


"""simple docstring"""


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			def update_area_of_max_square(_UpperCamelCase    , _UpperCamelCase      ) -> int:
						# BASE CASE
						if row >= rows or col >= cols:
									return 0

						__lowerCAmelCase				    =			update_area_of_max_square(_UpperCamelCase    , col + 1      )
						__lowerCAmelCase				    =			update_area_of_max_square(row + 1    , col + 1      )
						__lowerCAmelCase				    =			update_area_of_max_square(row + 1    , _UpperCamelCase      )

						if mat[row][col]:
									__lowerCAmelCase				    =			1 + min([right, diagonal, down]      )
									__lowerCAmelCase				    =			max(largest_square_area[0]    , _UpperCamelCase      )
									return sub_problem_sol
						else:
									return 0

			__lowerCAmelCase				    =			[0]
			update_area_of_max_square(0    , 0      )
			return largest_square_area[0]


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			def update_area_of_max_square_using_dp_array(
			    _UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ) -> int:
						if row >= rows or col >= cols:
									return 0
						if dp_array[row][col] != -1:
									return dp_array[row][col]

						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(_UpperCamelCase    , col + 1    , _UpperCamelCase      )
						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(row + 1    , col + 1    , _UpperCamelCase      )
						__lowerCAmelCase				    =			update_area_of_max_square_using_dp_array(row + 1    , _UpperCamelCase    , _UpperCamelCase      )

						if mat[row][col]:
									__lowerCAmelCase				    =			1 + min([right, diagonal, down]      )
									__lowerCAmelCase				    =			max(largest_square_area[0]    , _UpperCamelCase      )
									__lowerCAmelCase				    =			sub_problem_sol
									return sub_problem_sol
						else:
									return 0

			__lowerCAmelCase				    =			[0]
			__lowerCAmelCase				    =			[[-1] * cols for _ in range(_UpperCamelCase      )]
			update_area_of_max_square_using_dp_array(0    , 0    , _UpperCamelCase      )

			return largest_square_area[0]


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[[0] * (cols + 1) for _ in range(rows + 1      )]
			__lowerCAmelCase				    =			0
			for row in range(rows - 1    , -1    , -1      ):
						for col in range(cols - 1    , -1    , -1      ):
									__lowerCAmelCase				    =			dp_array[row][col + 1]
									__lowerCAmelCase				    =			dp_array[row + 1][col + 1]
									__lowerCAmelCase				    =			dp_array[row + 1][col]

									if mat[row][col] == 1:
												__lowerCAmelCase				    =			1 + min(_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      )
												__lowerCAmelCase				    =			max(dp_array[row][col]    , _UpperCamelCase      )
									else:
												__lowerCAmelCase				    =			0

			return largest_square_area


def _lowerCamelCase	(		_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      ):

			'''simple docstring'''




			__lowerCAmelCase				    =			[0] * (cols + 1)
			__lowerCAmelCase				    =			[0] * (cols + 1)
			__lowerCAmelCase				    =			0
			for row in range(rows - 1    , -1    , -1      ):
						for col in range(cols - 1    , -1    , -1      ):
									__lowerCAmelCase				    =			current_row[col + 1]
									__lowerCAmelCase				    =			next_row[col + 1]
									__lowerCAmelCase				    =			next_row[col]

									if mat[row][col] == 1:
												__lowerCAmelCase				    =			1 + min(_UpperCamelCase    , _UpperCamelCase    , _UpperCamelCase      )
												__lowerCAmelCase				    =			max(current_row[col]    , _UpperCamelCase      )
									else:
												__lowerCAmelCase				    =			0
						__lowerCAmelCase				    =			current_row

			return largest_square_area


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	print(largest_square_area_in_matrix_bottom_up(2, 2, [[1, 1], [1, 1]]))





"""simple docstring"""


from __future__ import annotations

from collections import Counter
from random import random


class 				a :


    def __init__(    self		:     Union[str, Any]    ):
      _UpperCAmelCase         =					{}


    def    lowerCAmelCase_     (    self		:     Optional[int]      , __lowerCAmelCase		:     str    ):
      _UpperCAmelCase         =					{}


    def    lowerCAmelCase_     (    self		:     str      , __lowerCAmelCase		:     str      , __lowerCAmelCase		:     str      , __lowerCAmelCase		:     float    ):
      if nodea not in self.connections:
        self.add_node(__lowerCAmelCase    )
      if nodea not in self.connections:
        self.add_node(__lowerCAmelCase    )
      _UpperCAmelCase         =					probability


    def    lowerCAmelCase_     (    self		:     Optional[Any]    ):
      return list(self.connections    )


    def    lowerCAmelCase_     (    self		:     List[Any]      , __lowerCAmelCase		:     str    ):
      _UpperCAmelCase         =					0
      _UpperCAmelCase         =					random()

      for dest in self.connections[node]:
        current_probability += self.connections[node][dest]
        if current_probability > random_value:
          return dest
      return ""






def 			__UpperCAmelCase    (	lowercase      ,lowercase      ,lowercase						):







  """simple docstring"""
  _UpperCAmelCase         =					MarkovChainGraphUndirectedUnweighted()

  for nodea, nodea, probability in transitions:
    graph.add_transition_probability(lowercase      ,lowercase      ,lowercase						)

  _UpperCAmelCase         =					Counter(graph.get_nodes()						)
  _UpperCAmelCase         =					start

  for _ in range(lowercase						):
    _UpperCAmelCase         =					graph.transition(lowercase						)
    visited[node] += 1

  return visited


if __name__ == "__main__":
    import doctest

    doctest.testmod()
