




'''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_				:




					'''simple docstring'''






					def __init__(       self,    __UpperCamelCase,    __UpperCamelCase					):
							_snake_case      			=			key
							_snake_case      			=			freq






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






def 						_lowercase						(      lowercase_		,				lowercase_		,				lowercase_		,				lowercase_		,				lowercase_		,				lowercase_    ):



		'''simple docstring'''







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

		_snake_case      			=			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(lowercase_		,				lowercase_		,				lowercase_		,				node - 1		,				key[node]		,				lowercase_    )
		print_binary_search_tree(lowercase_		,				lowercase_		,				node + 1		,				lowercase_		,				key[node]		,				lowercase_    )






def 						_lowercase						(      lowercase_    ):



		'''simple docstring'''







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

		_snake_case      			=			len(lowercase_    )

		_snake_case      			=			[nodes[i].key for i in range(lowercase_    )]
		_snake_case      			=			[nodes[i].freq for i in range(lowercase_    )]

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

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

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

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

		print("Binary search tree nodes:"    )
		for node in nodes:
				print(lowercase_    )

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






def 						_lowercase						(      ):



		'''simple docstring'''







		_snake_case      			=			[Node(lowercase_		,				randint(1		,				50    )    ) for i in range(10		,				0		,				-1    )]
		find_optimal_binary_search_tree(lowercase_    )


if __name__ == "__main__":
						main()











'''simple docstring'''







from collections import OrderedDict
from typing import Mapping

from packaging import version

from ...configuration_utils import PretrainedConfig
from ...onnx import OnnxConfig
from ...utils import logging


_lowerCamelCase				:		List[str]				      =    logging.get_logger(__name__)

_lowerCamelCase				:		Optional[Any]				      =    {
    'MBZUAI/swiftformer-xs': 'https://huggingface.co/MBZUAI/swiftformer-xs/resolve/main/config.json',
}





class 	lowerCamelCase_				(			UpperCAmelCase_				):




					'''simple docstring'''






					lowercase__       =					"""swiftformer"""






					def __init__(       self,    __UpperCamelCase=3,    __UpperCamelCase=[3, 3, 6, 4],    __UpperCamelCase=[48, 56, 112, 220],    __UpperCamelCase=4,    __UpperCamelCase=[True, True, True, True],    __UpperCamelCase="gelu",    __UpperCamelCase=3,    __UpperCamelCase=2,    __UpperCamelCase=1,    __UpperCamelCase=0.0,    __UpperCamelCase=True,    __UpperCamelCase=1E-5,    __UpperCamelCase=1E-5,    **__UpperCamelCase,    ):
							super().__init__(**__UpperCamelCase					)
							_snake_case      			=			num_channels
							_snake_case      			=			depths
							_snake_case      			=			embed_dims
							_snake_case      			=			mlp_ratio
							_snake_case      			=			downsamples
							_snake_case      			=			hidden_act
							_snake_case      			=			down_patch_size
							_snake_case      			=			down_stride
							_snake_case      			=			down_pad
							_snake_case      			=			drop_path_rate
							_snake_case      			=			use_layer_scale
							_snake_case      			=			layer_scale_init_value
							_snake_case      			=			batch_norm_eps





class 	lowerCamelCase_				(			UpperCAmelCase_				):




					'''simple docstring'''






					lowercase__       =					version.parse("""1.11"""				)






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return OrderedDict(
							    [
							        ("pixel_values", {0: "batch", 1: "num_channels", 2: "height", 3: "width"}),
							    ]					)






					@property
					def 							__SCREAMING_SNAKE_CASE      (       self					):
							return 1E-4





