text: import random
  from typing import Optional, List, Union
  
  import numpy as np
  
  from stable_baselines.common.segment_tree import SumSegmentTree, MinSegmentTree
  from stable_baselines.common.vec_env import VecNormalize
  
  
  class ReplayBuffer(object):
      def __init__(self, size: int):
          """
          Implements a ring buffer (FIFO).
  
          :param size: (int)  Max number of transitions to store in the buffer. When the buffer overflows the old
              memories are dropped.
          """
          self._storage = []
          self._maxsize = size
          self._next_idx = 0
  
      def __len__(self) -> int:
          return len(self._storage)
  
      @property
      def storage(self):
          """[(Union[np.ndarray, int], Union[np.ndarray, int], float, Union[np.ndarray, int], bool)]: content of the replay buffer"""
          return self._storage
  
      @property
      def buffer_size(self) -> int:
          """float: Max capacity of the buffer"""
          return self._maxsize
  
      def can_sample(self, n_samples: int) -> bool:
          """
          Check if n_samples samples can be sampled
          from the buffer.
  
          :param n_samples: (int)
          :return: (bool)
          """
          return len(self) >= n_samples
  
      def is_full(self) -> int:
          """
          Check whether the replay buffer is full or not.
  
          :return: (bool)
          """
          return len(self) == self.buffer_size
  
      def add(self, obs_t, action, reward, obs_tp1, done):
          """
          add a new transition to the buffer
  
          :param obs_t: (Union[np.ndarray, int]) the last observation
          :param action: (Union[np.ndarray, int]) the action
          :param reward: (float) the reward of the transition
          :param obs_tp1: (Union[np.ndarray, int]) the current observation
          :param done: (bool) is the episode done
          """
          data = (obs_t, action, reward, obs_tp1, done)
  
          if self._next_idx >= len(self._storage):
              self._storage.append(data)
          else:
              self._storage[self._next_idx] = data
          self._next_idx = (self._next_idx + 1) % self._maxsize
  
      def extend(self, obs_t, action, reward, obs_tp1, done):
          """
          add a new batch of transitions to the buffer
  
          :param obs_t: (Union[Tuple[Union[np.ndarray, int]], np.ndarray]) the last batch of observations
          :param action: (Union[Tuple[Union[np.ndarray, int]]], np.ndarray]) the batch of actions
          :param reward: (Union[Tuple[float], np.ndarray]) the batch of the rewards of the transition
          :param obs_tp1: (Union[Tuple[Union[np.ndarray, int]], np.ndarray]) the current batch of observations
          :param done: (Union[Tuple[bool], np.ndarray]) terminal status of the batch
  
          Note: uses the same names as .add to keep compatibility with named argument passing
                  but expects iterables and arrays with more than 1 dimensions
          """
          for data in zip(obs_t, action, reward, obs_tp1, done):
              if self._next_idx >= len(self._storage):
                  self._storage.append(data)
              else:
                  self._storage[self._next_idx] = data
              self._next_idx = (self._next_idx + 1) % self._maxsize
  
      @staticmethod
      def _normalize_obs(obs: np.ndarray,
                         env: Optional[VecNormalize] = None) -> np.ndarray:
          """
          Helper for normalizing the observation.
          """
          if env is not None:
              return env.normalize_obs(obs)
          return obs
  
      @staticmethod
      def _normalize_reward(reward: np.ndarray,
                            env: Optional[VecNormalize] = None) -> np.ndarray:
          """
          Helper for normalizing the reward.
          """
          if env is not None:
              return env.normalize_reward(reward)
          return reward
  
      def _encode_sample(self, idxes: Union[List[int], np.ndarray], env: Optional[VecNormalize] = None):
          obses_t, actions, rewards, obses_tp1, dones = [], [], [], [], []
          for i in idxes:
              data = self._storage[i]
              obs_t, action, reward, obs_tp1, done = data
              obses_t.append(np.array(obs_t, copy=False))
              actions.append(np.array(action, copy=False))
              rewards.append(reward)
              obses_tp1.append(np.array(obs_tp1, copy=False))
              dones.append(done)
          return (self._normalize_obs(np.array(obses_t), env),
                  np.array(actions),
                  self._normalize_reward(np.array(rewards), env),
                  self._normalize_obs(np.array(obses_tp1), env),
                  np.array(dones))
  
      def sample(self, batch_size: int, env: Optional[VecNormalize] = None, **_kwargs):
          """
          Sample a batch of experiences.
  
