# 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_					:






 '''simple docstring'''






 def __init__(     self   :    Optional[Any]     ,       lowercase__   :    Tuple     ,       lowercase__   :    int):







        '''simple docstring'''



        lowerCAmelCase__	      =   key
        lowerCAmelCase__	      =   freq




 def __str__(     self   :    List[str]):







        '''simple docstring'''



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






def  __lowerCamelCase						(		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  __lowerCamelCase						(		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  __lowerCamelCase						(		):
       # A sample binary search tree
       lowerCAmelCase__	      =   [Node(lowerCAmelCase__      ,    randint(1      ,    5_0      )      ) for i in range(1_0      ,    0      ,    -1      )]
       find_optimal_binary_search_tree(lowerCAmelCase__      )


if __name__ == "__main__":
    main()

from typing import Union

import torch
from PIL import Image
from torchvision import transforms as tfms
from tqdm.auto import tqdm
from transformers import CLIPTextModel, CLIPTokenizer

from diffusers import (
    AutoencoderKL,
    DDIMScheduler,
    DiffusionPipeline,
    LMSDiscreteScheduler,
    PNDMScheduler,
    UNetaDConditionModel,
)
class 							a_					(		SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 def __init__(     self   :    List[Any]     ,       lowercase__   :    AutoencoderKL     ,       lowercase__   :    CLIPTextModel     ,       lowercase__   :    CLIPTokenizer     ,       lowercase__   :    UNetaDConditionModel     ,       lowercase__   :    Union[PNDMScheduler, LMSDiscreteScheduler, DDIMScheduler]     ,       ):







        '''simple docstring'''



        super().__init__()

        self.register_modules(vae=lowercase__     ,       text_encoder=lowercase__     ,       tokenizer=lowercase__     ,       unet=lowercase__     ,       scheduler=lowercase__)




 def 						__snake_case		(     self   :    List[Any]     ,       lowercase__   :    str):







        '''simple docstring'''



        with torch.no_grad():
               lowerCAmelCase__	      =   self.vae.encode(tfms.ToTensor()(lowercase__).unsqueeze(0).to(self.device) * 2 - 1)
               lowerCAmelCase__	      =   0.18_215 * latent.latent_dist.sample()
        return latent




 def 						__snake_case		(     self   :    Tuple     ,       lowercase__   :    str):







        '''simple docstring'''



        lowerCAmelCase__	      =   (1 / 0.18_215) * latent
        with torch.no_grad():
               lowerCAmelCase__	      =   self.vae.decode(lowercase__).sample
        lowerCAmelCase__	      =   (img / 2 + 0.5).clamp(0     ,       1)
        lowerCAmelCase__	      =   img.detach().cpu().permute(0     ,       2     ,       3     ,       1).numpy()
        lowerCAmelCase__	      =   (img * 255).round().astype('uint8')
        return Image.fromarray(img[0])




 def 						__snake_case		(     self   :    Union[str, Any]     ,       lowercase__   :    Optional[int]):







        '''simple docstring'''



        lowerCAmelCase__	      =   self.tokenizer(
            lowercase__     ,       padding='max_length'     ,       max_length=self.tokenizer.model_max_length     ,       truncation=lowercase__     ,       return_tensors='pt'     ,       )

        lowerCAmelCase__	      =   self.text_encoder(text_input.input_ids.to(self.device))[0]

        lowerCAmelCase__	      =   self.tokenizer(
            ''     ,       padding='max_length'     ,       max_length=self.tokenizer.model_max_length     ,       truncation=lowercase__     ,       return_tensors='pt'     ,       )

        lowerCAmelCase__	      =   self.text_encoder(uncond_input.input_ids.to(self.device))[0]

        return torch.cat([uncond_embedding, text_embedding])




 def __call__(     self   :    List[Any]     ,       lowercase__   :    Image.Image     ,       lowercase__   :    str     ,       lowercase__   :    float = 0.3     ,       lowercase__   :    float = 0.6     ,       lowercase__   :    float = 0.5     ,       lowercase__   :    int = 42     ,       lowercase__   :    int = 50     ,       lowercase__   :    float = 7.5     ,       ):







        '''simple docstring'''



        lowerCAmelCase__	      =   steps - int(kmin * steps)
        lowerCAmelCase__	      =   steps - int(kmax * steps)

        lowerCAmelCase__	      =   self.prep_text(lowercase__)

        self.scheduler.set_timesteps(lowercase__)

        lowerCAmelCase__      ,   lowerCAmelCase__	      =   img.size
        lowerCAmelCase__	      =   self.encode(lowercase__)

        torch.manual_seed(lowercase__)
        lowerCAmelCase__	      =   torch.randn(
            (1, self.unet.config.in_channels, height // 8, width // 8)     ,       ).to(self.device)

        lowerCAmelCase__	      =   self.scheduler.add_noise(
            lowercase__     ,       lowercase__     ,       timesteps=self.scheduler.timesteps[tmax]     ,       )

        lowerCAmelCase__	      =   torch.cat([latents] * 2)

        lowerCAmelCase__	      =   self.scheduler.scale_model_input(lowercase__     ,       self.scheduler.timesteps[tmax])

        with torch.no_grad():
               lowerCAmelCase__	      =   self.unet(
                   lowercase__     ,       self.scheduler.timesteps[tmax]     ,       encoder_hidden_states=lowercase__     ,       ).sample

        lowerCAmelCase__      ,   lowerCAmelCase__	      =   pred.chunk(2)
        lowerCAmelCase__	      =   pred_uncond + guidance_scale * (pred_text - pred_uncond)

        lowerCAmelCase__	      =   self.scheduler.step(lowercase__     ,       self.scheduler.timesteps[tmax]     ,       lowercase__).prev_sample

        for i, t in enumerate(tqdm(self.scheduler.timesteps)):
               if i > tmax:
                      if i < tmin:  # layout generation phase
                             lowerCAmelCase__	      =   self.scheduler.add_noise(
                                 lowercase__     ,       lowercase__     ,       timesteps=lowercase__     ,       )

                             lowerCAmelCase__	      =   (mix_factor * latents) + (
                                 1 - mix_factor
                             ) * orig_latents  # interpolating between layout noise and conditionally generated noise to preserve layout sematics
                             lowerCAmelCase__	      =   torch.cat([input] * 2)

                      else:  # content generation phase
                             lowerCAmelCase__	      =   torch.cat([latents] * 2)

                      lowerCAmelCase__	      =   self.scheduler.scale_model_input(lowercase__     ,       lowercase__)

                      with torch.no_grad():
                             lowerCAmelCase__	      =   self.unet(
                                 lowercase__     ,       lowercase__     ,       encoder_hidden_states=lowercase__     ,       ).sample

                      lowerCAmelCase__      ,   lowerCAmelCase__	      =   pred.chunk(2)
                      lowerCAmelCase__	      =   pred_uncond + guidance_scale * (pred_text - pred_uncond)

                      lowerCAmelCase__	      =   self.scheduler.step(lowercase__     ,       lowercase__     ,       lowercase__).prev_sample

        return self.decode(lowercase__)
