
import math



def 		lowercase_    (     A__				,	A__ = 0				,	A__ = 0	)							->							list:
    """simple docstring"""

    snake_case				  =      end or len(A__	)
    for i in range(A__				,	A__	):
        snake_case				  =      i
        snake_case				  =      array[i]
        while temp_index != start and temp_index_value < array[temp_index - 1]:
            snake_case				  =      array[temp_index - 1]
            temp_index -= 1
        snake_case				  =      temp_index_value
    return array



def 		lowercase_    (     A__				,	A__				,	A__	)							->							None:  # Max Heap
    """simple docstring"""

    snake_case				  =      index
    snake_case				  =      2 * index + 1  # Left Node
    snake_case				  =      2 * index + 2  # Right Node

    if left_index < heap_size and array[largest] < array[left_index]:
        snake_case				  =      left_index

    if right_index < heap_size and array[largest] < array[right_index]:
        snake_case				  =      right_index

    if largest != index:
        snake_case  ,							snake_case				  =      array[largest], array[index]
        heapify(A__				,	A__				,	A__	)



def 		lowercase_    (     A__	)							->							list:
    """simple docstring"""

    snake_case				  =      len(A__	)

    for i in range(n // 2				,	-1				,	-1	):
        heapify(A__				,	A__				,	A__	)

    for i in range(n - 1				,	0				,	-1	):
        snake_case  ,							snake_case				  =      array[0], array[i]
        heapify(A__				,	0				,	A__	)

    return array



def 		lowercase_    (     A__				,	A__				,	A__				,	A__	)							->							int:
    """simple docstring"""

    if (array[first_index] > array[middle_index]) != (
        array[first_index] > array[last_index]
    ):
        return array[first_index]
    elif (array[middle_index] > array[first_index]) != (
        array[middle_index] > array[last_index]
    ):
        return array[middle_index]
    else:
        return array[last_index]



def 		lowercase_    (     A__				,	A__				,	A__				,	A__	)							->							int:
    """simple docstring"""

    snake_case				  =      low
    snake_case				  =      high
    while True:
        while array[i] < pivot:
            i += 1
        j -= 1
        while pivot < array[j]:
            j -= 1
        if i >= j:
            return i
        snake_case  ,							snake_case				  =      array[j], array[i]
        i += 1



def 		lowercase_    (     A__	)							->							list:
    """simple docstring"""

    if len(A__	) == 0:
        return array
    snake_case				  =      2 * math.ceil(math.loga(len(A__	)	)	)
    snake_case				  =      16
    return intro_sort(A__				,	0				,	len(A__	)				,	A__				,	A__	)



def 		lowercase_    (     A__				,	A__				,	A__				,	A__				,	A__	)							->							list:
    """simple docstring"""

    while end - start > size_threshold:
        if max_depth == 0:
            return heap_sort(A__	)
        max_depth -= 1
        snake_case				  =      median_of_a(A__				,	A__				,	start + ((end - start) // 2) + 1				,	end - 1	)
        snake_case				  =      partition(A__				,	A__				,	A__				,	A__	)
        intro_sort(A__				,	A__				,	A__				,	A__				,	A__	)
        snake_case				  =      p
    return insertion_sort(A__				,	A__				,	A__	)


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   _A						      =				input("Enter numbers separated by a comma : ").strip()
   _A						      =				[float(item) for item in user_input.split(",")]
   print(sort(unsorted))



import os
import sys
import tempfile

import torch

from .state import AcceleratorState
from .utils import PrecisionType, PrepareForLaunch, is_mps_available, patch_environment



def 		lowercase_    (     A__				,	A__=()				,	A__=None				,	A__="no"				,	A__="29500"	)							->							Optional[int]:
    """simple docstring"""

    snake_case				  =      False
    snake_case				  =      False
    if any(key.startswith("KAGGLE"	) for key in os.environ.keys()	):
        snake_case				  =      True
    elif "IPython" in sys.modules:
        snake_case				  =      "google.colab" in str(sys.modules["IPython"].get_ipython()	)