          :param batch_size: (int) How many transitions to sample.
          :param env: (Optional[VecNormalize]) associated gym VecEnv
              to normalize the observations/rewards when sampling
          :return:
              - obs_batch: (np.ndarray) batch of observations
              - act_batch: (numpy float) batch of actions executed given obs_batch
              - rew_batch: (numpy float) rewards received as results of executing act_batch
              - next_obs_batch: (np.ndarray) next set of observations seen after executing act_batch
              - done_mask: (numpy bool) done_mask[i] = 1 if executing act_batch[i] resulted in the end of an episode
                  and 0 otherwise.
          """
          idxes = [random.randint(0, len(self._storage) - 1) for _ in range(batch_size)]
          return self._encode_sample(idxes, env=env)
  
  
  class PrioritizedReplayBuffer(ReplayBuffer):
      def __init__(self, size, alpha):
          """
          Create Prioritized Replay buffer.
  
          See Also ReplayBuffer.__init__
  
          :param size: (int) Max number of transitions to store in the buffer. When the buffer overflows the old memories
              are dropped.
          :param alpha: (float) how much prioritization is used (0 - no prioritization, 1 - full prioritization)
          """
          super(PrioritizedReplayBuffer, self).__init__(size)
          assert alpha >= 0
          self._alpha = alpha
  
          it_capacity = 1
          while it_capacity < size:
              it_capacity *= 2
  
          self._it_sum = SumSegmentTree(it_capacity)
          self._it_min = MinSegmentTree(it_capacity)
          self._max_priority = 1.0
  
      def add(self, obs_t, action, reward, obs_tp1, done):
          """
          add a new transition to the buffer
  
          :param obs_t: (Any) the last observation
          :param action: ([float]) the action
          :param reward: (float) the reward of the transition
          :param obs_tp1: (Any) the current observation
          :param done: (bool) is the episode done
          """
          idx = self._next_idx
          super().add(obs_t, action, reward, obs_tp1, done)
          self._it_sum[idx] = self._max_priority ** self._alpha
          self._it_min[idx] = self._max_priority ** self._alpha
  
      def extend(self, obs_t, action, reward, obs_tp1, done):
          """
          add a new batch of transitions to the buffer
  
          :param obs_t: (Union[Tuple[Union[np.ndarray, int]], np.ndarray]) the last batch of observations
          :param action: (Union[Tuple[Union[np.ndarray, int]]], np.ndarray]) the batch of actions
          :param reward: (Union[Tuple[float], np.ndarray]) the batch of the rewards of the transition
          :param obs_tp1: (Union[Tuple[Union[np.ndarray, int]], np.ndarray]) the current batch of observations
          :param done: (Union[Tuple[bool], np.ndarray]) terminal status of the batch
  
          Note: uses the same names as .add to keep compatibility with named argument passing
              but expects iterables and arrays with more than 1 dimensions
          """
          idx = self._next_idx
          super().extend(obs_t, action, reward, obs_tp1, done)
          while idx != self._next_idx:
              self._it_sum[idx] = self._max_priority ** self._alpha
              self._it_min[idx] = self._max_priority ** self._alpha
              idx = (idx + 1) % self._maxsize
  
      def _sample_proportional(self, batch_size):
          mass = []
          total = self._it_sum.sum(0, len(self._storage) - 1)
          # TODO(szymon): should we ensure no repeats?
          mass = np.random.random(size=batch_size) * total
          idx = self._it_sum.find_prefixsum_idx(mass)
          return idx
  
      def sample(self, batch_size: int, beta: float = 0, env: Optional[VecNormalize] = None):
          """
          Sample a batch of experiences.
  
          compared to ReplayBuffer.sample
          it also returns importance weights and idxes
          of sampled experiences.
  
          :param batch_size: (int) How many transitions to sample.
          :param beta: (float) To what degree to use importance weights (0 - no corrections, 1 - full correction)
          :param env: (Optional[VecNormalize]) associated gym VecEnv
              to normalize the observations/rewards when sampling
          :return:
              - obs_batch: (np.ndarray) batch of observations
              - act_batch: (numpy float) batch of actions executed given obs_batch
              - rew_batch: (numpy float) rewards received as results of executing act_batch
              - next_obs_batch: (np.ndarray) next set of observations seen after executing act_batch
              - done_mask: (numpy bool) done_mask[i] = 1 if executing act_batch[i] resulted in the end of an episode
                  and 0 otherwise.
              - weights: (numpy float) Array of shape (batch_size,) and dtype np.float32 denoting importance weight of
                  each sampled transition
              - idxes: (numpy int) Array of shape (batch_size,) and dtype np.int32 idexes in buffer of sampled experiences
          """
          assert beta > 0
  
