




'''simple docstring'''






import sys
from random import randint

class   SCREAMING_SNAKE_CASE_		:



 def __init__(  self   ,		A   ,		A ):






        '''simple docstring'''




        lowercase  :		Dict						=      key
        lowercase  :		List[Any]						=      freq





 def __str__(  self ):






        '''simple docstring'''




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






def 		a_( lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase   ,				lowerCamelCase      )				->Union[str, Any]:






       '''simple docstring'''




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

       lowercase  :		Dict						=      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_( lowerCamelCase      )				->List[Any]:






       '''simple docstring'''




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

       lowercase  :		str						=      len(UpperCamelCase__      )

       lowercase  :		Union[str, Any]						=      [nodes[i].key for i in range(UpperCamelCase__      )]
       lowercase  :		Any						=      [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  :		Tuple						=      [[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  :		Optional[int]						=      [[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  :		Tuple						=      [[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  :		Optional[Any]						=      i + interval_length - 1

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

                            if dp[i][j] > cost:
                                   lowercase  :		List[str]						=      cost
                                   lowercase  :		Optional[int]						=      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  :		List[Any]						=      [Node(UpperCamelCase__   ,				randint(1   ,				50      )      ) for i in range(10   ,				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_torch_available


lowercase	:      Optional[int]				=       {
    '''configuration_prophetnet''': ['''PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''ProphetNetConfig'''],
    '''tokenization_prophetnet''': ['''ProphetNetTokenizer'''],
}

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      lowercase	:      List[str]				=       [
          '''PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST''',
          '''ProphetNetDecoder''',
          '''ProphetNetEncoder''',
          '''ProphetNetForCausalLM''',
          '''ProphetNetForConditionalGeneration''',
          '''ProphetNetModel''',
          '''ProphetNetPreTrainedModel''',
      ]


if TYPE_CHECKING:
      from .configuration_prophetnet import PROPHETNET_PRETRAINED_CONFIG_ARCHIVE_MAP, ProphetNetConfig
      from .tokenization_prophetnet import ProphetNetTokenizer

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_prophetnet import (
                PROPHETNET_PRETRAINED_MODEL_ARCHIVE_LIST,
                ProphetNetDecoder,
                ProphetNetEncoder,
                ProphetNetForCausalLM,
                ProphetNetForConditionalGeneration,
                ProphetNetModel,
                ProphetNetPreTrainedModel,
            )

else:
      import sys

      lowercase	:      int				=       _LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)




