





'''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    __a :

	def __init__(							self							:       str    ,       __magic_name__							:       int    ,       __magic_name__							:       str				)   ->    Optional[Any]:







							"""simple docstring"""
							UpperCAmelCase_     : Dict         =					key
							UpperCAmelCase_     : int         =					freq



	def __str__(							self							:       Any				)   ->    Union[str, Any]:







							"""simple docstring"""
							return F"""Node(key={self.key}, freq={self.freq})"""





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     List[str],     SCREAMING_SNAKE_CASE__ :     Optional[int],     SCREAMING_SNAKE_CASE__ :     List[str],     SCREAMING_SNAKE_CASE__ :     Tuple,     SCREAMING_SNAKE_CASE__ :     Optional[int],     SCREAMING_SNAKE_CASE__ :     List[Any]				)	->		Dict:





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

						UpperCAmelCase_     : List[Any]         =					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(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     node - 1,     key[node],     SCREAMING_SNAKE_CASE_				)
						print_binary_search_tree(SCREAMING_SNAKE_CASE_,     SCREAMING_SNAKE_CASE_,     node + 1,     SCREAMING_SNAKE_CASE_,     key[node],     SCREAMING_SNAKE_CASE_				)





def     lowerCamelCase_ (					SCREAMING_SNAKE_CASE__ :     Any				)	->		Optional[Any]:
						nodes.sort(key=lambda SCREAMING_SNAKE_CASE__				: node.key				)

						UpperCAmelCase_     : int         =					len(SCREAMING_SNAKE_CASE_				)

						UpperCAmelCase_     : Any         =					[nodes[i].key for i in range(SCREAMING_SNAKE_CASE_				)]
						UpperCAmelCase_     : Optional[int]         =					[nodes[i].freq for i in range(SCREAMING_SNAKE_CASE_				)]

						# 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.
						UpperCAmelCase_     : Union[str, Any]         =					[[freqs[i] if i == j else 0 for j in range(SCREAMING_SNAKE_CASE_				)] for i in range(SCREAMING_SNAKE_CASE_				)]
						# sum[i][j] stores the sum of key frequencies between i and j inclusive in nodes
						# array
						UpperCAmelCase_     : Dict         =					[[freqs[i] if i == j else 0 for j in range(SCREAMING_SNAKE_CASE_				)] for i in range(SCREAMING_SNAKE_CASE_				)]
						# stores tree roots that will be used later for constructing binary search tree
						UpperCAmelCase_     : Dict         =					[[i if i == j else 0 for j in range(SCREAMING_SNAKE_CASE_				)] for i in range(SCREAMING_SNAKE_CASE_				)]

						for interval_length in range(2,     n + 1				):
												for i in range(n - interval_length + 1				):
																		UpperCAmelCase_     : Union[str, Any]         =					i + interval_length - 1

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

																								if dp[i][j] > cost:
																														UpperCAmelCase_     : Dict         =					cost
																														UpperCAmelCase_     : int         =					r

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

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





def     lowerCamelCase_ (					)	->		Dict:
						UpperCAmelCase_     : Dict         =					[Node(SCREAMING_SNAKE_CASE_,     randint(1,     50				)				) for i in range(10,     0,     -1				)]
						find_optimal_binary_search_tree(SCREAMING_SNAKE_CASE_				)


if __name__ == "__main__":
					main()












'''simple docstring'''







# Copyright 2023 The HuggingFace Team. All rights reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TYPE_CHECKING

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


snake_case_       :    List[Any]          =					{
    "configuration_tvlt": ["TVLT_PRETRAINED_CONFIG_ARCHIVE_MAP", "TvltConfig"],
    "feature_extraction_tvlt": ["TvltFeatureExtractor"],
    "processing_tvlt": ["TvltProcessor"],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					snake_case_       :    Optional[int]          =					[
					    "TVLT_PRETRAINED_MODEL_ARCHIVE_LIST",
					    "TvltModel",
					    "TvltForPreTraining",
					    "TvltForAudioVisualClassification",
					    "TvltPreTrainedModel",
					]

try:
					if not is_vision_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					snake_case_       :    List[Any]          =					["TvltImageProcessor"]


if TYPE_CHECKING:
					from .configuration_tvlt import TVLT_PRETRAINED_CONFIG_ARCHIVE_MAP, TvltConfig
					from .processing_tvlt import TvltProcessor
					from .feature_extraction_tvlt import TvltFeatureExtractor

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_tvlt import (
										    TVLT_PRETRAINED_MODEL_ARCHIVE_LIST,
										    TvltForAudioVisualClassification,
										    TvltForPreTraining,
										    TvltModel,
										    TvltPreTrainedModel,
										)

					try:
										if not is_vision_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .image_processing_tvlt import TvltImageProcessor


else:
					import sys

					snake_case_       :    Any          =					_LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)





