
from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst






def 						__magic_name__			(   ):



     '''simple docstring'''




     UpperCamelCase__		,	UpperCamelCase__				=    9, 14  # noqa: F841
     UpperCamelCase__				=    [
         [0, 1, 4],
         [0, 7, 8],
         [1, 2, 8],
         [7, 8, 7],
         [7, 6, 1],
         [2, 8, 2],
         [8, 6, 6],
         [2, 3, 7],
         [2, 5, 4],
         [6, 5, 2],
         [3, 5, 14],
         [3, 4, 9],
         [5, 4, 10],
         [1, 7, 11],
     ]

     UpperCamelCase__				=    defaultdict(lowerCamelCase__						)
     for nodea, nodea, cost in edges:
          adjancency[nodea].append([nodea, cost]						)
          adjancency[nodea].append([nodea, cost]						)

     UpperCamelCase__				=    mst(lowerCamelCase__						)

     UpperCamelCase__				=    [
         [7, 6, 1],
         [2, 8, 2],
         [6, 5, 2],
         [0, 1, 4],
         [2, 5, 4],
         [2, 3, 7],
         [0, 7, 8],
         [3, 4, 9],
     ]

     for answer in expected:
          UpperCamelCase__				=    tuple(answer[:2]						)
          UpperCamelCase__				=    tuple(edge[::-1]						)
          assert edge in result or reverse in result







from __future__ import annotations






def 						__magic_name__			(   __a      :	list[list[int]]						):



     '''simple docstring'''




     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(__a						)						):
          matrix[i][0] += matrix[i - 1][0]

     # updating the path cost for current position
     for i in range(1	,		len(__a						)						):
          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()





