






from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst







def 		SCREAMING_SNAKE_CASE							( )			->     int:
     UpperCamelCase__    ,					UpperCamelCase__      :       Any	    =  9, 14  # noqa: F841
     UpperCamelCase__      :       Optional[Any]	    =  [
         [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__      :       int	    =  defaultdict(lowerCamelCase__      )
     for nodea, nodea, cost in edges:
          adjancency[nodea].append([nodea, cost]      )
          adjancency[nodea].append([nodea, cost]      )

     UpperCamelCase__      :       int	    =  mst(lowerCamelCase__      )

     UpperCamelCase__      :       str	    =  [
         [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	    =  tuple(answer[:2]      )
          UpperCamelCase__      :       Optional[int]	    =  tuple(edge[::-1]      )
          assert edge in result or reverse in result











def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     Any:
     # "extended trapezoidal rule"
     # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
     UpperCamelCase__      :       int	    =  (boundary[1] - boundary[0]) / steps
     UpperCamelCase__      :       Optional[Any]	    =  boundary[0]
     UpperCamelCase__      :       List[Any]	    =  boundary[1]
     UpperCamelCase__      :       List[Any]	    =  make_points(__lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )
     UpperCamelCase__      :       int	    =  0.0
     y += (h / 2.0) * f(__lowerCAmelCase      )
     for i in x_i:
          # print(i)
          y += h * f(__lowerCAmelCase      )
     y += (h / 2.0) * f(__lowerCAmelCase      )
     return y







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     List[str]:
     UpperCamelCase__      :       Optional[int]	    =  a + h
     while x < (b - h):
          yield x
          UpperCamelCase__      :       Union[str, Any]	    =  x + h







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase      )			->     Any:  # enter your function here
     UpperCamelCase__      :       Dict	    =  (x - 0) * (x - 0)
     return y







def 		SCREAMING_SNAKE_CASE							( )			->     Dict:
     UpperCamelCase__      :       List[Any]	    =  0.0  # Lower bound of integration
     UpperCamelCase__      :       Tuple	    =  1.0  # Upper bound of integration
     UpperCamelCase__      :       Any	    =  1_0.0  # define number of steps or resolution
     UpperCamelCase__      :       List[str]	    =  [a, b]  # define boundary of integration
     UpperCamelCase__      :       Any	    =  method_a(__lowerCAmelCase ,   __lowerCAmelCase      )
     print(f'y = {y}'      )


if __name__ == "__main__":
 main()