


"""simple docstring"""




from __future__ import annotations

def        lowercase							(		lowerCAmelCase__ :     str    ,					lowerCAmelCase__ :     str			) ->      bool:
		__a           =			get_failure_array(lowerCAmelCase__			)

		# 2) Step through text searching for pattern
		__a      ,     __a           =			0, 0  # index into text, pattern
		while i < len(lowerCAmelCase__			):
				if pattern[j] == text[i]:
						if j == (len(lowerCAmelCase__			) - 1):
								return True
						j += 1

				# if this is a prefix in our pattern
				# just go back far enough to continue
				elif j > 0:
						__a           =			failure[j - 1]
						continue
				i += 1
		return False

def        lowercase							(		lowerCAmelCase__ :     str			) ->      list[int]:
		__a           =			[0]
		__a           =			0
		__a           =			1
		while j < len(lowerCAmelCase__			):
				if pattern[i] == pattern[j]:
						i += 1
				elif i > 0:
						__a           =			failure[i - 1]
						continue
				j += 1
				failure.append(lowerCAmelCase__			)
		return failure


if __name__ == "__main__":
				# Test 1)
				lowercase_			     =  "abc1abc12"
				lowercase_			     =  "alskfjaldsabc1abc1abc12k23adsfabcabc"
				lowercase_			     =  "alskfjaldsk23adsfabcabc"
				assert kmp(pattern, texta) and not kmp(pattern, texta)

				# Test 2)
				lowercase_			     =  "ABABX"
				lowercase_			     =  "ABABZABABYABABX"
				assert kmp(pattern, text)

				# Test 3)
				lowercase_			     =  "AAAB"
				lowercase_			     =  "ABAAAAAB"
				assert kmp(pattern, text)

				# Test 4)
				lowercase_			     =  "abcdabcy"
				lowercase_			     =  "abcxabcdabxabcdabcdabcy"
				assert kmp(pattern, text)

				# Test 5)
				lowercase_			     =  "aabaabaaa"
				assert get_failure_array(pattern) == [0, 1, 0, 1, 2, 3, 4, 5, 2]










"""simple docstring"""




def        lowercase							(		lowerCAmelCase__ :     int    ,					lowerCAmelCase__ :     list			) ->      List[Any]:
		_enforce_args(lowerCAmelCase__    ,					lowerCAmelCase__			)
		if n == 0:
				return 0
		__a           =			float('''-inf'''			)
		for i in range(1    ,					n + 1			):
				__a           =			max(
				    lowerCAmelCase__    ,					prices[i - 1] + naive_cut_rod_recursive(n - i    ,					lowerCAmelCase__			)			)

		return max_revue

def        lowercase							(		lowerCAmelCase__ :     int    ,					lowerCAmelCase__ :     list			) ->      List[str]:
		_enforce_args(lowerCAmelCase__    ,					lowerCAmelCase__			)
		__a           =			[float('''-inf'''			) for _ in range(n + 1			)]
		return _top_down_cut_rod_recursive(lowerCAmelCase__    ,					lowerCAmelCase__    ,					lowerCAmelCase__			)

def        lowercase							(		lowerCAmelCase__ :     int    ,					lowerCAmelCase__ :     list    ,					lowerCAmelCase__ :     list			) ->      Union[str, Any]:
		if max_rev[n] >= 0:
				return max_rev[n]
		elif n == 0:
				return 0
		else:
				__a           =			float('''-inf'''			)
				for i in range(1    ,					n + 1			):
						__a           =			max(
						    lowerCAmelCase__    ,					prices[i - 1] + _top_down_cut_rod_recursive(n - i    ,					lowerCAmelCase__    ,					lowerCAmelCase__			)    ,					)

				__a           =			max_revenue

		return max_rev[n]

def        lowercase							(		lowerCAmelCase__ :     int    ,					lowerCAmelCase__ :     list			) ->      Dict:
		_enforce_args(lowerCAmelCase__    ,					lowerCAmelCase__			)

		# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
		# length 0.
		__a           =			[float('''-inf'''			) for _ in range(n + 1			)]
		__a           =			0

		for i in range(1    ,					n + 1			):
				__a           =			max_rev[i]
				for j in range(1    ,					i + 1			):
						__a           =			max(lowerCAmelCase__    ,					prices[j - 1] + max_rev[i - j]			)

				__a           =			max_revenue_i

		return max_rev[n]

def        lowercase							(		lowerCAmelCase__ :     int    ,					lowerCAmelCase__ :     list			) ->      str:
		if n < 0:
				__a           =			f'''n must be greater than or equal to 0. Got n = {n}'''
				raise ValueError(lowerCAmelCase__			)

		if n > len(lowerCAmelCase__			):
				__a           =			(
				    '''Each integral piece of rod must have a corresponding price. '''
				    f'''Got n = {n} but length of prices = {len(lowerCAmelCase__			)}'''
				)
				raise ValueError(lowerCAmelCase__			)

def        lowercase							(		) ->      int:
		__a           =			[6, 10, 12, 15, 20, 23]
		__a           =			len(lowerCAmelCase__			)

		# the best revenue comes from cutting the rod into 6 pieces, each
		# of length 1 resulting in a revenue of 6 * 6 = 36.
		__a           =			36

		__a           =			top_down_cut_rod(lowerCAmelCase__    ,					lowerCAmelCase__			)
		__a           =			bottom_up_cut_rod(lowerCAmelCase__    ,					lowerCAmelCase__			)
		__a           =			naive_cut_rod_recursive(lowerCAmelCase__    ,					lowerCAmelCase__			)

		assert expected_max_revenue == max_rev_top_down
		assert max_rev_top_down == max_rev_bottom_up
		assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
				main()






