"""simple docstring"""




from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase






def      UpperCAmelCase    (		UpperCamelCase__ ):






							"""simple docstring"""





							A__		   =							analyze_text(__lowerCamelCase )
							A__		   =							list(' ' + ascii_lowercase )
							# what is our total sum of probabilities.
							A__		   =							sum(single_char_strings.values() )

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

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

							# two len string
							A__		   =							sum(two_char_strings.values() )
							A__		   =							0
							# for each alpha (two in size) calculate entropy.
							for cha in my_alphas:
														for cha in my_alphas:
																					A__		   =							cha + cha
																					if sequence in two_char_strings:
																												A__		   =							two_char_strings[sequence]
																												A__		   =							int(__lowerCamelCase ) / all_sum
																												my_sec_sum += prob * math.loga(__lowerCamelCase )

    # 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      UpperCAmelCase    (		UpperCamelCase__ ):






							"""simple docstring"""





							A__		   =							Counter()  # type: ignore
							A__		   =							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(__lowerCamelCase ) - 1 ):
														single_char_strings[text[i]] += 1
														two_char_strings[text[i : i + 2]] += 1
							return single_char_strings, two_char_strings






def      UpperCAmelCase    (		):






							"""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()







"""simple docstring"""





from __future__ import annotations







def 	__a     (		__lowerCamelCase,		__lowerCamelCase  ):
   UpperCAmelCase_     ,   UpperCAmelCase_					:					str			     =    set(__lowerCamelCase  ), [start]

   while stack:
      UpperCAmelCase_					:					Any			     =    stack.pop()
      explored.add(__lowerCamelCase  )
      # Differences from BFS:
      # 1) pop last element instead of first one
      # 2) add adjacent elements to stack without exploring them
      for adj in reversed(graph[v]  ):
         if adj not in explored:
            stack.append(__lowerCamelCase  )
   return explored


_a		       =							{
    'A': ['B', 'C', 'D'],
    'B': ['A', 'D', 'E'],
    'C': ['A', 'F'],
    'D': ['B', 'D'],
    'E': ['B', 'F'],
    'F': ['C', 'E', 'G'],
    'G': ['F'],
}

if __name__ == "__main__":
    import doctest

    doctest.testmod()
    print(depth_first_search(G, 'A'))