    try:
        snake_case				  =      PrecisionType(mixed_precision.lower()	)
    except ValueError:
        raise ValueError(
            F'Unknown mixed_precision mode: {args.mixed_precision.lower()}. Choose between {PrecisionType.list()}.'	)

    if (in_colab or in_kaggle) and (os.environ.get("TPU_NAME"				,	A__	) is not None):
        # TPU launch
        import torch_xla.distributed.xla_multiprocessing as xmp

        if len(AcceleratorState._shared_state	) > 0:
            raise ValueError(
                "To train on TPU in Colab or Kaggle Kernel, the `Accelerator` should only be initialized inside "
                "your training function. Restart your notebook and make sure no cells initializes an "
                "`Accelerator`."	)
        if num_processes is None:
            snake_case				  =      8

        snake_case				  =      PrepareForLaunch(A__				,	distributed_type="TPU"	)
        print(F'Launching a training on {num_processes} TPU cores.'	)
        xmp.spawn(A__				,	args=A__				,	nprocs=A__				,	start_method="fork"	)
    elif in_colab:
        # No need for a distributed launch otherwise as it's either CPU or one GPU.
        if torch.cuda.is_available():
            print("Launching training on one GPU."	)
        else:
            print("Launching training on one CPU."	)
        function(*A__	)
    else:
        if num_processes is None:
            raise ValueError(
                "You have to specify the number of GPUs you would like to use, add `num_processes=...` to your call."	)

        if num_processes > 1:
            # Multi-GPU launch
            from torch.multiprocessing import start_processes
            from torch.multiprocessing.spawn import ProcessRaisedException

            if len(AcceleratorState._shared_state	) > 0:
                raise ValueError(
                    "To launch a multi-GPU training from your notebook, the `Accelerator` should only be initialized "
                    "inside your training function. Restart your notebook and make sure no cells initializes an "
                    "`Accelerator`."	)

            if torch.cuda.is_initialized():
                raise ValueError(
                    "To launch a multi-GPU training from your notebook, you need to avoid running any instruction "
                    "using `torch.cuda` in any cell. Restart your notebook and make sure no cells use any CUDA "
                    "function."	)

            # torch.distributed will expect a few environment variable to be here. We set the ones common to each
            # process here (the other ones will be set be the launcher).
            with patch_environment(
                world_size=A__				,	master_addr="127.0.01"				,	master_port=A__				,	mixed_precision=A__	):
                snake_case				  =      PrepareForLaunch(A__				,	distributed_type="MULTI_GPU"	)
                print(F'Launching training on {num_processes} GPUs.'	)
                try:
                    start_processes(A__				,	args=A__				,	nprocs=A__				,	start_method="fork"	)
                except ProcessRaisedException as e:
                    if "Cannot re-initialize CUDA in forked subprocess" in e.args[0]:
                        raise RuntimeError(
                            "CUDA has been initialized before the `notebook_launcher` could create a forked subprocess. "
                            "This likely stems from an outside import causing issues once the `notebook_launcher()` is called. "
                            "Please review your imports and test them when running the `notebook_launcher()` to identify "
                            "which one is problematic."	) from e

        else:
            # No need for a distributed launch otherwise as it's either CPU, GPU or MPS.
            if is_mps_available():
                snake_case				  =      "1"
                print("Launching training on MPS."	)
            elif torch.cuda.is_available():
                print("Launching training on one GPU."	)
            else:
                print("Launching training on CPU."	)
            function(*A__	)





def 		lowercase_    (     A__				,	A__=()				,	A__=2	)							->							Dict:
    """simple docstring"""

    from torch.multiprocessing import start_processes

    with tempfile.NamedTemporaryFile() as tmp_file:
        # torch.distributed will expect a few environment variable to be here. We set the ones common to each
        # process here (the other ones will be set be the launcher).
        with patch_environment(
            world_size=A__				,	master_addr="127.0.01"				,	master_port="29500"				,	accelerate_mixed_precision="no"				,	accelerate_debug_rdv_file=tmp_file.name				,	accelerate_use_cpu="yes"				,	):
            snake_case				  =      PrepareForLaunch(A__				,	debug=A__	)
            start_processes(A__				,	args=A__				,	nprocs=A__				,	start_method="fork"	)

