

"""simple docstring"""





# This Python program implements an optimal binary search tree (abbreviated BST)
# building dynamic programming algorithm that delivers O(n^2) performance.
#
# The goal of the optimal BST problem is to build a low-cost BST for a
# given set of nodes, each with its own key and frequency. The frequency
# of the node is defined as how many time the node is being searched.
# The search cost of binary search tree is given by this formula:
#
# cost(1, n) = sum{i = 1 to n}((depth(node_i) + 1) * node_i_freq)
#
# where n is number of nodes in the BST. The characteristic of low-cost
# BSTs is having a faster overall search time than other implementations.
# The reason for their fast search time is that the nodes with high
# frequencies will be placed near the root of the tree while the nodes
# with low frequencies will be placed near the leaves of the tree thus
# reducing search time in the most frequent instances.
import sys
from random import randint




class    _lowerCAmelCase    :







 """simple docstring"""







 def __init__(     self				:     Any,   UpperCAmelCase__				:     int,   UpperCAmelCase__				:     Any      ):
    __lowercase								=		key
    __lowercase								=		freq



 def __str__(     self				:     int      ):
    return F"""Node(key={self.key}, freq={self.freq})"""







def     _A    (    UpperCamelCase_	:			int,     UpperCamelCase_	:			Tuple,     UpperCamelCase_	:			List[str],     UpperCamelCase_	:			Any,     UpperCamelCase_	:			Optional[int],     UpperCamelCase_	:			List[Any])      ->		Union[str, Any]:
   '''simple docstring'''


   if i > j or i < 0 or j > len(UpperCamelCase_) - 1:
      return

   __lowercase								=		root[i][j]
   if parent == -1:  # root does not have a parent
      print(F"""{key[node]} is the root of the binary search tree.""")
   elif is_left:
      print(F"""{key[node]} is the left child of key {parent}.""")
   else:
      print(F"""{key[node]} is the right child of key {parent}.""")

   print_binary_search_tree(UpperCamelCase_,     UpperCamelCase_,     UpperCamelCase_,     node - 1,     key[node],     UpperCamelCase_)
   print_binary_search_tree(UpperCamelCase_,     UpperCamelCase_,     node + 1,     UpperCamelCase_,     key[node],     UpperCamelCase_)




def     _A    (    UpperCamelCase_	:			int)      ->		Tuple:
   '''simple docstring'''


   nodes.sort(key=lambda UpperCamelCase_: node.key)

   __lowercase								=		len(UpperCamelCase_)

   __lowercase								=		[nodes[i].key for i in range(UpperCamelCase_)]
   __lowercase								=		[nodes[i].freq for i in range(UpperCamelCase_)]

   # This 2D array stores the overall tree cost (which's as minimized as possible);
   # for a single key, cost is equal to frequency of the key.
   __lowercase								=		[[freqs[i] if i == j else 0 for j in range(UpperCamelCase_)] for i in range(UpperCamelCase_)]
   # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
   # array
   __lowercase								=		[[freqs[i] if i == j else 0 for j in range(UpperCamelCase_)] for i in range(UpperCamelCase_)]
   # stores tree roots that will be used later for constructing binary search tree
   __lowercase								=		[[i if i == j else 0 for j in range(UpperCamelCase_)] for i in range(UpperCamelCase_)]

   for interval_length in range(2,     n + 1):
      for i in range(n - interval_length + 1):
         __lowercase								=		i + interval_length - 1

         __lowercase								=		sys.maxsize  # set the value to "infinity"
         __lowercase								=		total[i][j - 1] + freqs[j]

         # Apply Knuth's optimization
         # Loop without optimization: for r in range(i, j + 1):
         for r in range(root[i][j - 1],     root[i + 1][j] + 1):  # r is a temporal root
            __lowercase								=		dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
            __lowercase								=		dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
            __lowercase								=		left + total[i][j] + right

            if dp[i][j] > cost:
               __lowercase								=		cost
               __lowercase								=		r

   print("Binary search tree nodes:")
   for node in nodes:
      print(UpperCamelCase_)

   print(F"""\nThe cost of optimal BST for given tree nodes is {dp[0][n - 1]}.""")
   print_binary_search_tree(UpperCamelCase_,     UpperCamelCase_,     0,     n - 1,     -1,     UpperCamelCase_)




def     _A    (    )      ->		Any:
   '''simple docstring'''


