





"""simple docstring"""




def        _lowercase   (  _UpperCAmelCase     , _UpperCAmelCase     , _UpperCAmelCase     , _UpperCAmelCase			)  ->					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        _lowercase   (  _UpperCAmelCase     , _UpperCAmelCase     , _UpperCAmelCase			)  ->					bool:

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





def        _lowercase   (  _UpperCAmelCase     , _UpperCAmelCase = 0			)  ->					list[int]:
				lowerCamelCase			=[-1] * (len(_UpperCAmelCase			) + 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(_UpperCAmelCase     , _UpperCAmelCase     , 1			) else []












import unittest

from .lib import (
    Matrix,
    Vector,
    axpy,
    square_zero_matrix,
    unit_basis_vector,
    zero_vector,
)

class  __A       (  unittest.TestCase      ):


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3]							)
								self.assertEqual(x.component(0							)				,	1							)
								self.assertEqual(x.component(2							)				,	3							)
								lowerCamelCase			=Vector()


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([0, 0, 0, 0, 0, 1]							)
								self.assertEqual(str(UpperCAmelCase_							)				,	"""(0,0,0,0,0,1)"""							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3, 4]							)
								self.assertEqual(len(UpperCAmelCase_							)				,	4							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2]							)
								lowerCamelCase			=Vector([1, 2, 3, 4, 5]							)
								lowerCamelCase			=Vector([0, 0, 0, 0, 0, 0, 0, 0, 0, 0]							)
								lowerCamelCase			=Vector([1, -1, 1, -1, 2, -3, 4, -5]							)
								self.assertAlmostEqual(x.euclidean_length()				,	2.2_3_6				,	3							)
								self.assertAlmostEqual(y.euclidean_length()				,	7.4_1_6				,	3							)
								self.assertEqual(z.euclidean_length()				,	0							)
								self.assertAlmostEqual(w.euclidean_length()				,	7.6_1_6				,	3							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3]							)
								lowerCamelCase			=Vector([1, 1, 1]							)
								self.assertEqual((x + y).component(0							)				,	2							)
								self.assertEqual((x + y).component(1							)				,	3							)
								self.assertEqual((x + y).component(2							)				,	4							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3]							)
								lowerCamelCase			=Vector([1, 1, 1]							)
								self.assertEqual((x - y).component(0							)				,	0							)
								self.assertEqual((x - y).component(1							)				,	1							)
								self.assertEqual((x - y).component(2							)				,	2							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3]							)
								lowerCamelCase			=Vector([2, -1, 4]							)  # for test of dot product
								lowerCamelCase			=Vector([1, -2, -1]							)
								self.assertEqual(str(x * 3.0							)				,	"""(3.0,6.0,9.0)"""							)
								self.assertEqual((a * b)				,	0							)


				def _snake_case    (						self							):
								self.assertEqual(str(zero_vector(10							)							).count("""0"""							)				,	10							)


				def _snake_case    (						self							):
								self.assertEqual(str(unit_basis_vector(3				,	1							)							)				,	"""(0,1,0)"""							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 2, 3]							)
								lowerCamelCase			=Vector([1, 0, 1]							)
								self.assertEqual(str(axpy(2				,	UpperCAmelCase_				,	UpperCAmelCase_							)							)				,	"""(3,4,7)"""							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 0, 0, 0, 0, 0]							)
								lowerCamelCase			=x.copy()
								self.assertEqual(str(UpperCAmelCase_							)				,	str(UpperCAmelCase_							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Vector([1, 0, 0]							)
								x.change_component(0				,	0							)
								x.change_component(1				,	1							)
								self.assertEqual(str(UpperCAmelCase_							)				,	"""(0,1,0)"""							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								self.assertEqual("""|1,2,3|\n|2,4,5|\n|6,7,8|\n"""				,	str(UpperCAmelCase_							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								lowerCamelCase			=[[-3, -14, -10], [-5, -10, -5], [-2, -1, 0]]
								for x in range(a.height()							):
												for y in range(a.width()							):
																self.assertEqual(minors[x][y]				,	a.minor(UpperCAmelCase_				,	UpperCAmelCase_							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								lowerCamelCase			=[[-3, 14, -10], [5, -10, 5], [-2, 1, 0]]
								for x in range(a.height()							):
												for y in range(a.width()							):
																self.assertEqual(cofactors[x][y]				,	a.cofactor(UpperCAmelCase_				,	UpperCAmelCase_							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								self.assertEqual(-5				,	a.determinant()							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]]				,	3				,	3							)
								lowerCamelCase			=Vector([1, 2, 3]							)
								self.assertEqual("""(14,32,50)"""				,	str(a * x							)							)
								self.assertEqual("""|2,4,6|\n|8,10,12|\n|14,16,18|\n"""				,	str(a * 2							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								a.change_component(0				,	2				,	5							)
								self.assertEqual("""|1,2,5|\n|2,4,5|\n|6,7,8|\n"""				,	str(UpperCAmelCase_							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								self.assertEqual(7				,	a.component(2				,	1							)				,	0.0_1							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								lowerCamelCase			=Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]				,	3				,	3							)
								self.assertEqual("""|2,4,10|\n|4,8,10|\n|12,14,18|\n"""				,	str(a + b							)							)


				def _snake_case    (						self							):
								lowerCamelCase			=Matrix([[1, 2, 3], [2, 4, 5], [6, 7, 8]]				,	3				,	3							)
								lowerCamelCase			=Matrix([[1, 2, 7], [2, 4, 5], [6, 7, 10]]				,	3				,	3							)
								self.assertEqual("""|0,0,-4|\n|0,0,0|\n|0,0,-2|\n"""				,	str(a - b							)							)


				def _snake_case    (						self							):
								self.assertEqual(
								    """|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n|0,0,0,0,0|\n"""				,	str(square_zero_matrix(5							)							)				,	)


if __name__ == "__main__":
							unittest.main()





