How are deques in Python implemented, and when are

Question

I've recently gotten into investigating how various data structures are implemented in Python in order to make my code more efficient. In investigating how lists and deques work, I found that I can get benefits when I want to shift and unshift reducing the time from O(n) in lists to O(1) in deques (lists being implemented as fixed-length arrays that have to be copied completely each time something is inserted at the front, etc...). What I can't seem to find are the specifics of how a deque is implemented, and the specifics of its downsides v.s. lists. Can someone enlighten me on these two questions?

Answer 1

While, I am not exactly sure how Python has implemented it, here I wrote an implementation of Queues using only arrays. It has the same complexity as Python's Queues.

class ArrayQueue:
""" Implements a queue data structure """

def __init__(self, capacity):
    """ Initialize the queue """

    self.data = [None] * capacity
    self.size = 0
    self.front = 0

def __len__(self):
    """ return the length of the queue """

    return self.size

def isEmpty(self):
    """ return True if the queue is Empty """

    return self.data == 0

def printQueue(self):
    """ Prints the queue """

    print self.data 

def first(self):
    """ Return the first element of the queue """

    if self.isEmpty():
        raise Empty("Queue is empty")
    else:
        return self.data[0]

def enqueue(self, e):
    """ Enqueues the element e in the queue """

    if self.size == len(self.data):
        self.resize(2 * len(self.data))
    avail = (self.front + self.size) % len(self.data) 
    self.data[avail] = e
    self.size += 1

def resize(self, num):
    """ Resize the queue """

    old = self.data
    self.data = [None] * num
    walk = self.front
    for k in range(self.size):
        self.data[k] = old[walk]
        walk = (1+walk)%len(old)
    self.front = 0

def dequeue(self):
    """ Removes and returns an element from the queue """

    if self.isEmpty():
        raise Empty("Queue is empty")
    answer = self.data[self.front]
    self.data[self.front] = None 
    self.front = (self.front + 1) % len(self.data)
    self.size -= 1
    return answer

class Empty(Exception):
""" Implements a new exception to be used when stacks are empty """

pass

And here you can test it with some code:

def main():
""" Tests the queue """ 

Q = ArrayQueue(5)
for i in range(10):
    Q.enqueue(i)
Q.printQueue()    
for i in range(10):
    Q.dequeue()
Q.printQueue()    


if __name__ == '__main__':
    main()

It won't work as fast as the C implementation, but it uses the same logic.

Answer 2

In addition to all the other helpful answers, here is some more information comparing the time complexity (Big-Oh) of various operations on Python lists, deques, sets, and dictionaries. This should help in selecting the right data structure for a particular problem.

Answer 3

Check out collections.deque. From the docs:

Deques support thread-safe, memory efficient appends and pops from either side of the deque with approximately the same O(1) performance in either direction.

Though list objects support similar operations, they are optimized for fast fixed-length operations and incur O(n) memory movement costs for pop(0) and insert(0, v) operations which change both the size and position of the underlying data representation.

Just as it says, using pop(0) or insert(0, v) incur large penalties with list objects. You can't use slice/index operations on a deque, but you can use popleft/appendleft, which are operations deque is optimized for. Here is a simple benchmark to demonstrate this:

import time
from collections import deque

num = 100000

def append(c):
    for i in range(num):
        c.append(i)

def appendleft(c):
    if isinstance(c, deque):
        for i in range(num):
            c.appendleft(i)
    else:
        for i in range(num):
            c.insert(0, i)
def pop(c):
    for i in range(num):
        c.pop()

def popleft(c):
    if isinstance(c, deque):
        for i in range(num):
            c.popleft()
    else:
        for i in range(num):
            c.pop(0)

for container in [deque, list]:
    for operation in [append, appendleft, pop, popleft]:
        c = container(range(num))
        start = time.time()
        operation(c)
        elapsed = time.time() - start
        print "Completed %s/%s in %.2f seconds: %.1f ops/sec" % (container.__name__, operation.__name__, elapsed, num / elapsed)

Results on my machine:

Completed deque/append in 0.02 seconds: 5582877.2 ops/sec
Completed deque/appendleft in 0.02 seconds: 6406549.7 ops/sec
Completed deque/pop in 0.01 seconds: 7146417.7 ops/sec
Completed deque/popleft in 0.01 seconds: 7271174.0 ops/sec
Completed list/append in 0.01 seconds: 6761407.6 ops/sec
Completed list/appendleft in 16.55 seconds: 6042.7 ops/sec
Completed list/pop in 0.02 seconds: 4394057.9 ops/sec
Completed list/popleft in 3.23 seconds: 30983.3 ops/sec

Answer 4

https://hg.python.org/cpython/file/3.5/Modules/_collectionsmodule.c

A dequeobject is composed of a doubly-linked list of block nodes.

So yes, a deque is a (doubly-)linked list as another answer suggests.

Elaborating: What this means is that Python lists are much better for random-access and fixed-length operations, including slicing, while deques are much more useful for pushing and popping things off the ends, with indexing (but not slicing, interestingly) being possible but slower than with lists.

Answer 5

The documentation entry for deque objects spells out most of what you need to know, I suspect. Notable quotes:

Deques support thread-safe, memory efficient appends and pops from either side of the deque with approximately the same O(1) performance in either direction.

But...

Indexed access is O(1) at both ends but slows to O(n) in the middle. For fast random access, use lists instead.

I'd have to take a look at the source to tell whether the implementation is a linked list or something else, but it sounds to me as though a deque has roughly the same characteristics as a doubly-linked list.