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Double-Ended Queues

Explore how double-ended queues (deques) work, enabling insertion and deletion at both the front and rear. Understand their implementation in Python using collections.deque, their O(1) time operations, different types of deques, and why they are valuable in solving problems like sliding window maximum and BFS optimization.

A deque stands for a double-ended queue. It is a more flexible version of a queue that allows insertion and deletion from both the front and the rear.

In a normal queue, insertion happens only at the rear and deletion happens only at the front. In a deque, both ends are fully active.

Visualization of a deque
Visualization of a deque

This makes the deque a generalization that can behave like a queue, a stack, or something in between, depending on how it is used.

A deque is useful when a problem needs controlled access to both ends of the structure. It appears in sliding window problems, palindrome checking, scheduling, and caching systems.

Example

To understand how a deque works, consider the following example. If a deque currently contains:

A deque with 3 elements
A deque with 3 elements

After inserting 88 at the front, the deque becomes:

Inserting an element at the front of a deque
Inserting an element at the front of a deque

After inserting 91 at the rear, the deque becomes:

Inserting an element at the rear of a deque
Inserting an element at the rear of a deque

After removing 88 from the front, the deque becomes:

Removing an element from the front of a deque
Removing an element from the front of a deque

After removing 91 from the rear, the deque becomes:

Removing an element from the rear of a deque
Removing an element from the rear of a deque

This two-sided behavior is what makes the deque more versatile than a regular queue. ...