   __lowercase								=		[Node(UpperCamelCase_,     randint(1,     50)) for i in range(10,     0,     -1)]
   find_optimal_binary_search_tree(UpperCamelCase_)


if __name__ == "__main__":
   main()







"""simple docstring"""





import tempfile
import unittest

from diffusers import (
    DDIMScheduler,
    DDPMScheduler,
    DPMSolverMultistepScheduler,
    EulerAncestralDiscreteScheduler,
    EulerDiscreteScheduler,
    PNDMScheduler,
    logging,
)
from diffusers.configuration_utils import ConfigMixin, register_to_config
from diffusers.utils.testing_utils import CaptureLogger




class    _lowerCAmelCase    (      lowercase  ):







 """simple docstring"""







 __UpperCAmelCase      :   Tuple  						=      "config.json"


 @register_to_config
 def __init__(     self				:     List[str],   UpperCAmelCase__				:     Dict=2,   UpperCAmelCase__				:     str=5,   UpperCAmelCase__				:     List[Any]=(2, 5),   UpperCAmelCase__				:     Dict="for diffusion",   UpperCAmelCase__				:     Optional[int]=[1, 3],   ):
    pass







class    _lowerCAmelCase    (      lowercase  ):







 """simple docstring"""







 __UpperCAmelCase      :   List[str]  						=      "config.json"


 @register_to_config
 def __init__(     self				:     Optional[int],   UpperCAmelCase__				:     List[str]=2,   UpperCAmelCase__				:     List[str]=5,   UpperCAmelCase__				:     List[Any]=(2, 5),   UpperCAmelCase__				:     str="for diffusion",   UpperCAmelCase__				:     str=[1, 3],   ):
    pass







class    _lowerCAmelCase    (      lowercase  ):







 """simple docstring"""







 __UpperCAmelCase      :   str  						=      "config.json"


 @register_to_config
 def __init__(     self				:     Union[str, Any],   UpperCAmelCase__				:     Union[str, Any]=2,   UpperCAmelCase__				:     str=5,   UpperCAmelCase__				:     Optional[int]=(2, 5),   UpperCAmelCase__				:     str="for diffusion",   UpperCAmelCase__				:     str=[1, 3],   UpperCAmelCase__				:     Dict=[1, 3],   ):
    pass







class    _lowerCAmelCase    (      lowercase  ):







 """simple docstring"""







 __UpperCAmelCase      :   List[str]  						=      "config.json"


 @register_to_config
 def __init__(     self				:     Union[str, Any],   UpperCAmelCase__				:     Any=2,   UpperCAmelCase__				:     Union[str, Any]=5,   UpperCAmelCase__				:     Optional[Any]=(2, 5),   UpperCAmelCase__				:     List[str]="for diffusion",   UpperCAmelCase__				:     Optional[Any]=[1, 5],   UpperCAmelCase__				:     Dict=[5, 4],   ):
    pass







class    _lowerCAmelCase    (      unittest.TestCase  ):







 """simple docstring"""







 def    _lowercase					(     self				:     Optional[int]      ):
    with self.assertRaises(UpperCAmelCase__      ):
       ConfigMixin.load_config("dummy_path"      )


 def    _lowercase					(     self				:     Optional[int]      ):
    __lowercase								=		SampleObject()
    __lowercase								=		obj.config
    assert config["a"] == 2
    assert config["b"] == 5
    assert config["c"] == (2, 5)
    assert config["d"] == "for diffusion"
    assert config["e"] == [1, 3]

    # init ignore private arguments
    __lowercase								=		SampleObject(_name_or_path="lalala"      )
    __lowercase								=		obj.config
    assert config["a"] == 2
    assert config["b"] == 5
    assert config["c"] == (2, 5)
    assert config["d"] == "for diffusion"
    assert config["e"] == [1, 3]

    # can override default
    __lowercase								=		SampleObject(c=6      )
    __lowercase								=		obj.config
    assert config["a"] == 2
    assert config["b"] == 5
    assert config["c"] == 6
    assert config["d"] == "for diffusion"
    assert config["e"] == [1, 3]

