from __future__ import annotations




def    lowerCAmelCase_  (		lowercase:				list[list[int]]		)     ->					int:







 '''simple docstring'''

 # preprocessing the first row
 for i in range(1	,       len(matrix[0]		)		):
  matrix[0][i] += matrix[0][i - 1]

 # preprocessing the first column
 for i in range(1	,       len(lowercase		)		):
  matrix[i][0] += matrix[i - 1][0]

 # updating the path cost for current position
 for i in range(1	,       len(lowercase		)		):
  for j in range(1	,       len(matrix[0]		)		):
   matrix[i][j] += min(matrix[i - 1][j]	,       matrix[i][j - 1]		)

 return matrix[-1][-1]


if __name__ == "__main__":
  import doctest

  doctest.testmod()
import random




def    lowerCAmelCase_  (		lowercase:				int	,       lowercase:				float	,       lowercase:				bool = False		)     ->					dict:







 '''simple docstring'''
 _UpperCamelCase:  dict    						=			{i: [] for i in range(lowercase		)}

 # if probability is greater or equal than 1, then generate a complete graph
 if probability >= 1:
  return complete_graph(lowercase		)
 # if probability is lower or equal than 0, then return a graph without edges
 if probability <= 0:
  return graph

 # for each couple of nodes, add an edge from u to v
 # if the number randomly generated is greater than probability probability
 for i in range(lowercase		):
  for j in range(i + 1	,       lowercase		):
   if random.random() < probability:
    graph[i].append(lowercase		)
    if not directed:
     # if the graph is undirected, add an edge in from j to i, either
     graph[j].append(lowercase		)
 return graph




def    lowerCAmelCase_  (		lowercase:				int		)     ->					dict:







 '''simple docstring'''
 return {
     i: [j for j in range(lowercase		) if i != j] for i in range(lowercase		)
 }


if __name__ == "__main__":
  import doctest

  doctest.testmod()