





from __future__ import annotations

import math
from collections.abc import Callable


def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase		,      _UpperCAmelCase = 100		,      )     ->	float:
    lowerCamelCase__       : str   					=						x_start
    lowerCamelCase__       : List[Any]   					=						fnc(_UpperCAmelCase					)
    lowerCamelCase__       : int   					=						0.0

    for _ in range(_UpperCAmelCase					):
        # Approximates curve as a sequence of linear lines and sums their length
        lowerCamelCase__       : int   					=						(x_end - x_start) / steps + xa
        lowerCamelCase__       : List[str]   					=						fnc(_UpperCAmelCase					)
        length += math.hypot(xa - xa		,      fxa - fxa					)

        # Increment step
        lowerCamelCase__       : Dict   					=						xa
        lowerCamelCase__       : Dict   					=						fxa

    return length


if __name__ == "__main__":


    def 			SCREAMING_SNAKE_CASE (			_UpperCAmelCase					)     ->	int:
        return math.sin(10 * x					)

    print("""f(x) = sin(10 * x)""")
    print("""The length of the curve from x = -10 to x = 10 is:""")
    _UpperCAmelCase							:			Union[str, Any]        =							10
    while i <= 10_00_00:
        print(F"""With {i} steps: {line_length(f, -10, 10, 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()





