

from __future__ import annotations

from typing import Any


class       SCREAMING_SNAKE_CASE__					:





    def __init__(      self						,   a						,   a						,   a = 0):
         lowercase__      , lowercase__    :   Dict      =       row, column
         lowercase__    :   Optional[Any]      =       [[default_value for c in range(a)] for r in range(a)]





    def __str__(      self):
         lowercase__    :   Tuple      =       f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

         # Make string identifier
         lowercase__    :   Optional[int]      =       0
         for row_vector in self.array:
              for obj in row_vector:
                   lowercase__    :   List[str]      =       max(a						,   len(str(a)))
         lowercase__    :   Optional[int]      =       f"""%{max_element_length}s"""

         # Make string and return
         def single_line(a) -> str:
              nonlocal string_format_identifier
              lowercase__    :   Tuple      =       '['
              line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
              line += "]"
              return line

         s += "\n".join(single_line(a) for row_vector in self.array)
         return s





    def __repr__(      self):
         return str(self)





    def       snake_case_				(      self						,   a):
         if not (isinstance(a						,   (list, tuple)) and len(a) == 2):
              return False
         elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
              return False
         else:
              return True





    def __getitem__(      self						,   a):
         assert self.validate_indicies(a)
         return self.array[loc[0]][loc[1]]





    def __setitem__(      self						,   a						,   a):
         assert self.validate_indicies(a)
         lowercase__    :   List[str]      =       value





    def __add__(      self						,   a):
         assert isinstance(a						,   a)
         assert self.row == another.row and self.column == another.column

         # Add
         lowercase__    :   List[str]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   Dict      =       self[r, c] + another[r, c]
         return result





    def __neg__(      self):
         lowercase__    :   List[Any]      =       Matrix(self.row						,   self.column)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   int      =       -self[r, c]
         return result





    def __sub__(      self						,   a):
         return self + (-another)





    def __mul__(      self						,   a):

         if isinstance(a						,   (int, float)):  # Scalar multiplication
              lowercase__    :   Optional[Any]      =       Matrix(self.row						,   self.column)
              for r in range(self.row):
                   for c in range(self.column):
                        lowercase__    :   Union[str, Any]      =       self[r, c] * another
              return result
         elif isinstance(a						,   a):  # Matrix multiplication
              assert self.column == another.row
              lowercase__    :   List[Any]      =       Matrix(self.row						,   another.column)
              for r in range(self.row):
                   for c in range(another.column):
                        for i in range(self.column):
                             result[r, c] += self[r, i] * another[i, c]
              return result
         else:
              lowercase__    :   Optional[Any]      =       f"""Unsupported type given for another ({type(a)})"""
              raise TypeError(a)





    def       snake_case_				(      self):
         lowercase__    :   Optional[int]      =       Matrix(self.column						,   self.row)
         for r in range(self.row):
              for c in range(self.column):
                   lowercase__    :   str      =       self[r, c]
         return result





    def       snake_case_				(      self						,   a						,   a):
         assert isinstance(a						,   a) and isinstance(a						,   a)
         assert self.row == self.column == u.row == v.row  # u, v should be column vector
         assert u.column == v.column == 1  # u, v should be column vector

         # Calculate
         lowercase__    :   int      =       v.transpose()
         lowercase__    :   Tuple      =       (v_t * self * u)[0, 0] + 1
         if numerator_factor == 0:
              return None  # It's not invertable
         return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

       def 	snake_case__			(    ):



            '''simple docstring'''





            lowercase__    :   Any      =       Matrix(3	,     3	,     0			)
            for i in range(3			):
                 lowercase__    :   str      =       1
            print(f"""a^(-1) is {ainv}"""			)
            # u, v
            lowercase__    :   Optional[Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   List[Any]      =       1, 2, -3
            lowercase__    :   Union[str, Any]      =       Matrix(3	,     1	,     0			)
            lowercase__      , lowercase__      , lowercase__    :   Any      =       4, -2, 5
            print(f"""u is {u}"""			)
            print(f"""v is {v}"""			)
            print(f"""uv^T is {u * v.transpose()}"""			)
            # Sherman Morrison
            print(f"""(a + uv^T)^(-1) is {ainv.sherman_morrison(SCREAMING_SNAKE_CASE_	,     SCREAMING_SNAKE_CASE_			)}"""			)

       def 	snake_case__			(    ):



