


import time
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_torch, torch_device

from ..test_modeling_common import ids_tensor


if is_torch_available():
 import torch

 from transformers.generation import (
     MaxLengthCriteria,
     MaxNewTokensCriteria,
     MaxTimeCriteria,
     StoppingCriteriaList,
     validate_stopping_criteria,
 )






@require_torch
class _lowerCamelCase(						unittest.TestCase   ):
       def 			UpperCamelCase     (					self,      lowerCamelCase)       ->   Optional[Any]:




           """simple docstring"""

           _lowercase       :							Union[str, Any]      		=		3
           _lowercase       :							Dict      		=		2_50

           _lowercase       :							Optional[int]      		=		ids_tensor((batch_size, length),      lowerCamelCase)
           _lowercase       :							List[Any]      		=		torch.ones((batch_size, length),      device=lowerCamelCase,      dtype=torch.float) / length
           return input_ids, scores
       def 			UpperCamelCase     (					self)       ->   Union[str, Any]:




           """simple docstring"""

           _lowercase		,				_lowercase       :							List[Any]      		=		self._get_tensors(5)

           _lowercase       :							Optional[int]      		=		StoppingCriteriaList(
               [
                   MaxLengthCriteria(max_length=10),
                   MaxTimeCriteria(max_time=0.1),
               ])

           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							Tuple      		=		self._get_tensors(9)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							Dict      		=		self._get_tensors(10)
           self.assertTrue(criteria(lowerCamelCase,      lowerCamelCase))
       def 			UpperCamelCase     (					self)       ->   List[str]:




           """simple docstring"""

           _lowercase       :							List[str]      		=		MaxLengthCriteria(max_length=10)

           _lowercase		,				_lowercase       :							str      		=		self._get_tensors(5)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							List[str]      		=		self._get_tensors(9)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							Optional[int]      		=		self._get_tensors(10)
           self.assertTrue(criteria(lowerCamelCase,      lowerCamelCase))
       def 			UpperCamelCase     (					self)       ->   Any:




           """simple docstring"""

           _lowercase       :							Union[str, Any]      		=		MaxNewTokensCriteria(start_length=5,      max_new_tokens=5)

           _lowercase		,				_lowercase       :							Optional[int]      		=		self._get_tensors(5)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							List[str]      		=		self._get_tensors(9)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase		,				_lowercase       :							Union[str, Any]      		=		self._get_tensors(10)
           self.assertTrue(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase       :							int      		=		StoppingCriteriaList([criteria])
           self.assertEqual(criteria_list.max_length,      10)
       def 			UpperCamelCase     (					self)       ->   int:




           """simple docstring"""

           _lowercase		,				_lowercase       :							Optional[int]      		=		self._get_tensors(5)

           _lowercase       :							List[Any]      		=		MaxTimeCriteria(max_time=0.1)
           self.assertFalse(criteria(lowerCamelCase,      lowerCamelCase))

           _lowercase       :							Union[str, Any]      		=		MaxTimeCriteria(max_time=0.1,      initial_timestamp=time.time() - 0.2)
           self.assertTrue(criteria(lowerCamelCase,      lowerCamelCase))




       def 			UpperCamelCase     (					self)       ->   int:




           """simple docstring"""

           validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10)]),      10)

           with self.assertWarns(lowerCamelCase):
               validate_stopping_criteria(StoppingCriteriaList([MaxLengthCriteria(10)]),      11)

           _lowercase       :							Optional[Any]      		=		validate_stopping_criteria(StoppingCriteriaList(),      11)

           self.assertEqual(len(lowerCamelCase),      1)






from __future__ import annotations

from math import ceil, floor, sqrt



def 				UpperCamelCase_(      lowerCamelCase_ = 200_0000 )    ->						int:
    _lowercase       :							list[int]      		=		[0]
    _lowercase       :							int

    for idx in range(1							, ceil(sqrt(target * 2 ) * 1.1 ) ):
        triangle_numbers.append(triangle_numbers[-1] + idx )

    # we want this to be as close as possible to target
    _lowercase       :							int      		=		0
    # the area corresponding to the grid that gives the product closest to target
    _lowercase       :							int      		=		0
    # an estimate of b, using the quadratic formula
    _lowercase       :							float
    # the largest integer less than b_estimate
    _lowercase       :							int
    # the largest integer less than b_estimate
    _lowercase       :							int
    # the triangle number corresponding to b_floor
    _lowercase       :							int
    # the triangle number corresponding to b_ceil
    _lowercase       :							int

    for idx_a, triangle_a in enumerate(triangle_numbers[1:]							, 1 ):
        _lowercase       :							Optional[int]      		=		(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
        _lowercase       :							List[str]      		=		floor(lowerCamelCase_ )
        _lowercase       :							Dict      		=		ceil(lowerCamelCase_ )
        _lowercase       :							List[str]      		=		triangle_numbers[b_floor]
        _lowercase       :							List[str]      		=		triangle_numbers[b_ceil]

        if abs(target - triangle_b_first_guess * triangle_a ) < abs(
            target - best_product ):
            _lowercase       :							Union[str, Any]      		=		triangle_b_first_guess * triangle_a
            _lowercase       :							Union[str, Any]      		=		idx_a * b_floor

        if abs(target - triangle_b_second_guess * triangle_a ) < abs(
            target - best_product ):
            _lowercase       :							Any      		=		triangle_b_second_guess * triangle_a
            _lowercase       :							Optional[Any]      		=		idx_a * b_ceil

    return area


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


