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Learn Data Structures and Algorithms in C#

Double-Ended Queues

Explore how double-ended queues (deques) allow insertion and deletion from both ends, making them versatile data structures in C#. Learn their implementation with LinkedList, core operations, and their role in solving problems like sliding window maximum and undo/redo functionality.

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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. ...