




from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase







def lowerCamelCase__       (      _lowercase				):

     '''simple docstring'''


     UpperCAmelCase_,   UpperCAmelCase_      :							str       =      analyze_text(lowercase_				)
     UpperCAmelCase_      :							List[Any]       =      list(''' ''' + ascii_lowercase				)
     # what is our total sum of probabilities.
     UpperCAmelCase_      :							Optional[int]       =      sum(single_char_strings.values()				)

     # one length string
     UpperCAmelCase_      :							Dict       =      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:
               UpperCAmelCase_      :							str       =      single_char_strings[ch]
               UpperCAmelCase_      :							Dict       =      my_str / all_sum
               my_fir_sum += prob * math.loga(lowercase_				)  # entropy formula.

    # print entropy
     print(f'''{round(-1 * my_fir_sum				):.1f}'''				)

     # two len string
     UpperCAmelCase_      :							Dict       =      sum(two_char_strings.values()				)
     UpperCAmelCase_      :							List[Any]       =      0
     # for each alpha (two in size) calculate entropy.
     for cha in my_alphas:
          for cha in my_alphas:
               UpperCAmelCase_      :							str       =      cha + cha
               if sequence in two_char_strings:
                    UpperCAmelCase_      :							str       =      two_char_strings[sequence]
                    UpperCAmelCase_      :							Union[str, Any]       =      int(lowercase_				) / all_sum
                    my_sec_sum += prob * math.loga(lowercase_				)

    # print second entropy
     print(f'''{round(-1 * my_sec_sum				):.1f}'''				)

     # print the difference between them
     print(f'''{round((-1 * my_sec_sum) - (-1 * my_fir_sum)				):.1f}'''				)







def lowerCamelCase__       (      _lowercase				):

     '''simple docstring'''


     UpperCAmelCase_      :							Union[str, Any]       =      Counter()  # type: ignore
     UpperCAmelCase_      :							Dict       =      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(lowercase_				) - 1				):
          single_char_strings[text[i]] += 1
          two_char_strings[text[i : i + 2]] += 1
     return single_char_strings, two_char_strings







def lowerCamelCase__       (      ):

     '''simple docstring'''


     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()





def lowerCamelCase__       (      _lowercase			,						_lowercase				):

     '''simple docstring'''


     return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2







def lowerCamelCase__       (      _lowercase			,						_lowercase=0				):

     '''simple docstring'''


     return sorted(_lowercase			,						key=lambda _lowercase				: x[column]				)







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase=float('''inf'''				)				):

     '''simple docstring'''


     for i in range(points_counts - 1				):
          for j in range(i + 1			,						_lowercase				):
               UpperCAmelCase_      :							Optional[int]       =      euclidean_distance_sqr(points[i]			,						points[j]				)
               if current_dis < min_dis:
                    UpperCAmelCase_      :							Optional[Any]       =      current_dis
     return min_dis







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase=float('''inf'''				)				):

     '''simple docstring'''


     for i in range(min(6			,						points_counts - 1				)			,						_lowercase				):
          for j in range(max(0			,						i - 6				)			,						_lowercase				):
               UpperCAmelCase_      :							List[str]       =      euclidean_distance_sqr(points[i]			,						points[j]				)
               if current_dis < min_dis:
                    UpperCAmelCase_      :							Optional[int]       =      current_dis
     return min_dis







def lowerCamelCase__       (      _lowercase			,						_lowercase			,						_lowercase				):

     '''simple docstring'''


     if points_counts <= 3:
          return dis_between_closest_pair(_lowercase			,						_lowercase				)

     # recursion
     UpperCAmelCase_      :							Optional[int]       =      points_counts // 2
     UpperCAmelCase_      :							List[Any]       =      closest_pair_of_points_sqr(
         _lowercase			,						points_sorted_on_y[:mid]			,						_lowercase				)
     UpperCAmelCase_      :							Dict       =      closest_pair_of_points_sqr(
         _lowercase			,						points_sorted_on_y[mid:]			,						points_counts - mid				)
     UpperCAmelCase_      :							Union[str, Any]       =      min(_lowercase			,						_lowercase				)
     UpperCAmelCase_      :							str       =      []
     for point in points_sorted_on_x:
          if abs(point[0] - points_sorted_on_x[mid][0]				) < closest_pair_dis:
               cross_strip.append(_lowercase				)

     UpperCAmelCase_      :							Optional[Any]       =      dis_between_closest_in_strip(
         _lowercase			,						len(_lowercase				)			,						_lowercase				)
     return min(_lowercase			,						_lowercase				)







def lowerCamelCase__       (      _lowercase			,						_lowercase				):

     '''simple docstring'''


     UpperCAmelCase_      :							Tuple       =      column_based_sort(_lowercase			,						column=0				)
     UpperCAmelCase_      :							List[Any]       =      column_based_sort(_lowercase			,						column=1				)
     return (
         closest_pair_of_points_sqr(
             _lowercase			,						_lowercase			,						_lowercase				)
     ) ** 0.5


if __name__ == "__main__":
     __a          =			[(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
     print('Distance:', closest_pair_of_points(points, len(points)))