
'''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__     :    str ,							__magic_name__     :    Dict							):


				"""simple docstring"""

				lowerCAmelCase__									=							key
				lowerCAmelCase__									=							freq







	def __str__(   self     :    List[Any]							):


				"""simple docstring"""

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







def 					A       ( UpperCamelCase_   :       Union[str, Any]  ,		UpperCamelCase_   :       List[Any]  ,		UpperCamelCase_   :       Any  ,		UpperCamelCase_   :       int  ,		UpperCamelCase_   :       Optional[int]  ,		UpperCamelCase_   :       str )   ->    List[str]:







			'''simple docstring'''



			if i > j or i < 0 or j > len(UpperCamelCase_ ) - 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(UpperCamelCase_  ,		UpperCamelCase_  ,		UpperCamelCase_  ,		node - 1  ,		key[node]  ,		UpperCamelCase_ )
			print_binary_search_tree(UpperCamelCase_  ,		UpperCamelCase_  ,		node + 1  ,		UpperCamelCase_  ,		key[node]  ,		UpperCamelCase_ )







def 					A       ( UpperCamelCase_   :       Optional[int] )   ->    Dict:







			'''simple docstring'''



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

			lowerCAmelCase__									=							len(UpperCamelCase_ )

			lowerCAmelCase__									=							[nodes[i].key for i in range(UpperCamelCase_ )]
			lowerCAmelCase__									=							[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.
			lowerCAmelCase__									=							[[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
			lowerCAmelCase__									=							[[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
			lowerCAmelCase__									=							[[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 ):
									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(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       ( )   ->    Union[str, Any]:







			'''simple docstring'''



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


if __name__ == "__main__":
		main()







'''simple docstring'''

import sys
from typing import Tuple

import numpy as np
import torch
from PIL import Image
from torch import nn

from transformers.image_utils import PILImageResampling
from utils import img_tensorize






class 				A       :





	def __init__(   self     :    Union[str, Any] ,							__magic_name__     :    Union[str, Any] ,							__magic_name__     :    Optional[Any]=sys.maxsize							):


				"""simple docstring"""

				lowerCAmelCase__									=							"bilinear"
				lowerCAmelCase__									=							max_size
				lowerCAmelCase__									=							short_edge_length







	def __call__(   self     :    List[str] ,							__magic_name__     :    int							):


				"""simple docstring"""

				lowerCAmelCase__									=							[]
				for img in imgs:
							lowerCAmelCase__		,lowerCAmelCase__									=							img.shape[:2]
							# later: provide list and randomly choose index for resize
							lowerCAmelCase__									=							np.random.randint(self.short_edge_length[0] ,							self.short_edge_length[1] + 1							)
							if size == 0:
										return img
							lowerCAmelCase__									=							size * 1.0 / min(__magic_name__ ,							__magic_name__							)
							if h < w:
										lowerCAmelCase__		,lowerCAmelCase__									=							size, scale * w
							else:
										lowerCAmelCase__		,lowerCAmelCase__									=							scale * h, size
							if max(__magic_name__ ,							__magic_name__							) > self.max_size:
										lowerCAmelCase__									=							self.max_size * 1.0 / max(__magic_name__ ,							__magic_name__							)
										lowerCAmelCase__									=							newh * scale
										lowerCAmelCase__									=							neww * scale
							lowerCAmelCase__									=							int(neww + 0.5							)
							lowerCAmelCase__									=							int(newh + 0.5							)

							if img.dtype == np.uinta:
										lowerCAmelCase__									=							Image.fromarray(__magic_name__							)
										lowerCAmelCase__									=							pil_image.resize((neww, newh) ,							PILImageResampling.BILINEAR							)
										lowerCAmelCase__									=							np.asarray(__magic_name__							)
							else:
										lowerCAmelCase__									=							img.permute(2 ,							0 ,							1							).unsqueeze(0							)  # 3, 0, 1)  # hw(c) -> nchw
										lowerCAmelCase__									=							nn.functional.interpolate(
										    __magic_name__ ,							(newh, neww) ,							mode=self.interp_method ,							align_corners=__magic_name__							).squeeze(0							)
							img_augs.append(__magic_name__							)

				return img_augs






class 				A       :





	def __init__(   self     :    str ,							__magic_name__     :    Union[str, Any]							):


