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368 lines
8.0 KiB
Markdown
368 lines
8.0 KiB
Markdown
## queues
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<br>
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* queues are **first in, first out (FIFO) abstract structures** (*i.e.*, items are removed at the same order they are added) that can be implemented with two arrays or a dynamic array (linked list), as long as items are added and removed from opposite sides.
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* queues support **enqueue** (add to one end) and **dequeue** (remove from the other end, or tail).
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* if implemented with a dynamic array, a more efficient solution is to use a circular queue (ring buffer), *i.e.*, a fixed-size array and two pointers to indicate the starting and ending positions.
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* an advantage of circular queues is that we can use the spaces in front of the queue.
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* in a normal queue, once the queue becomes full, we cannot insert the next element even if there is a space in front of the queue. but using the circular queue, we can use the space to store new values.
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* queues are often used in **breath-first search** (where you store a list of nodes to be processed) or when implementing a cache.
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<br>
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---
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### designing a circular queue
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<br>
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* a circular queue can be built with either arrays or linked lists (nodes).
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<br>
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#### with an array
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<br>
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* to build a ring with a fixed size array, any of the elements could be considered as the head.
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* to enqueue, you loop the queue with the tail index until find a `None` (even if it has to loop back):
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<br>
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```python
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while self.queue[self.tail] is not None:
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self.tail += 1
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if self.tail == self.size:
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self.tail = 0
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self.queue[self.tail] = value
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```
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<br>
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* to dequeue, you simply pop the head value:
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<br>
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```python
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value = self.queue[self.head]
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self.queue[self.head] = None
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self.head += 1
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```
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<br>
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* as long as we know the length of the queue, we can instantly locate its tails based on this formula:
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<br>
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```
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tail_index = (head_index + current_length - 1) % size
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```
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<br>
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* there is one occasion when `tail` index is set to zero:
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* when the enqueue operation adds to the last position in the array and tail has to loop back (`self.tail == self.size`).
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* there are two occasions when `head` index is set to zero:
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* when the queue is checked as empty
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* when the dequeue operation popped the last element in the array and head has to loop back (`self.head == self.size`).
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<br>
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```python
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class CircularQueue:
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def __init__(self, size):
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self.head = 0
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self.tail = 0
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self.size = size
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self.queue = [None] * self.size
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def enqueue(self, value: int) -> bool:
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if self.is_full():
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return False
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if self.is_empty():
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self.head = 0
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while self.queue[self.tail] is not None:
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self.tail += 1
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if self.tail == self.size:
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self.tail = 0
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self.queue[self.tail] = value
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return True
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def dequeue(self) -> bool:
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if self.is_empty():
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return False
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value = self.queue[self.head]
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self.queue[self.head] = None
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self.head += 1
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if self.head == self.size:
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self.head = 0
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return True
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def front(self) -> int:
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return self.queue[self.head] or False
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def rear(self) -> int:
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return self.queue[self.tail] or False
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def is_empty(self) -> bool:
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for n in self.queue:
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if n is not None:
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return False
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return True
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def is_full(self) -> bool:
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for n in self.queue:
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if n is None:
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return False
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return True
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```
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<br>
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* another version used only one index (for `head`) and calculates the tail with the equation:
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<br>
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```python
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(self.head + self.count - 1) % self.size
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````
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<br>
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* and the next tail with:
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<br>
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```python
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(self.head + self.count) % self.size
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```
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<br>
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* and the next `head` is always given by:
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<br>
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```python
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(self.head + 1) % self.size
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```
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<br>
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* * in this example we also implement the methods `is_empty` and `is_full` using an extra counter variable `self.count` that can be compared to `self.size` or `0` and used to validate `rear` and `front`.
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<br>
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```python
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class CircularQueue:
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def __init__(self, size):
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self.head = 0
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self.count = 0
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self.queue = [0] * size
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self.size = size
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def _get_tail(self):
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return (self.head + self.count - 1) % self.size
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def _get_next_tail(self):
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return (self.head + self.count) % self.size
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def _get_next_head(self):
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return (self.head + 1) % self.size
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def enqueue(self, value: int) -> bool:
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if self.is_empty():
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return False
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self.queue[self._get_next_tail()] = value
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self.count += 1
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return True
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def dequeue(self) -> bool:
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if self.is_empty():
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return False
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self.head = self._get_next_head()
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self.count -= 1
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return True
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def Front(self) -> int:
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if self.is_empty():
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return False
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return self.queue[self.head]
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def Rear(self) -> int:
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if self.is_empty():
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return False
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return self.queue[self._get_tail()]
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def isEmpty(self) -> bool:
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return self.count == 0
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def isFull(self) -> bool:
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return self.count == self.size
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```
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<br>
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#### with linked lists
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<br>
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* a linked list could be more memory efficient, since it does not pre-allocate memory for unused capacity (and size of the queue is not "artificial" like before).
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* note that this queue is not thread-safe: the data structure could be corrupted in a multi-threaded environment (as race-condition could occur). to mitigate this problem, one could add the protection of a lock.
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<br>
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```python
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class Node:
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def __init__(self, value, next=None):
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self.value = value
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self.next = next
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class Queue:
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def __init__(self, size):
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self.size = size
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self.count = 0
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self.head = None
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self.tail = None
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def enqueue(self, value: int) -> bool:
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if self.is_full():
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return False
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if self.is_empty():
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self.head = self.tail = Node(value)
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else:
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self.tail.next = Node(value)
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self.tail = self.tail.next
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self.count += 1
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return True
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def dequeue(self) -> bool:
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if self.is_empty():
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return False
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self.head = self.head.next
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self.count -= 1
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return True
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def front(self) -> int:
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if self.is_empty():
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return False
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return self.head.value
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def rear(self) -> int:
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if self.is_empty():
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return False
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return self.tail.value
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def is_empty(self) -> bool:
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return self.count == 0
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def is_full(self) -> bool:
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return self.count == self.size
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```
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<br>
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---
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### a stream with rate limiter
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<br>
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```python
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class Logger:
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def __init__(self):
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self.msg_set = set()
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self.msg_queue = deque()
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def print_message(self, timestamp, message) -> bool:
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while self.msg_queue:
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msg, msg_timestamp = self.msg_queue[0]
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if timestamp - msg_timestamp >= 10:
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self.msg_queue.popleft()
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self.msg_set.remove(msg)
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else:
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break
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if message not in self.msg_set:
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self.msg_set.add(message)
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self.msg_queue.append((message, timestamp))
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return True
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return False
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```
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<br>
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---
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### moving average
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<br>
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* given a stream of integers and a window size, the moving average in the sliding window can be calculated with a queue:
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<br>
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```python
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class MovingAverage:
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def __init__(self, size: int):
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self.queue = []
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self.size = size
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def next(self, val: int) -> float:
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self.queue.append(val)
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if len(self.queue) > self.size:
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self.queue.pop(0)
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return sum(self.queue) / len(self.queue)
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```
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