# 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     __UpperCAmelCase:






 """simple docstring"""




 def __init__(    self ,       __magic_name__ ,       __magic_name__      ):

        """simple docstring"""

        A_							:       str	      =				key
        A_							:       List[Any]	      =				freq
 def __str__(    self      ):

        """simple docstring"""

        return f"""Node(key={self.key}, freq={self.freq})"""


def       a__      (					a  ,   a  ,   a  ,   a  ,   a  ,   a							)		->	Tuple:
       if i > j or i < 0 or j > len(a							) - 1:
              return

       A_							:       Tuple	      =				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(a  ,   a  ,   a  ,   node - 1  ,   key[node]  ,   a							)
       print_binary_search_tree(a  ,   a  ,   node + 1  ,   a  ,   key[node]  ,   a							)


def       a__      (					a							)		->	str:
       nodes.sort(key=lambda a							: node.key							)

       A_							:       Optional[int]	      =				len(a							)

       A_							:       Any	      =				[nodes[i].key for i in range(a							)]
       A_							:       Tuple	      =				[nodes[i].freq for i in range(a							)]

       # 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_							:       Any	      =				[[freqs[i] if i == j else 0 for j in range(a							)] for i in range(a							)]
       # sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
       # array
       A_							:       List[Any]	      =				[[freqs[i] if i == j else 0 for j in range(a							)] for i in range(a							)]
       # stores tree roots that will be used later for constructing binary search tree
       A_							:       List[Any]	      =				[[i if i == j else 0 for j in range(a							)] for i in range(a							)]

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

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

                            if dp[i][j] > cost:
                                   A_							:       str	      =				cost
                                   A_							:       List[Any]	      =				r

       print('''Binary search tree nodes:'''							)
       for node in nodes:
              print(a							)

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


def       a__      (					)		->	Optional[Any]:
       # A sample binary search tree
       A_							:       str	      =				[Node(a  ,   randint(1  ,   5_0							)							) for i in range(1_0  ,   0  ,   -1							)]
       find_optimal_binary_search_tree(a							)


if __name__ == "__main__":
    main()



from typing import Any, Dict, List, Union

import numpy as np

from ..utils import add_end_docstrings, is_torch_available, is_vision_available, logging, requires_backends
from .base import PIPELINE_INIT_ARGS, Pipeline


if is_vision_available():
    from PIL import Image

    from ..image_utils import load_image

if is_torch_available():
    from ..models.auto.modeling_auto import (
        MODEL_FOR_IMAGE_SEGMENTATION_MAPPING,
        MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING,
        MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING,
        MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING,
    )


_lowerCAmelCase        =       logging.get_logger(__name__)


_lowerCAmelCase        =       Dict[str, Any]
_lowerCAmelCase        =       List[Prediction]






@add_end_docstrings(A__				)
class     __UpperCAmelCase(    A__				):






 """simple docstring"""




 def __init__(    self ,       *__magic_name__ ,       **__magic_name__      ):

        """simple docstring"""

        super().__init__(*__magic_name__ ,       **__magic_name__      )

        if self.framework == "tf":
               raise ValueError(f"""The {self.__class__} is only available in PyTorch."""      )

        requires_backends(self ,       '''vision'''      )
        self.check_model_type(
            dict(
                MODEL_FOR_IMAGE_SEGMENTATION_MAPPING.items()
                + MODEL_FOR_SEMANTIC_SEGMENTATION_MAPPING.items()
                + MODEL_FOR_INSTANCE_SEGMENTATION_MAPPING.items()
                + MODEL_FOR_UNIVERSAL_SEGMENTATION_MAPPING.items()      )      )
 def  UpperCAmelCase   (    self ,       **__magic_name__      ):

        """simple docstring"""

        A_							:       str	      =				{}
        A_							:       List[Any]	      =				{}
        if "subtask" in kwargs:
               A_							:       Optional[int]	      =				kwargs['''subtask''']
               A_							:       Dict	      =				kwargs['''subtask''']
        if "threshold" in kwargs:
               A_							:       Tuple	      =				kwargs['''threshold''']
        if "mask_threshold" in kwargs:
               A_							:       int	      =				kwargs['''mask_threshold''']
        if "overlap_mask_area_threshold" in kwargs:
               A_							:       Optional[Any]	      =				kwargs['''overlap_mask_area_threshold''']

        return preprocess_kwargs, {}, postprocess_kwargs
 def __call__(    self ,       __magic_name__ ,       **__magic_name__      ):

