
def   lowerCamelCase__							(							__lowerCAmelCase    :    list[list[int]]       ,				__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    int       ,				__lowerCAmelCase    :    list[int]							):




			"""simple docstring"""


			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   lowerCamelCase__							(							__lowerCAmelCase    :    list[list[int]]       ,				__lowerCAmelCase    :    list[int]       ,				__lowerCAmelCase    :    int							):




			"""simple docstring"""


			if curr_ind == len(__lowerCAmelCase							):
						# 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(__lowerCAmelCase							)							):
						if valid_connection(__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase       ,				__lowerCAmelCase							):
									# Insert current vertex  into path as next transition
									lowerCAmelCase_         =      next_ver
									# Validate created path
									if util_hamilton_cycle(__lowerCAmelCase       ,				__lowerCAmelCase       ,				curr_ind + 1							):
												return True
									# Backtrack
									lowerCAmelCase_         =      -1
			return False






def   lowerCamelCase__							(							__lowerCAmelCase    :    list[list[int]]       ,				__lowerCAmelCase    :    int = 0							):




			"""simple docstring"""


			lowerCAmelCase_         =      [-1] * (len(__lowerCAmelCase							) + 1)
			# initialize start and end of path with starting index
			lowerCAmelCase_         =      lowerCAmelCase_         =      start_index
			# evaluate and if we find answer return path either return empty array
			return path if util_hamilton_cycle(__lowerCAmelCase       ,				__lowerCAmelCase       ,				1							) else []





from collections.abc import Callable






def   lowerCamelCase__							(							__lowerCAmelCase    :    Callable[[float], float]       ,				__lowerCAmelCase    :    float       ,				__lowerCAmelCase    :    float							):




			"""simple docstring"""


			lowerCAmelCase_         =      a
			lowerCAmelCase_         =      b
			if function(__lowerCAmelCase							) == 0:  # one of the a or b is a root for the function
						return a
			elif function(__lowerCAmelCase							) == 0:
						return b
			elif (
			    function(__lowerCAmelCase							) * function(__lowerCAmelCase							) > 0
			):  # if none of these are root and they are both positive or negative,
						# then this algorithm can't find the root
						raise ValueError("could not find root in given interval."							)
			else:
						lowerCAmelCase_         =      start + (end - start) / 2.0
						while abs(start - mid							) > 10**-7:  # until precisely equals to 10^-7
									if function(__lowerCAmelCase							) == 0:
												return mid
									elif function(__lowerCAmelCase							) * function(__lowerCAmelCase							) < 0:
												lowerCAmelCase_         =      mid
									else:
												lowerCAmelCase_         =      mid
									lowerCAmelCase_         =      start + (end - start) / 2.0
						return mid






def   lowerCamelCase__							(							__lowerCAmelCase    :    float							):




			"""simple docstring"""


			return x**3 - 2 * x - 5


if __name__ == "__main__":
			print(bisection(f, 1, 10_00))

			import doctest

			doctest.testmod()