				"""simple docstring"""

				lowerCAmelCase__									=							ResizeShortestEdge([cfg.INPUT.MIN_SIZE_TEST, cfg.INPUT.MIN_SIZE_TEST] ,							cfg.INPUT.MAX_SIZE_TEST							)
				lowerCAmelCase__									=							cfg.INPUT.FORMAT
				lowerCAmelCase__									=							cfg.SIZE_DIVISIBILITY
				lowerCAmelCase__									=							cfg.PAD_VALUE
				lowerCAmelCase__									=							cfg.INPUT.MAX_SIZE_TEST
				lowerCAmelCase__									=							cfg.MODEL.DEVICE
				lowerCAmelCase__									=							torch.tensor(cfg.MODEL.PIXEL_STD							).to(self.device							).view(len(cfg.MODEL.PIXEL_STD							) ,							1 ,							1							)
				lowerCAmelCase__									=							torch.tensor(cfg.MODEL.PIXEL_MEAN							).to(self.device							).view(len(cfg.MODEL.PIXEL_STD							) ,							1 ,							1							)
				lowerCAmelCase__									=							lambda __magic_name__							: (x - self.pixel_mean) / self.pixel_std





	def 							__SCREAMING_SNAKE_CASE					(   self     :    Optional[Any] ,							__magic_name__     :    Optional[int]							):


				"""simple docstring"""

				lowerCAmelCase__									=							tuple(max(__magic_name__							) for s in zip(*[img.shape for img in images]							)							)
				lowerCAmelCase__									=							[im.shape[-2:] for im in images]
				lowerCAmelCase__									=							[
				    nn.functional.pad(
				        __magic_name__ ,							[0, max_size[-1] - size[1], 0, max_size[-2] - size[0]] ,							value=self.pad_value ,							)
				    for size, im in zip(__magic_name__ ,							__magic_name__							)
				]

				return torch.stack(__magic_name__							), torch.tensor(__magic_name__							)







	def __call__(   self     :    List[str] ,							__magic_name__     :    int ,							__magic_name__     :    Optional[int]=False							):


				"""simple docstring"""

				with torch.no_grad():
							if not isinstance(__magic_name__ ,							__magic_name__							):
										lowerCAmelCase__									=							[images]
							if single_image:
										assert len(__magic_name__							) == 1
							for i in range(len(__magic_name__							)							):
										if isinstance(images[i] ,							torch.Tensor							):
													images.insert(__magic_name__ ,							images.pop(__magic_name__							).to(self.device							).float()							)
										elif not isinstance(images[i] ,							torch.Tensor							):
													images.insert(
													    __magic_name__ ,							torch.as_tensor(img_tensorize(images.pop(__magic_name__							) ,							input_format=self.input_format							)							)
													    .to(self.device							)
													    .float() ,							)
            # resize smallest edge
							lowerCAmelCase__									=							torch.tensor([im.shape[:2] for im in images]							)
							lowerCAmelCase__									=							self.aug(__magic_name__							)
							# transpose images and convert to torch tensors
							# images = [torch.as_tensor(i.astype("float32")).permute(2, 0, 1).to(self.device) for i in images]
							# now normalize before pad to avoid useless arithmetic
							lowerCAmelCase__									=							[self.normalizer(__magic_name__							) for x in images]
							# now pad them to do the following operations
							lowerCAmelCase__		,lowerCAmelCase__									=							self.pad(__magic_name__							)
							# Normalize

							if self.size_divisibility > 0:
										raise NotImplementedError()
							# pad
							lowerCAmelCase__									=							torch.true_divide(__magic_name__ ,							__magic_name__							)
							if single_image:
										return images[0], sizes[0], scales_yx[0]
							else:
										return images, sizes, scales_yx







def 					A       ( UpperCamelCase_   :       int  ,		UpperCamelCase_   :       Optional[Any] )   ->    List[str]:







			'''simple docstring'''



			boxes[:, 0::2] *= scale_yx[:, 1]
			boxes[:, 1::2] *= scale_yx[:, 0]
			return boxes







def 					A       ( UpperCamelCase_   :       Optional[Any]  ,		UpperCamelCase_   :       Tuple[int, int] )   ->    Tuple:







			'''simple docstring'''



			assert torch.isfinite(UpperCamelCase_ ).all(), "Box tensor contains infinite or NaN!"
			lowerCAmelCase__		,lowerCAmelCase__									=							box_size
			tensor[:, 0].clamp_(min=0  ,		max=UpperCamelCase_ )
			tensor[:, 1].clamp_(min=0  ,		max=UpperCamelCase_ )
			tensor[:, 2].clamp_(min=0  ,		max=UpperCamelCase_ )
			tensor[:, 3].clamp_(min=0  ,		max=UpperCamelCase_ )





