"""simple docstring"""







from math import isclose, sqrt



def     lowercase__( __SCREAMING_SNAKE_CASE							:  float  ,    __SCREAMING_SNAKE_CASE							:  float  ,    __SCREAMING_SNAKE_CASE							:  float   ):
     lowercase_			:       List[Any]									=			point_y / 4 / point_x
     lowercase_			:       int									=			2 * normal_gradient / (1 + normal_gradient * normal_gradient)
     lowercase_			:       Any									=			(1 - normal_gradient * normal_gradient) / (
         1 + normal_gradient * normal_gradient
     )
     lowercase_			:       List[str]									=			(sa - ca * incoming_gradient) / (ca + sa * incoming_gradient)

     # to find the next point, solve the simultaeneous equations:
     # y^2 + 4x^2 = 100
     # y - b = m * (x - a)
     # ==> A x^2 + B x + C = 0
     lowercase_			:       Union[str, Any]									=			outgoing_gradient**2 + 4
     lowercase_			:       Dict									=			2 * outgoing_gradient * (point_y - outgoing_gradient * point_x)
     lowercase_			:       Tuple									=			(point_y - outgoing_gradient * point_x) ** 2 - 1_00

     lowercase_			:       Tuple									=			(
         -linear_term - sqrt(linear_term**2 - 4 * quadratic_term * constant_term   )
     ) / (2 * quadratic_term)
     lowercase_			:       str									=			(
         -linear_term + sqrt(linear_term**2 - 4 * quadratic_term * constant_term   )
     ) / (2 * quadratic_term)

     # two solutions, one of which is our input point
     lowercase_			:       List[str]									=			x_minus if isclose(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   ) else x_plus
     lowercase_			:       Optional[int]									=			point_y + outgoing_gradient * (next_x - point_x)

     return next_x, next_y, outgoing_gradient



def     lowercase__( __SCREAMING_SNAKE_CASE							:  float = 1.4  ,    __SCREAMING_SNAKE_CASE							:  float = -9.6   ):
     lowercase_			:       int									=			0
     lowercase_			:       float									=			first_x_coord
     lowercase_			:       float									=			first_y_coord
     lowercase_			:       float									=			(10.1 - point_y) / (0.0 - point_x)

     while not (-0.01 <= point_x <= 0.01 and point_y > 0):
          lowercase_							,						lowercase_							,						lowercase_			:       Optional[int]									=			next_point(__SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE  ,    __SCREAMING_SNAKE_CASE   )
          num_reflections += 1

     return num_reflections


if __name__ == "__main__":
       print(F"{solution() = }")


"""simple docstring"""







# Lint as: python3
# pylint: enable=line-too-long
# pylint: disable=g-import-not-at-top,g-bad-import-order,wrong-import-position

__SCREAMING_SNAKE_CASE								="2.13.1"

import platform

import pyarrow
from packaging import version


if version.parse(platform.python_version()) < version.parse("3.7"):
       raise ImportWarning(
           "To use `datasets`, Python>=3.7 is required, and the current version of Python doesn't match this condition."
       )

if version.parse(pyarrow.__version__).major < 8:
       raise ImportWarning(
           "To use `datasets`, the module `pyarrow>=8.0.0` is required, and the current version of `pyarrow` doesn't match this condition.\n"
           "If you are running this in a Google Colab, you should probably just restart the runtime to use the right version of `pyarrow`."
       )

del platform
del pyarrow
del version

from .arrow_dataset import Dataset
from .arrow_reader import ReadInstruction
from .builder import ArrowBasedBuilder, BeamBasedBuilder, BuilderConfig, DatasetBuilder, GeneratorBasedBuilder
from .combine import concatenate_datasets, interleave_datasets
from .dataset_dict import DatasetDict, IterableDatasetDict
from .download import *
from .features import *
from .fingerprint import disable_caching, enable_caching, is_caching_enabled, set_caching_enabled
from .info import DatasetInfo, MetricInfo
from .inspect import (
    get_dataset_config_info,
    get_dataset_config_names,
    get_dataset_infos,
    get_dataset_split_names,
    inspect_dataset,
    inspect_metric,
    list_datasets,
    list_metrics,
)
from .iterable_dataset import IterableDataset
from .load import load_dataset, load_dataset_builder, load_from_disk, load_metric
from .metric import Metric
from .splits import (
    NamedSplit,
    NamedSplitAll,
    Split,
    SplitBase,
    SplitDict,
    SplitGenerator,
    SplitInfo,
    SubSplitInfo,
    percent,
)
from .tasks import *
from .utils import *
from .utils import logging


# deprecated modules
from datasets import arrow_dataset as _arrow_dataset  # isort:skip
from datasets import utils as _utils  # isort:skip
from datasets.utils import download_manager as _deprecated_download_manager  # isort:skip

__SCREAMING_SNAKE_CASE								=concatenate_datasets
__SCREAMING_SNAKE_CASE								=DownloadConfig
__SCREAMING_SNAKE_CASE								=DownloadManager
__SCREAMING_SNAKE_CASE								=DownloadMode
__SCREAMING_SNAKE_CASE								=DownloadConfig
__SCREAMING_SNAKE_CASE								=DownloadMode
__SCREAMING_SNAKE_CASE								=DownloadManager

del _arrow_dataset, _utils, _deprecated_download_manager

