
"""simple docstring"""







from __future__ import annotations

_SCREAMING_SNAKE_CASE	       =      [
    [-1, 0],  # left
    [0, -1],  # down
    [1, 0],  # right
    [0, 1],  # up
]
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    )  ->     tuple[list[list[int]], list[list[int]]]:







							"""simple docstring"""


							__snake_case     			=       [
							    [0 for col in range(len(grid[0] ) )] for row in range(len(SCREAMING_SNAKE_CASE ) )
							]  # the reference grid
							__snake_case     			=       1
							__snake_case     			=       [
							    [0 for col in range(len(grid[0] ) )] for row in range(len(SCREAMING_SNAKE_CASE ) )
							]  # the action grid

							__snake_case     			=       init[0]
							__snake_case     			=       init[1]
							__snake_case     			=       0
							__snake_case     			=       g + heuristic[x][y]  # cost from starting cell to destination cell
							__snake_case     			=       [[f, g, x, y]]

							__snake_case     			=       False  # flag that is set when search is complete
							__snake_case     			=       False  # flag set if we can't find expand

							while not found and not resign:
														if len(SCREAMING_SNAKE_CASE ) == 0:
																					raise ValueError("Algorithm is unable to find solution" )
														else:  # to choose the least costliest action so as to move closer to the goal
																					cell.sort()
																					cell.reverse()
																					__snake_case     			=       cell.pop()
																					__snake_case     			=       next_cell[2]
																					__snake_case     			=       next_cell[3]
																					__snake_case     			=       next_cell[1]

																					if x == goal[0] and y == goal[1]:
																												__snake_case     			=       True
																					else:
																												for i in range(len(SCREAMING_SNAKE_CASE ) ):  # to try out different valid actions
																																			__snake_case     			=       x + DIRECTIONS[i][0]
																																			__snake_case     			=       y + DIRECTIONS[i][1]
																																			if xa >= 0 and xa < len(SCREAMING_SNAKE_CASE ) and ya >= 0 and ya < len(grid[0] ):
																																										if closed[xa][ya] == 0 and grid[xa][ya] == 0:
																																																	__snake_case     			=       g + cost
																																																	__snake_case     			=       ga + heuristic[xa][ya]
																																																	cell.append([fa, ga, xa, ya] )
																																																	__snake_case     			=       1
																																																	__snake_case     			=       i
							__snake_case     			=       []
							__snake_case     			=       goal[0]
							__snake_case     			=       goal[1]
							invpath.append([x, y] )  # we get the reverse path from here
							while x != init[0] or y != init[1]:
														__snake_case     			=       x - DIRECTIONS[action[x][y]][0]
														__snake_case     			=       y - DIRECTIONS[action[x][y]][1]
														__snake_case     			=       xa
														__snake_case     			=       ya
														invpath.append([x, y] )

							__snake_case     			=       []
							for i in range(len(SCREAMING_SNAKE_CASE ) ):
														path.append(invpath[len(SCREAMING_SNAKE_CASE ) - 1 - i] )
							return path, action


if __name__ == "__main__":
		_SCREAMING_SNAKE_CASE	       =      [
		    [0, 1, 0, 0, 0, 0],
		    [0, 1, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
		    [0, 1, 0, 0, 0, 0],
		    [0, 1, 0, 0, 1, 0],
		    [0, 0, 0, 0, 1, 0],
		]

		_SCREAMING_SNAKE_CASE	       =      [0, 0]
		# all coordinates are given in format [y,x]
		_SCREAMING_SNAKE_CASE	       =      [len(grid) - 1, len(grid[0]) - 1]
		_SCREAMING_SNAKE_CASE	       =      1

		# the cost map which pushes the path closer to the goal
		_SCREAMING_SNAKE_CASE	       =      [[0 for row in range(len(grid[0]))] for col in range(len(grid))]
		for i in range(len(grid)):
				for j in range(len(grid[0])):
						_SCREAMING_SNAKE_CASE	       =      abs(i - goal[0]) + abs(j - goal[1])
						if grid[i][j] == 1:
								# added extra penalty in the heuristic map
								_SCREAMING_SNAKE_CASE	       =      99

		_SCREAMING_SNAKE_CASE       ,							_SCREAMING_SNAKE_CASE	       =      search(grid, init, goal, cost, heuristic)

		print("""ACTION MAP""")
		for i in range(len(action)):
				print(action[i])

		for i in range(len(path)):
				print(path[i])


"""simple docstring"""







from __future__ import annotations

from collections.abc import Callable
def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE							,    SCREAMING_SNAKE_CASE = 1_00							,    )  ->     float:







							"""simple docstring"""


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


if __name__ == "__main__":
		def   __UpperCamelCase   (					SCREAMING_SNAKE_CASE )  ->     List[Any]:







									"""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:""")
		_SCREAMING_SNAKE_CASE	       =      10
		while i <= 100_000:
				print(F"""with {i} steps: {trapezoidal_area(f, -5, 5, i)}""")
				i *= 10