            '''simple docstring'''





            import doctest

            doctest.testmod()

       testa()




from __future__ import annotations

from collections.abc import Callable
from typing import Generic, TypeVar

snake_case_			  = TypeVar('''T''')
snake_case_			  = TypeVar('''U''')


class       SCREAMING_SNAKE_CASE__					(Generic[T, U]     ):





    def __init__(      self						,   a						,   a):
         lowercase__    :   List[Any]      =       key
         lowercase__    :   List[Any]      =       val
         lowercase__    :   DoubleLinkedListNode[T, U] | None      =       None
         lowercase__    :   DoubleLinkedListNode[T, U] | None      =       None





    def __repr__(      self):
         return (
             f"""Node: key: {self.key}, val: {self.val}, """
             f"""has next: {bool(self.next)}, has prev: {bool(self.prev)}"""
         )



class       SCREAMING_SNAKE_CASE__					(Generic[T, U]     ):





    def __init__(      self):
         lowercase__    :   DoubleLinkedListNode[T, U]      =       DoubleLinkedListNode(a						,   a)
         lowercase__    :   DoubleLinkedListNode[T, U]      =       DoubleLinkedListNode(a						,   a)
         lowercase__      , lowercase__    :   Union[str, Any]      =       self.rear, self.head





    def __repr__(      self):
         lowercase__    :   Any      =       ['DoubleLinkedList']
         lowercase__    :   List[str]      =       self.head
         while node.next is not None:
              rep.append(str(a))
              lowercase__    :   Tuple      =       node.next
         rep.append(str(self.rear))
         return ",\n    ".join(a)





    def       snake_case_				(      self						,   a):
         lowercase__    :   Optional[Any]      =       self.rear.prev

         # All nodes other than self.head are guaranteed to have non-None previous
         assert previous is not None

         lowercase__    :   Dict      =       node
         lowercase__    :   int      =       previous
         lowercase__    :   Union[str, Any]      =       node
         lowercase__    :   Optional[int]      =       self.rear





    def       snake_case_				(      self						,   a):

         if node.prev is None or node.next is None:
              return None

         lowercase__    :   Union[str, Any]      =       node.next
         lowercase__    :   Tuple      =       node.prev
         lowercase__    :   Union[str, Any]      =       None
         lowercase__    :   List[Any]      =       None
         return node



class       SCREAMING_SNAKE_CASE__					(Generic[T, U]     ):
    __lowerCamelCase						:       dict[Callable[[T], U], LRUCache[T, U]]														=     {}





    def __init__(      self						,   a):
         lowercase__    :   DoubleLinkedList[T, U]      =       DoubleLinkedList()
         lowercase__    :   Optional[Any]      =       capacity
         lowercase__    :   Union[str, Any]      =       0
         lowercase__    :   Tuple      =       0
         lowercase__    :   int      =       0
         lowercase__    :   dict[T, DoubleLinkedListNode[T, U]]      =       {}





    def __repr__(      self):
         return (
             f"""CacheInfo(hits={self.hits}, misses={self.miss}, """
             f"""capacity={self.capacity}, current size={self.num_keys})"""
         )





    def __contains__(      self						,   a):
         return key in self.cache





    def       snake_case_				(      self						,   a):
         # Note: pythonic interface would throw KeyError rather than return None

         if key in self.cache:
              self.hits += 1
              lowercase__    :   DoubleLinkedListNode[T, U]      =       self.cache[key]
              lowercase__    :   str      =       self.list.remove(self.cache[key])
              assert node == value_node

              # node is guaranteed not None because it is in self.cache
              assert node is not None
              self.list.add(a)
              return node.val
         self.miss += 1
         return None





    def       snake_case_				(      self						,   a						,   a):

         if key not in self.cache:
              if self.num_keys >= self.capacity:
                   # delete first node (oldest) when over capacity
                   lowercase__    :   Optional[int]      =       self.list.head.next

                   # guaranteed to have a non-None first node when num_keys > 0
                   # explain to type checker via assertions
                   assert first_node is not None
                   assert first_node.key is not None
                   assert (
                       self.list.remove(a) is not None
                   )  # node guaranteed to be in list assert node.key is not None

                   del self.cache[first_node.key]
                   self.num_keys -= 1
              lowercase__    :   Optional[Any]      =       DoubleLinkedListNode(a						,   a)
              self.list.add(self.cache[key])
              self.num_keys += 1

         else:
              # bump node to the end of the list, update value
              lowercase__    :   Any      =       self.list.remove(self.cache[key])
              assert node is not None  # node guaranteed to be in list
              lowercase__    :   Union[str, Any]      =       value
              self.list.add(a)





    @classmethod
    def       snake_case_				(      cls						,   a = 128):

         def cache_decorator_inner(a) -> Callable[..., U]:
              def cache_decorator_wrapper(*a) -> U:
                   if func not in cls.decorator_function_to_instance_map:
                        lowercase__    :   Dict      =       LRUCache(a)

                   lowercase__    :   str      =       cls.decorator_function_to_instance_map[func].get(args[0])
                   if result is None:
                        lowercase__    :   str      =       func(*a)
                        cls.decorator_function_to_instance_map[func].put(args[0]						,   a)
                   return result

              def cache_info() -> LRUCache[T, U]:
                   return cls.decorator_function_to_instance_map[func]

              setattr(a						,   'cache_info'						,   a)  # noqa: B010

              return cache_decorator_wrapper

         return cache_decorator_inner


if __name__ == "__main__":
       import doctest

       doctest.testmod()

