




'''simple docstring'''
import sys
from random import randint






class 					lowerCAmelCase_     :






       def __init__(   self ,    _UpperCamelCase ,    _UpperCamelCase      )->			Dict:
            _A				=       key
            _A				=       freq






       def __str__(   self      )->			Dict:
            return F'Node(key={self.key}, freq={self.freq})'






def 				lowerCamelCase_   (   __UpperCamelCase				:					Dict       ,						__UpperCamelCase				:					Any       ,						__UpperCamelCase				:					Optional[Any]       ,						__UpperCamelCase				:					Any       ,						__UpperCamelCase				:					Tuple       ,						__UpperCamelCase				:					List[Any]		)				->  List[Any]:







     """simple docstring"""
     if i > j or i < 0 or j > len(__UpperCamelCase		) - 1:
          return

     _A				=       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 				lowerCamelCase_   (   __UpperCamelCase				:					List[Any]		)				->  List[Any]:







     """simple docstring"""
     nodes.sort(key=lambda __UpperCamelCase		: node.key		)

     _A				=       len(__UpperCamelCase		)

     _A				=       [nodes[i].key for i in range(__UpperCamelCase		)]
     _A				=       [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.
     _A				=       [[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
     _A				=       [[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
     _A				=       [[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		):
               _A				=       i + interval_length - 1

               _A				=       sys.maxsize  # set the value to "infinity"
               _A				=       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
                    _A				=       dp[i][r - 1] if r != i else 0  # optimal cost for left subtree
                    _A				=       dp[r + 1][j] if r != j else 0  # optimal cost for right subtree
                    _A				=       left + total[i][j] + right

                    if dp[i][j] > cost:
                         _A				=       cost
                         _A				=       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 				lowerCamelCase_   (   )				->  Tuple:







     """simple docstring"""
     _A				=       [Node(__UpperCamelCase       ,						randint(1       ,						5_0		)		) for i in range(1_0       ,						0       ,						-1		)]
     find_optimal_binary_search_tree(__UpperCamelCase		)


if __name__ == "__main__":
    main()









'''simple docstring'''
from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_tf_available,
    is_torch_available,
    is_vision_available,
)


lowerCAmelCase  =				{
    """configuration_segformer""": ["""SEGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""", """SegformerConfig""", """SegformerOnnxConfig"""]
}

try:
    if not is_vision_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase  =				["""SegformerFeatureExtractor"""]
    lowerCAmelCase  =				["""SegformerImageProcessor"""]

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase  =				[
        """SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """SegformerDecodeHead""",
        """SegformerForImageClassification""",
        """SegformerForSemanticSegmentation""",
        """SegformerLayer""",
        """SegformerModel""",
        """SegformerPreTrainedModel""",
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase  =				[
        """TF_SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
        """TFSegformerDecodeHead""",
        """TFSegformerForImageClassification""",
        """TFSegformerForSemanticSegmentation""",
        """TFSegformerModel""",
        """TFSegformerPreTrainedModel""",
    ]


if TYPE_CHECKING:
    from .configuration_segformer import SEGFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP, SegformerConfig, SegformerOnnxConfig

    try:
        if not is_vision_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .feature_extraction_segformer import SegformerFeatureExtractor
        from .image_processing_segformer import SegformerImageProcessor

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_segformer import (
            SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
            SegformerDecodeHead,
            SegformerForImageClassification,
            SegformerForSemanticSegmentation,
            SegformerLayer,
            SegformerModel,
            SegformerPreTrainedModel,
        )
    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_segformer import (
            TF_SEGFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFSegformerDecodeHead,
            TFSegformerForImageClassification,
            TFSegformerForSemanticSegmentation,
            TFSegformerModel,
            TFSegformerPreTrainedModel,
        )

else:
    import sys

    lowerCAmelCase  =				_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)





