

from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase

def  lowerCamelCase__ (					_a):
	SCREAMING_SNAKE_CASE     ,SCREAMING_SNAKE_CASE   :      Tuple				     =       analyze_text(_a)
	SCREAMING_SNAKE_CASE   :      List[str]				     =       list(" " + ascii_lowercase)
	# what is our total sum of probabilities.
	SCREAMING_SNAKE_CASE   :      str				     =       sum(single_char_strings.values())

	# one length string
	SCREAMING_SNAKE_CASE   :      List[Any]				     =       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:
			SCREAMING_SNAKE_CASE   :      Union[str, Any]				     =       single_char_strings[ch]
			SCREAMING_SNAKE_CASE   :      List[str]				     =       my_str / all_sum
			my_fir_sum += prob * math.loga(_a)  # entropy formula.

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

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

    # 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__ (					_a):
	SCREAMING_SNAKE_CASE   :      List[Any]				     =       Counter()  # type: ignore
	SCREAMING_SNAKE_CASE   :      int				     =       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(_a) - 1):
		single_char_strings[text[i]] += 1
		two_char_strings[text[i : i + 2]] += 1
	return single_char_strings, two_char_strings

def  lowerCamelCase__ (					):
	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__ (					_a							,			_a							,			_a							,			_a):
	global f  # a global dp table for knapsack
	if f[i][j] < 0:
		if j < wt[i - 1]:
			SCREAMING_SNAKE_CASE   :      Union[str, Any]				     =       mf_knapsack(i - 1							,			_a							,			_a							,			_a)
		else:
			SCREAMING_SNAKE_CASE   :      Any				     =       max(
			    mf_knapsack(i - 1							,			_a							,			_a							,			_a)							,			mf_knapsack(i - 1							,			_a							,			_a							,			j - wt[i - 1]) + val[i - 1]							,			)
		SCREAMING_SNAKE_CASE   :      Tuple				     =       val
	return f[i][j]

def  lowerCamelCase__ (					_a							,			_a							,			_a							,			_a):
	SCREAMING_SNAKE_CASE   :      Union[str, Any]				     =       [[0] * (w + 1) for _ in range(n + 1)]

	for i in range(1							,			n + 1):
		for w_ in range(1							,			w + 1):
			if wt[i - 1] <= w_:
				SCREAMING_SNAKE_CASE   :      Union[str, Any]				     =       max(val[i - 1] + dp[i - 1][w_ - wt[i - 1]]							,			dp[i - 1][w_])
			else:
				SCREAMING_SNAKE_CASE   :      int				     =       dp[i - 1][w_]

	return dp[n][w_], dp

def  lowerCamelCase__ (					_a							,			_a							,			_a):
	if not (isinstance(_a							,			(list, tuple)) and isinstance(_a							,			(list, tuple))):
		raise ValueError(
		    "Both the weights and values vectors must be either lists or tuples")

	SCREAMING_SNAKE_CASE   :      int				     =       len(_a)
	if num_items != len(_a):
		SCREAMING_SNAKE_CASE   :      List[str]				     =       (
		    "The number of weights must be the same as the number of values.\n"
		    f"But got {num_items} weights and {len(_a)} values"
		)
		raise ValueError(_a)
	for i in range(_a):
		if not isinstance(wt[i]							,			_a):
			SCREAMING_SNAKE_CASE   :      int				     =       (
			    "All weights must be integers but got weight of "
			    f"type {type(wt[i])} at index {i}"
			)
			raise TypeError(_a)

	SCREAMING_SNAKE_CASE     ,SCREAMING_SNAKE_CASE   :      Tuple				     =       knapsack(_a							,			_a							,			_a							,			_a)
	SCREAMING_SNAKE_CASE   :      set				     =       set()
	_construct_solution(_a							,			_a							,			_a							,			_a							,			_a)

	return optimal_val, example_optional_set

def  lowerCamelCase__ (					_a							,			_a							,			_a							,			_a							,			_a):
	# for the current item i at a maximum weight j to be part of an optimal subset,
	# the optimal value at (i, j) must be greater than the optimal value at (i-1, j).
	# where i - 1 means considering only the previous items at the given maximum weight
	if i > 0 and j > 0:
		if dp[i - 1][j] == dp[i][j]:
			_construct_solution(_a							,			_a							,			i - 1							,			_a							,			_a)
		else:
			optimal_set.add(_a)
			_construct_solution(_a							,			_a							,			i - 1							,			j - wt[i - 1]							,			_a)


if __name__ == "__main__":
			a_						     =    [3, 2, 4, 4]
			a_						     =    [4, 3, 2, 3]
			a_						     =    4
			a_						     =    6
			a_						     =    [[0] * (w + 1)] + [[0] + [-1] * (w + 1) for _ in range(n + 1)]
			a_     ,	a_						     =    knapsack(w, wt, val, n)
			print(optimal_solution)
			print(mf_knapsack(n, wt, val, w))  # switched the n and w

			# testing the dynamic programming problem with example
			# the optimal subset for the above example are items 3 and 4
			a_     ,	a_						     =    knapsack_with_example_solution(w, wt, val)
			assert optimal_solution == 8
			assert optimal_subset == {3, 4}
			print('optimal_value = ', optimal_solution)
			print('An optimal subset corresponding to the optimal value', optimal_subset)