

"""simple docstring"""


def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     bool:

		# 1. Validate that path exists between current and next vertices
		if graph[path[curr_ind - 1]][next_ver] == 0:
				return False

		# 2. Validate that next vertex is not already in path
		return not any(vertex == next_ver for vertex in path			)






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     bool:

		# Base Case
		if curr_ind == len(__SCREAMING_SNAKE_CASE			):
				# return whether path exists between current and starting vertices
				return graph[path[curr_ind - 1]][path[0]] == 1

		# Recursive Step
		for next_ver in range(0 ,			len(__SCREAMING_SNAKE_CASE			)			):
				if valid_connection(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			):
						# Insert current vertex  into path as next transition
						__lowerCAmelCase:	List[str]   				=      next_ver
						# Validate created path
						if util_hamilton_cycle(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			curr_ind + 1			):
								return True
						# Backtrack
						__lowerCAmelCase:	List[Any]   				=      -1
		return False






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE = 0			)     ->     list[int]:
		__lowerCAmelCase:	Any   				=      [-1] * (len(__SCREAMING_SNAKE_CASE			) + 1)
		# initialize start and end of path with starting index
		__lowerCAmelCase:	Union[str, Any]   				=      start_index
		# evaluate and if we find answer return path either return empty array
		return path if util_hamilton_cycle(__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			1			) else []





"""simple docstring"""


from __future__ import annotations

from decimal import Decimal
from math import *  # noqa: F403

from sympy import diff






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE = 1_0**-1_0			)     ->     float:
		__lowerCAmelCase:	Union[str, Any]   				=      a
		while True:
				__lowerCAmelCase:	Optional[int]   				=      Decimal(__SCREAMING_SNAKE_CASE			) - (
				    Decimal(eval(__SCREAMING_SNAKE_CASE			)			) / Decimal(eval(str(diff(__SCREAMING_SNAKE_CASE			)			)			)			)  # noqa: S307
				)
				# This number dictates the accuracy of the answer
				if abs(eval(__SCREAMING_SNAKE_CASE			)			) < precision:  # noqa: S307
						return float(__SCREAMING_SNAKE_CASE			)


# Let's Execute
if __name__ == "__main__":
			# Find root of trigonometric function
			# Find value of pi
			print(F'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')
			# Find root of polynomial
			print(F'''The root of x**2 - 5*x + 2 = 0 is {newton_raphson("x**2 - 5*x + 2", 0.4)}''')
			# Find Square Root of 5
			print(F'''The root of log(x) - 1 = 0 is {newton_raphson("log(x) - 1", 2)}''')
			# Exponential Roots
			print(F'''The root of exp(x) - 1 = 0 is {newton_raphson("exp(x) - 1", 0)}''')


