




from __future__ import annotations

from collections.abc import Callable



def 				_A  (		lowerCAmelCase_	:   Callable[[int | float], int | float]  ,							lowerCAmelCase_	:   int | float  ,							lowerCAmelCase_	:   int | float  ,							lowerCAmelCase_	:   int = 100  ,							):
     """simple docstring"""

     lowerCAmelCase__            =					x_start
     lowerCAmelCase__            =					fnc(lowerCAmelCase_     )
     lowerCAmelCase__            =					0.0
     for _ in range(lowerCAmelCase_     ):
          # Approximates small segments of curve as linear and solve
          # for trapezoidal area
          lowerCAmelCase__            =					(x_end - x_start) / steps + xa
          lowerCAmelCase__            =					fnc(lowerCAmelCase_     )
          area += abs(fxa + fxa     ) * (xa - xa) / 2
          # Increment step
          lowerCAmelCase__            =					xa
          lowerCAmelCase__            =					fxa
     return area


if __name__ == "__main__":



     def 				_A  (		lowerCAmelCase_	:   int     ):
          """simple docstring"""

          return x**3 + x**2

     print('f(x) = x^3 + x^2')
     print('The area between the curve, x = -5, x = 5 and the x axis is:')
     UpperCamelCase								=	10
     while i <= 10_0000:
          print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
          i *= 10




# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.




def    a__    (		snake_case__					:							Dict     ):
  _UpperCAmelCase		:							str							=     [False] * len(snake_case__     )
  _UpperCAmelCase		:							str							=     [-1] * len(snake_case__     )

  def dfs(snake_case__					:							Dict						,   snake_case__					:							Optional[Any]     ):
    _UpperCAmelCase		:							str							=     True
    _UpperCAmelCase		:							Optional[Any]							=     c
    for u in graph[v]:
      if not visited[u]:
        dfs(snake_case__						,   1 - c     )

  for i in range(len(snake_case__     )     ):
    if not visited[i]:
      dfs(snake_case__						,   0     )

  for i in range(len(snake_case__     )     ):
    for j in graph[i]:
      if color[i] == color[j]:
        return False

  return True


# Adjacency list of graph
SCREAMING_SNAKE_CASE__					:     Optional[Any]       =     {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}





print(check_bipartite_dfs(graph))





