implementation of entropy algorithm. (#2110)

* implementation of entropy algorithm.

* add tests, fix requested changes

* open_file() --> analyze_text()

* Create bidirectional_breadth_first_search.py

* # type: ignore

Co-authored-by: Christian Clauss <cclauss@me.com>

graphs/bidirectional_breadth_first_search.py

@@ -100,7 +100,8 @@ class BreadthFirstSearch:
 
 class BidirectionalBreadthFirstSearch:
     """
-    >>> bd_bfs = BidirectionalBreadthFirstSearch((0, 0), (len(grid) - 1, len(grid[0]) - 1))
+    >>> bd_bfs = BidirectionalBreadthFirstSearch((0, 0), (len(grid) - 1,
+    ...                                                   len(grid[0]) - 1))
     >>> bd_bfs.fwd_bfs.start.pos == bd_bfs.bwd_bfs.target.pos
     True
     >>> bd_bfs.retrace_bidirectional_path(bd_bfs.fwd_bfs.start,

maths/entropy.py

@@ -0,0 +1,131 @@
+#!/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:
+    :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()