          idxes = self._sample_proportional(batch_size)
          weights = []
          p_min = self._it_min.min() / self._it_sum.sum()
          max_weight = (p_min * len(self._storage)) ** (-beta)
          p_sample = self._it_sum[idxes] / self._it_sum.sum()
          weights = (p_sample * len(self._storage)) ** (-beta) / max_weight
          encoded_sample = self._encode_sample(idxes, env=env)
          return tuple(list(encoded_sample) + [weights, idxes])
  
      def update_priorities(self, idxes, priorities):
          """
          Update priorities of sampled transitions.
  
          sets priority of transition at index idxes[i] in buffer
          to priorities[i].
  
          :param idxes: ([int]) List of idxes of sampled transitions
          :param priorities: ([float]) List of updated priorities corresponding to transitions at the sampled idxes
              denoted by variable `idxes`.
          """
          assert len(idxes) == len(priorities)
          assert np.min(priorities) > 0
          assert np.min(idxes) >= 0
          assert np.max(idxes) < len(self.storage)
          self._it_sum[idxes] = priorities ** self._alpha
          self._it_min[idxes] = priorities ** self._alpha
  
          self._max_priority = max(self._max_priority, np.max(priorities))
  
  class TwoWayPrioritizedReplayBuffer(ReplayBuffer):
      def __init__(self, size, alpha):
          super(PrioritizedReplayBuffer, self).__init__(size)
          assert alpha >= 0
          self._alpha = alpha
  
          it_capacity = 1
          while it_capacity < size:
              it_capacity *= 2
  
          self._it_sum = SumSegmentTree(it_capacity)
          self._it_min = MinSegmentTree(it_capacity)
          self._max_priority = 1.0
  
      def add(self, obs_t, action, reward, obs_tp1, done):
          idx = self._next_idx
          super().add(obs_t, action, reward, obs_tp1, done)
          self._it_sum[idx] = self._max_priority ** self._alpha
          self._it_min[idx] = self._max_priority ** self._alpha
  
      def extend(self, obs_t, action, reward, obs_tp1, done):
          idx = self._next_idx
          super().extend(obs_t, action, reward, obs_tp1, done)
          while idx != self._next_idx:
              self._it_sum[idx] = self._max_priority ** self._alpha
              self._it_min[idx] = self._max_priority ** self._alpha
              idx = (idx + 1) % self._maxsize
  
      def _sample_proportional(self, batch_size):
          mass = []
          total = self._it_sum.sum(0, len(self._storage) - 1)
          # TODO(szymon): should we ensure no repeats?
          mass = np.random.random(size=batch_size) * total
          idx = self._it_sum.find_prefixsum_idx(mass)
          return idx
  
      def sample(self, batch_size: int, beta: float = 0, env: Optional[VecNormalize] = None):
          assert beta > 0
  
          idxes = self._sample_proportional(batch_size)
          weights = []
          p_min = self._it_min.min() / self._it_sum.sum()
          max_weight = (p_min * len(self._storage)) ** (-beta)
          p_sample = self._it_sum[idxes] / self._it_sum.sum()
          weights = (p_sample * len(self._storage)) ** (-beta) / max_weight
          encoded_sample = self._encode_sample(idxes, env=env)
          return tuple(list(encoded_sample) + [weights, idxes])
  	
      def _sample_invproportional(self, batch_size):
          mass = []
          total = self._it_sum.sum(len(self._storage) - 1, 0)
          # TODO(szymon): should we ensure no repeats?
          mass = np.random.random(size=batch_size) * total
          idx = self._it_sum.find_prefixsum_idx(mass)
          return idx
  	
      def invsample(self, batch_size: int, beta: float = 0, env: Optional[VecNormalize] = None):
          assert beta > 0
  
          idxes = self._sample_invproportional(batch_size)
          encoded_sample = self._encode_sample(idxes, env=env)
          return list(encoded_sample)
  
      def update_priorities(self, idxes, priorities):
          assert len(idxes) == len(priorities)
          assert np.min(priorities) > 0
          assert np.min(idxes) >= 0
          assert np.max(idxes) < len(self.storage)
          self._it_sum[idxes] = priorities ** self._alpha
          self._it_min[idxes] = priorities ** self._alpha
  
          self._max_priority = max(self._max_priority, np.max(priorities))