



'''simple docstring'''

from __future__ import annotations

import numpy as np
from numpy import floataa
from numpy.typing import NDArray
def     __lowercase  (_lowercase,						_lowercase,						_lowercase,						_lowercase,						)   ->     list[float]:


     """simple docstring"""
     __lowerCamelCase						:       Union[str, Any]				   =				coefficient_matrix.shape
     __lowerCamelCase						:       Any				   =				constant_matrix.shape

     if rowsa != colsa:
          __lowerCamelCase						:       str				   =				f"Coefficient matrix dimensions must be nxn but received {rowsa}x{colsa}"
          raise ValueError(lowerCamelCase__     )

     if colsa != 1:
          __lowerCamelCase						:       Optional[Any]				   =				f"Constant matrix must be nx1 but received {rowsa}x{colsa}"
          raise ValueError(lowerCamelCase__     )

     if rowsa != rowsa:
          __lowerCamelCase						:       Optional[int]				   =				(
              "Coefficient and constant matrices dimensions must be nxn and nx1 but "
              f"received {rowsa}x{colsa} and {rowsa}x{colsa}"
          )
          raise ValueError(lowerCamelCase__     )

     if len(lowerCamelCase__     ) != rowsa:
          __lowerCamelCase						:       List[str]				   =				(
              "Number of initial values must be equal to number of rows in coefficient "
              f"matrix but received {len(lowerCamelCase__     )} and {rowsa}"
          )
          raise ValueError(lowerCamelCase__     )

     if iterations <= 0:
          raise ValueError("""Iterations must be at least 1"""     )

     __lowerCamelCase						:       NDArray[floataa]				   =				np.concatenate(
         (coefficient_matrix, constant_matrix),						axis=1     )

     __lowerCamelCase						:       Tuple				   =				table.shape

     strictly_diagonally_dominant(lowerCamelCase__     )

     # Iterates the whole matrix for given number of times
     for _ in range(lowerCamelCase__     ):
          __lowerCamelCase						:       int				   =				[]
          for row in range(lowerCamelCase__     ):
               __lowerCamelCase						:       List[str]				   =				0
               for col in range(lowerCamelCase__     ):
                    if col == row:
                         __lowerCamelCase						:       int				   =				table[row][col]
                    elif col == cols - 1:
                         __lowerCamelCase						:       Any				   =				table[row][col]
                    else:
                         temp += (-1) * table[row][col] * init_val[col]
               __lowerCamelCase						:       List[Any]				   =				(temp + val) / denom
               new_val.append(lowerCamelCase__     )
          __lowerCamelCase						:       str				   =				new_val

     return [float(lowerCamelCase__     ) for i in new_val]
def     __lowercase  (_lowercase     )   ->     bool:


     """simple docstring"""
     __lowerCamelCase						:       Optional[int]				   =				table.shape

     __lowerCamelCase						:       str				   =				True

     for i in range(0,						lowerCamelCase__     ):
          __lowerCamelCase						:       Union[str, Any]				   =				0
          for j in range(0,						cols - 1     ):
               if i == j:
                    continue
               else:
                    total += table[i][j]

          if table[i][i] <= total:
               raise ValueError("""Coefficient matrix is not strictly diagonally dominant"""     )

     return is_diagonally_dominant


# Test Cases
if __name__ == "__main__":
   import doctest

   doctest.testmod()











'''simple docstring'''

from __future__ import annotations

from random import random







class 	SCREAMING_SNAKE_CASE	:




       def __init__(					self      : Tuple	,    A__      : int | None = None					):


            """simple docstring"""







            __lowerCamelCase						:       int				   =				value
            __lowerCamelCase						:       Dict				   =				random()
            __lowerCamelCase						:       Node | None				   =				None
            __lowerCamelCase						:       Node | None				   =				None




       def __repr__(					self      : Any					):


            """simple docstring"""







            from pprint import pformat

            if self.left is None and self.right is None:
                 return f"'{self.value}: {self.prior:.5}'"
            else:
                 return pformat(
                     {f"{self.value}: {self.prior:.5}": (self.left, self.right)}	,    indent=1					)




       def __str__(					self      : List[Any]					):


            """simple docstring"""







            __lowerCamelCase						:       List[str]				   =				str(self.value					) + """ """
            __lowerCamelCase						:       Any				   =				str(self.left or """"""					)
            __lowerCamelCase						:       List[str]				   =				str(self.right or """"""					)
            return value + left + right

def     __lowercase  (_lowercase,						_lowercase     )   ->     tuple[Node | None, Node | None]:


     """simple docstring"""
     if root is None:  # None tree is split into 2 Nones
          return None, None
     elif root.value is None:
          return None, None
     else:
          if value < root.value:
               __lowerCamelCase   ,      __lowerCamelCase						:       int				   =				split(root.left,						_lowercase     )
               return left, root
          else:
               __lowerCamelCase   ,      __lowerCamelCase						:       Union[str, Any]				   =				split(root.right,						_lowercase     )
               return root, right
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     if (not left) or (not right):  # If one node is None, return the other
          return left or right
     elif left.prior < right.prior:
          __lowerCamelCase						:       Tuple				   =				merge(left.right,						_lowercase     )
          return left
     else:
          __lowerCamelCase						:       int				   =				merge(_lowercase,						right.left     )
          return right
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     __lowerCamelCase						:       List[str]				   =				Node(_lowercase     )
     __lowerCamelCase   ,      __lowerCamelCase						:       List[Any]				   =				split(_lowercase,						_lowercase     )
     return merge(merge(_lowercase,						_lowercase     ),						_lowercase     )
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     __lowerCamelCase   ,      __lowerCamelCase						:       int				   =				split(_lowercase,						value - 1     )
     __lowerCamelCase   ,      __lowerCamelCase						:       List[str]				   =				split(_lowercase,						_lowercase     )
     return merge(_lowercase,						_lowercase     )
def     __lowercase  (_lowercase     )   ->     None:


     """simple docstring"""
     if not root:  # None
          return
     else:
          inorder(root.left     )
          print(root.value,						end=""","""     )
          inorder(root.right     )
def     __lowercase  (_lowercase,						_lowercase     )   ->     Node | None:


     """simple docstring"""
     for arg in args.split():
          if arg[0] == "+":
               __lowerCamelCase						:       Dict				   =				insert(_lowercase,						int(arg[1:]     )     )

          elif arg[0] == "-":
               __lowerCamelCase						:       List[str]				   =				erase(_lowercase,						int(arg[1:]     )     )

          else:
               print("""Unknown command"""     )

     return root
def     __lowercase  ()   ->     None:


     """simple docstring"""
     __lowerCamelCase						:       str				   =				None
     print(
         """enter numbers to create a tree, + value to add value into treap, """
         """- value to erase all nodes with value. 'q' to quit. """     )

     __lowerCamelCase						:       int				   =				input()
     while args != "q":
          __lowerCamelCase						:       List[Any]				   =				interact_treap(_lowercase,						_lowercase     )
          print(_lowercase     )
          __lowerCamelCase						:       List[Any]				   =				input()

     print("""good by!"""     )


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   main()