        """simple docstring"""

        return super().__call__(__magic_name__ ,       **__magic_name__      )
 def  UpperCAmelCase   (    self ,       __magic_name__ ,       __magic_name__=None      ):

        """simple docstring"""

        A_							:       Optional[int]	      =				load_image(__magic_name__      )
        A_							:       int	      =				[(image.height, image.width)]
        if self.model.config.__class__.__name__ == "OneFormerConfig":
               if subtask is None:
                      A_							:       int	      =				{}
               else:
                      A_							:       str	      =				{'''task_inputs''': [subtask]}
               A_							:       List[Any]	      =				self.image_processor(images=[image] ,       return_tensors='''pt''' ,       **__magic_name__      )
               A_							:       int	      =				self.tokenizer(
                   inputs['''task_inputs'''] ,       padding='''max_length''' ,       max_length=self.model.config.task_seq_len ,       return_tensors=self.framework ,       )['''input_ids''']
        else:
               A_							:       Any	      =				self.image_processor(images=[image] ,       return_tensors='''pt'''      )
        A_							:       Optional[int]	      =				target_size
        return inputs
 def  UpperCAmelCase   (    self ,       __magic_name__      ):

        """simple docstring"""

        A_							:       Dict	      =				model_inputs.pop('''target_size'''      )
        A_							:       Union[str, Any]	      =				self.model(**__magic_name__      )
        A_							:       Any	      =				target_size
        return model_outputs
 def  UpperCAmelCase   (    self ,       __magic_name__ ,       __magic_name__=None ,       __magic_name__=0.9 ,       __magic_name__=0.5 ,       __magic_name__=0.5      ):

        """simple docstring"""

        A_							:       Tuple	      =				None
        if subtask in {"panoptic", None} and hasattr(self.image_processor ,       '''post_process_panoptic_segmentation'''      ):
               A_							:       Dict	      =				self.image_processor.post_process_panoptic_segmentation
        elif subtask in {"instance", None} and hasattr(self.image_processor ,       '''post_process_instance_segmentation'''      ):
               A_							:       Tuple	      =				self.image_processor.post_process_instance_segmentation

        if fn is not None:
               A_							:       Dict	      =				fn(
                   __magic_name__ ,       threshold=__magic_name__ ,       mask_threshold=__magic_name__ ,       overlap_mask_area_threshold=__magic_name__ ,       target_sizes=model_outputs['''target_size'''] ,       )[0]

               A_							:       Optional[Any]	      =				[]
               A_							:       Optional[int]	      =				outputs['''segmentation''']

               for segment in outputs["segments_info"]:
                      A_							:       Optional[int]	      =				(segmentation == segment['''id''']) * 255
                      A_							:       int	      =				Image.fromarray(mask.numpy().astype(np.uinta      ) ,       mode='''L'''      )
                      A_							:       Union[str, Any]	      =				self.model.config.idalabel[segment['''label_id''']]
                      A_							:       Optional[int]	      =				segment['''score''']
                      annotation.append({'''score''': score, '''label''': label, '''mask''': mask}      )

        elif subtask in {"semantic", None} and hasattr(self.image_processor ,       '''post_process_semantic_segmentation'''      ):
               A_							:       int	      =				self.image_processor.post_process_semantic_segmentation(
                   __magic_name__ ,       target_sizes=model_outputs['''target_size''']      )[0]

               A_							:       Tuple	      =				[]
               A_							:       Any	      =				outputs.numpy()
               A_							:       Optional[Any]	      =				np.unique(__magic_name__      )

               for label in labels:
                      A_							:       Any	      =				(segmentation == label) * 255
                      A_							:       str	      =				Image.fromarray(mask.astype(np.uinta      ) ,       mode='''L'''      )
                      A_							:       List[str]	      =				self.model.config.idalabel[label]
                      annotation.append({'''score''': None, '''label''': label, '''mask''': mask}      )
        else:
               raise ValueError(f"""Subtask {subtask} is not supported for model {type(self.model      )}"""      )
        return annotation


