






import numpy as np
import requests




def       _a   (							)  ->      Dict:
 lowerCamelCase_							:    str							=     requests.get(
     'https://raw.githubusercontent.com/yashLadha/The_Math_of_Intelligence/'
     'master/Week1/ADRvsRating.csv'				)
 lowerCamelCase_							:    Optional[int]							=     response.text.splitlines()
 lowerCamelCase_							:    List[Any]							=     []
 for item in lines:
  lowerCamelCase_							:    Tuple							=     item.split(','				)
  data.append(lowerCamelCase__				)
 data.pop(0				)  # This is for removing the labels from the list
 lowerCamelCase_							:    Optional[int]							=     np.matrix(lowerCamelCase__				)
 return dataset




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      str:
 lowerCamelCase_							:    str							=     len_data

 lowerCamelCase_							:    Optional[Any]							=     np.dot(lowerCamelCase__ ,			data_x.transpose()				)
 prod -= data_y.transpose()
 lowerCamelCase_							:    Optional[Any]							=     np.dot(lowerCamelCase__ ,			lowerCamelCase__				)
 lowerCamelCase_							:    List[str]							=     theta - (alpha / n) * sum_grad
 return theta




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      List[Any]:
 lowerCamelCase_							:    Optional[Any]							=     np.dot(lowerCamelCase__ ,			data_x.transpose()				)
 prod -= data_y.transpose()
 lowerCamelCase_							:    Optional[int]							=     np.sum(np.square(lowerCamelCase__				)				)
 lowerCamelCase_							:    Any							=     sum_elem / (2 * len_data)
 return error




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      int:
 lowerCamelCase_							:    Any							=     10_00_00
 lowerCamelCase_							:    Union[str, Any]							=     0.0001550

 lowerCamelCase_							:    Optional[Any]							=     data_x.shape[1]
 lowerCamelCase_							:    int							=     data_x.shape[0] - 1

 lowerCamelCase_							:    Dict							=     np.zeros((1, no_features)				)

 for i in range(0 ,			lowerCamelCase__				):
  lowerCamelCase_							:    Union[str, Any]							=     run_steep_gradient_descent(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
  lowerCamelCase_							:    Dict							=     sum_of_square_error(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
  print(F'At Iteration {i + 1} - Error is {error:.5f}'				)

 return theta




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      int:
 lowerCamelCase_							:    Union[str, Any]							=     sum(abs(y - predicted_y[i]				) for i, y in enumerate(lowerCamelCase__				)				)
 return total / len(lowerCamelCase__				)




def       _a   (							)  ->      Tuple:
 lowerCamelCase_							:    Dict							=     collect_dataset()

 lowerCamelCase_							:    int							=     data.shape[0]
 lowerCamelCase_							:    Union[str, Any]							=     np.c_[np.ones(lowerCamelCase__				), data[:, :-1]].astype(lowerCamelCase__				)
 lowerCamelCase_							:    Union[str, Any]							=     data[:, -1].astype(lowerCamelCase__				)

 lowerCamelCase_							:    List[Any]							=     run_linear_regression(lowerCamelCase__ ,			lowerCamelCase__				)
 lowerCamelCase_							:    int							=     theta.shape[1]
 print('Resultant Feature vector : '				)
 for i in range(0 ,			lowerCamelCase__				):
  print(F'{theta[0, i]:.5f}'				)


if __name__ == "__main__":
       main()








import math




class 	lowerCamelCase__				:






      def __init__(self					:    int		,		_snake_case					:    Dict		)       ->   Union[str, Any]:


       """simple docstring"""






       lowerCamelCase_							:    Optional[Any]							=     len(_snake_case		)
       lowerCamelCase_							:    Optional[Any]							=     [0] * (
           4 * self.N
       )  # approximate the overall size of segment tree with array N
       self.build(1		,		0		,		self.N - 1		)






      def      UpperCAmelCase_     (self					:    List[str]		,		_snake_case					:    List[str]		)       ->   int:


       """simple docstring"""






       return idx * 2






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    Dict		)       ->   Optional[Any]:


       """simple docstring"""






       return idx * 2 + 1






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    str		,		_snake_case					:    List[Any]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if l == r:
        lowerCamelCase_							:    List[Any]							=     A[l]
       else:
        lowerCamelCase_							:    int							=     (l + r) // 2
        self.build(self.left(_snake_case		)		,		_snake_case		,		_snake_case		)
        self.build(self.right(_snake_case		)		,		mid + 1		,		_snake_case		)
        lowerCamelCase_							:    Tuple							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)






      def      UpperCAmelCase_     (self					:    str		,		_snake_case					:    Tuple		,		_snake_case					:    Any		,		_snake_case					:    str		)       ->   Tuple:


       """simple docstring"""






       return self.update_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    Tuple		,		_snake_case					:    List[str]		,		_snake_case					:    Tuple		,		_snake_case					:    Optional[int]		,		_snake_case					:    int		,		_snake_case					:    Tuple		,		_snake_case					:    List[str]		)       ->   Optional[Any]:  # noqa: E741


       """simple docstring"""






       if r < a or l > b:
        return True
       if l == r:
        lowerCamelCase_							:    Tuple							=     val
        return True
       lowerCamelCase_							:    Optional[int]							=     (l + r) // 2
       self.update_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       self.update_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     max(self.st[self.left(_snake_case		)]		,		self.st[self.right(_snake_case		)]		)
       return True






      def      UpperCAmelCase_     (self					:    List[Any]		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[int]		)       ->   str:


       """simple docstring"""






       return self.query_recursive(1		,		0		,		self.N - 1		,		a - 1		,		b - 1		)






      def      UpperCAmelCase_     (self					:    Any		,		_snake_case					:    List[Any]		,		_snake_case					:    Optional[Any]		,		_snake_case					:    int		,		_snake_case					:    Optional[int]		,		_snake_case					:    Optional[Any]		)       ->   str:  # noqa: E741


       """simple docstring"""






       if r < a or l > b:
        return -math.inf
       if l >= a and r <= b:
        return self.st[idx]
       lowerCamelCase_							:    int							=     (l + r) // 2
       lowerCamelCase_							:    Optional[Any]							=     self.query_recursive(self.left(_snake_case		)		,		_snake_case		,		_snake_case		,		_snake_case		,		_snake_case		)
       lowerCamelCase_							:    Union[str, Any]							=     self.query_recursive(self.right(_snake_case		)		,		mid + 1		,		_snake_case		,		_snake_case		,		_snake_case		)
       return max(_snake_case		,		_snake_case		)






      def      UpperCAmelCase_     (self					:    str		)       ->   Tuple:


       """simple docstring"""






       lowerCamelCase_							:    Dict							=     []
       for i in range(1		,		N + 1		):
        show_list += [self.query(_snake_case		,		_snake_case		)]
       print(_snake_case		)


if __name__ == "__main__":
       UpperCamelCase											=      [1, 2, -4, 7, 3, -5, 6, 1_1, -2_0, 9, 1_4, 1_5, 5, 2, -8]
       UpperCamelCase											=      1_5
       UpperCamelCase											=      SegmentTree(A)
       print(segt.query(4, 6))
       print(segt.query(7, 1_1))
       print(segt.query(7, 1_2))
       segt.update(1, 3, 1_1_1)
       print(segt.query(1, 1_5))
       segt.update(7, 8, 2_3_5)
       segt.show_data()
