfulfilment")

>>> calculate_prob(text)

4.0

6.0

2.0

>>> text = ("The Ministry of Truth—Minitrue, in Newspeak [Newspeak was the official"

... "face in elegant lettering, the three")

>>> calculate_prob(text)

4.0

5.0

1.0

>>> text = ("Had repulsive dashwoods suspicion sincerity but advantage now him. "

... "Remark easily garret nor nay. Civil those mrs enjoy shy fat merry. "

... "You greatest jointure saw horrible. He private he on be imagine "

... "suppose. Fertile beloved evident through no service elderly is. Blind "

... "there if every no so at. Own neglected you preferred way sincerity "

... "delivered his attempted. To of message cottage windows do besides "

... "against uncivil. Delightful unreserved impossible few estimating "

... "men favourable see entreaties. She propriety immediate was improving. "

... "He or entrance humoured likewise moderate. Much nor game son say "

... "feel. Fat make met can must form into gate. Me we offending prevailed "

... "discovery.")

>>> calculate_prob(text)

4.0

7.0

3.0

"""

single_char_strings, two_char_strings = analyze_text(text)

my_alphas = list(" " + ascii_lowercase)

# what is our total sum of probabilities.

all_sum = sum(single_char_strings.values())

# one length string

my_fir_sum = 0

# for each alpha we go in our dict and if it is in it we calculate entropy

for ch in my_alphas:

if ch in single_char_strings:

my_str = single_char_strings[ch]

prob = my_str / all_sum

my_fir_sum += prob * math.log2(prob) # entropy formula.

# print entropy

print("{0:.1f}".format(round(-1 * my_fir_sum)))

# two len string

all_sum = sum(two_char_strings.values())

my_sec_sum = 0

# for each alpha (two in size) calculate entropy.

for ch0 in my_alphas:

for ch1 in my_alphas:

sequence = ch0 + ch1

if sequence in two_char_strings:

my_str = two_char_strings[sequence]

prob = int(my_str) / all_sum

my_sec_sum += prob * math.log2(prob)

# print second entropy

print("{0:.1f}".format(round(-1 * my_sec_sum)))

# print the difference between them

print("{0:.1f}".format(round(((-1 * my_sec_sum) - (-1 * my_fir_sum)))))

def analyze_text(text: str) -> Tuple[dict, dict]:

"""

Convert text input into two dicts of counts.

The first dictionary stores the frequency of single character strings.

The second dictionary stores the frequency of two character strings.

"""

single_char_strings = Counter() # type: ignore

two_char_strings = Counter() # type: ignore

single_char_strings[text[-1]] += 1

# first case when we have space at start.

two_char_strings[" " + text[0]] += 1

for i in range(0, len(text) - 1):

single_char_strings[text[i]] += 1

two_char_strings[text[i : i + 2]] += 1

return single_char_strings, two_char_strings

def main():

import doctest

doctest.testmod()

# text = (

# "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "

# "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "

# "jointure saw horrible. He private he on be imagine suppose. Fertile "

# "beloved evident through no service elderly is. Blind there if every no so "

# "at. Own neglected you preferred way sincerity delivered his attempted. To "

# "of message cottage windows do besides against uncivil. Delightful "

# "unreserved impossible few estimating men favourable see entreaties. She "

# "propriety immediate was improving. He or entrance humoured likewise "

# "moderate. Much nor game son say feel. Fat make met can must form into "

# "gate. Me we offending prevailed discovery. "

# )

# calculate_prob(text)

if __name__ == "__main__":

main()

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