    # can use positional arguments.
    __lowercase								=		SampleObject(1,   c=6      )
    __lowercase								=		obj.config
    assert config["a"] == 1
    assert config["b"] == 5
    assert config["c"] == 6
    assert config["d"] == "for diffusion"
    assert config["e"] == [1, 3]


 def    _lowercase					(     self				:     Tuple      ):
    __lowercase								=		SampleObject()
    __lowercase								=		obj.config

    assert config["a"] == 2
    assert config["b"] == 5
    assert config["c"] == (2, 5)
    assert config["d"] == "for diffusion"
    assert config["e"] == [1, 3]

    with tempfile.TemporaryDirectory() as tmpdirname:
       obj.save_config(UpperCAmelCase__      )
       __lowercase								=		SampleObject.from_config(SampleObject.load_config(UpperCAmelCase__      )      )
       __lowercase								=		new_obj.config

    # unfreeze configs
    __lowercase								=		dict(UpperCAmelCase__      )
    __lowercase								=		dict(UpperCAmelCase__      )

    assert config.pop("c"      ) == (2, 5)  # instantiated as tuple
    assert new_config.pop("c"      ) == [2, 5]  # saved & loaded as list because of json
    config.pop("_use_default_values"      )
    assert config == new_config


 def    _lowercase					(     self				:     Any      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		DDIMScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler"      )

    assert ddim.__class__ == DDIMScheduler
    # no warning should be thrown
    assert cap_logger.out == ""


 def    _lowercase					(     self				:     int      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		EulerDiscreteScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler"      )

    assert euler.__class__ == EulerDiscreteScheduler
    # no warning should be thrown
    assert cap_logger.out == ""


 def    _lowercase					(     self				:     Optional[Any]      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		EulerAncestralDiscreteScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler"      )

    assert euler.__class__ == EulerAncestralDiscreteScheduler
    # no warning should be thrown
    assert cap_logger.out == ""


 def    _lowercase					(     self				:     str      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		PNDMScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler"      )

    assert pndm.__class__ == PNDMScheduler
    # no warning should be thrown
    assert cap_logger.out == ""


 def    _lowercase					(     self				:     Optional[Any]      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		DDPMScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler",   prediction_type="sample",   beta_end=8,   )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger_a:
       __lowercase								=		DDPMScheduler.from_pretrained("google/ddpm-celebahq-256",   beta_start=8_8      )

    assert ddpm.__class__ == DDPMScheduler
    assert ddpm.config.prediction_type == "sample"
    assert ddpm.config.beta_end == 8
    assert ddpm_a.config.beta_start == 8_8

    # no warning should be thrown
    assert cap_logger.out == ""
    assert cap_logger_a.out == ""


 def    _lowercase					(     self				:     List[Any]      ):
    __lowercase								=		logging.get_logger("diffusers.configuration_utils"      )
    # 30 for warning
    logger.setLevel(3_0      )

    with CaptureLogger(UpperCAmelCase__      ) as cap_logger:
       __lowercase								=		DPMSolverMultistepScheduler.from_pretrained(
           "hf-internal-testing/tiny-stable-diffusion-torch",   subfolder="scheduler"      )

    assert dpm.__class__ == DPMSolverMultistepScheduler
    # no warning should be thrown
    assert cap_logger.out == ""



 def    _lowercase					(     self				:     str      ):
    # let's first save a config that should be in the form
    #    a=2,
    #    b=5,
    #    c=(2, 5),
    #    d="for diffusion",
    #    e=[1, 3],

    __lowercase								=		SampleObject()

    __lowercase								=		{k: v for k, v in config.config.items() if not k.startswith("_"      )}

    # make sure that default config has all keys in `_use_default_values`
    assert set(config_dict.keys()      ) == set(config.config._use_default_values      )

    with tempfile.TemporaryDirectory() as tmpdirname:
       config.save_config(UpperCAmelCase__      )

       # now loading it with SampleObject2 should put f into `_use_default_values`
       __lowercase								=		SampleObjecta.from_config(UpperCAmelCase__      )

       assert "f" in config._use_default_values
       assert config.f == [1, 3]

    # now loading the config, should **NOT** use [1, 3] for `f`, but the default [1, 4] value
    # **BECAUSE** it is part of `config._use_default_values`
    __lowercase								=		SampleObjecta.from_config(config.config      )
    assert new_config.f == [5, 4]

    config.config._use_default_values.pop()
    __lowercase								=		SampleObjecta.from_config(config.config      )
    assert new_config_a.f == [1, 3]

    # Nevertheless "e" should still be correctly loaded to [1, 3] from SampleObject2 instead of defaulting to [1, 5]
    assert new_config_a.e == [1, 3]




