




"""simple docstring"""





from __future__ import annotations

from collections.abc import Callable

def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase					,							UpperCamelCase					,							UpperCamelCase = 100					,							)      ->      float:


			"""simple docstring"""
			__UpperCAmelCase						:			Optional[int]												=       x_start
			__UpperCAmelCase						:			List[str]												=       fnc(UpperCamelCase				)
			__UpperCAmelCase						:			Tuple												=       0.0
			for _ in range(UpperCamelCase				):
						# Approximates small segments of curve as linear and solve
						# for trapezoidal area
						__UpperCAmelCase						:			int												=       (x_end - x_start) / steps + xa
						__UpperCAmelCase						:			Tuple												=       fnc(UpperCamelCase				)
						area += abs(fxa + fxa				) * (xa - xa) / 2
						# Increment step
						__UpperCAmelCase						:			List[Any]												=       xa
						__UpperCAmelCase						:			Dict												=       fxa
			return area


if __name__ == "__main__":

					def        _UpperCamelCase     (      UpperCamelCase				)      ->      Optional[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:""")
					A				=							10
					while i <= 100_000:
										print(f'''with {i} steps: {trapezoidal_area(f, -5, 5, i)}''')
										i *= 10









from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt


def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase					)     ->	tuple[int | None, int | None, float]:
    if not arr:
        return None, None, 0
    if low == high:
        return low, high, arr[low]

    lowerCamelCase__       : Union[str, Any]   					=						(low + high) // 2
    lowerCamelCase__					,				lowerCamelCase__					,				lowerCamelCase__       : str   					=						max_subarray(_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase					)
    lowerCamelCase__					,				lowerCamelCase__					,				lowerCamelCase__       : Optional[Any]   					=						max_subarray(_UpperCAmelCase		,      mid + 1		,      _UpperCAmelCase					)
    lowerCamelCase__					,				lowerCamelCase__					,				lowerCamelCase__       : int   					=						max_cross_sum(_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase					)
    if left_sum >= right_sum and left_sum >= cross_sum:
        return left_low, left_high, left_sum
    elif right_sum >= left_sum and right_sum >= cross_sum:
        return right_low, right_high, right_sum
    return cross_left, cross_right, cross_sum


def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase					)     ->	tuple[int, int, float]:
    lowerCamelCase__					,				lowerCamelCase__       : Union[str, Any]   					=						float('-inf'					), -1
    lowerCamelCase__					,				lowerCamelCase__       : Tuple   					=						float('-inf'					), -1

    lowerCamelCase__       : int | float   					=						0
    for i in range(_UpperCAmelCase		,      low - 1		,      -1					):
        summ += arr[i]
        if summ > left_sum:
            lowerCamelCase__       : Optional[int]   					=						summ
            lowerCamelCase__       : Tuple   					=						i

    lowerCamelCase__       : int   					=						0
    for i in range(mid + 1		,      high + 1					):
        summ += arr[i]
        if summ > right_sum:
            lowerCamelCase__       : int   					=						summ
            lowerCamelCase__       : List[Any]   					=						i

    return max_left, max_right, (left_sum + right_sum)


def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase					)     ->	float:
    lowerCamelCase__       : Any   					=						[randint(1		,      _UpperCAmelCase					) for _ in range(_UpperCAmelCase					)]
    lowerCamelCase__       : Tuple   					=						time.time()
    max_subarray(_UpperCAmelCase		,      0		,      input_size - 1					)
    lowerCamelCase__       : List[Any]   					=						time.time()
    return end - start


def 			SCREAMING_SNAKE_CASE (			)     ->	None:
    lowerCamelCase__       : Optional[Any]   					=						[10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
    lowerCamelCase__       : Optional[Any]   					=						[time_max_subarray(_UpperCAmelCase					) for input_size in input_sizes]
    print('No of Inputs\t\tTime Taken'					)
    for input_size, runtime in zip(_UpperCAmelCase		,      _UpperCAmelCase					):
        print(_UpperCAmelCase		,      '\t\t'		,      _UpperCAmelCase					)
    plt.plot(_UpperCAmelCase		,      _UpperCAmelCase					)
    plt.xlabel('Number of Inputs'					)
    plt.ylabel('Time taken in seconds'					)
    plt.show()


if __name__ == "__main__":
    from doctest import testmod

    testmod()





