
"""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     :




				def __init__(							self       ,	UpperCAmelCase       ,	UpperCAmelCase      ):
							lowerCamelCase_ 		=     key
							lowerCamelCase_ 		=     freq





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






def    lowercase	(  lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__	):
			if i > j or i < 0 or j > len(lowerCAmelCase__	) - 1:
						return

			lowerCamelCase_ 		=     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(lowerCAmelCase__  ,lowerCAmelCase__  ,lowerCAmelCase__  ,node - 1  ,key[node]  ,lowerCAmelCase__	)
			print_binary_search_tree(lowerCAmelCase__  ,lowerCAmelCase__  ,node + 1  ,lowerCAmelCase__  ,key[node]  ,lowerCAmelCase__	)






def    lowercase	(  lowerCAmelCase__	):
			nodes.sort(key=lambda lowerCAmelCase__	: node.key	)

			lowerCamelCase_ 		=     len(lowerCAmelCase__	)

			lowerCamelCase_ 		=     [nodes[i].key for i in range(lowerCAmelCase__	)]
			lowerCamelCase_ 		=     [nodes[i].freq for i in range(lowerCAmelCase__	)]

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

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

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

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

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

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






def    lowercase	(  ):
			# A sample binary search tree
			lowerCamelCase_ 		=     [Node(lowerCAmelCase__  ,randint(1  ,50	)	) for i in range(10  ,0  ,-1	)]
			find_optimal_binary_search_tree(lowerCAmelCase__	)


if __name__ == "__main__":
						main()





"""simple docstring"""


from typing import TYPE_CHECKING

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available, is_vision_available


A_						       =				{
    """configuration_flava""": [
        """FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """FlavaConfig""",
        """FlavaImageCodebookConfig""",
        """FlavaImageConfig""",
        """FlavaMultimodalConfig""",
        """FlavaTextConfig""",
    ],
}

try:
						if not is_vision_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_						       =				["""FlavaFeatureExtractor"""]
						A_						       =				["""FlavaImageProcessor"""]
						A_						       =				["""FlavaProcessor"""]

try:
						if not is_torch_available():
												raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
						pass
else:
						A_						       =				[
						    """FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST""",
						    """FlavaForPreTraining""",
						    """FlavaImageCodebook""",
						    """FlavaImageModel""",
						    """FlavaModel""",
						    """FlavaMultimodalModel""",
						    """FlavaPreTrainedModel""",
						    """FlavaTextModel""",
						]

if TYPE_CHECKING:
						from .configuration_flava import (
						    FLAVA_PRETRAINED_CONFIG_ARCHIVE_MAP,
						    FlavaConfig,
						    FlavaImageCodebookConfig,
						    FlavaImageConfig,
						    FlavaMultimodalConfig,
						    FlavaTextConfig,
						)

						try:
												if not is_vision_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .feature_extraction_flava import FlavaFeatureExtractor
												from .image_processing_flava import FlavaImageProcessor
												from .processing_flava import FlavaProcessor

						try:
												if not is_torch_available():
																		raise OptionalDependencyNotAvailable()
						except OptionalDependencyNotAvailable:
												pass
						else:
												from .modeling_flava import (
												    FLAVA_PRETRAINED_MODEL_ARCHIVE_LIST,
												    FlavaForPreTraining,
												    FlavaImageCodebook,
												    FlavaImageModel,
												    FlavaModel,
												    FlavaMultimodalModel,
												    FlavaPreTrainedModel,
												    FlavaTextModel,
												)

else:
						import sys

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



