A <u>queue</u> is a linear data structure that follows the First-In-First-Out (FIFO) rule. As the name suggests, a queue simulates the phenomenon of lining up, where newcomers join the queue at the rear, and the person at the front leaves the queue first.
As shown in the figure below, we call the front of the queue the "head" and the back the "tail." The operation of adding elements to the rear of the queue is termed "enqueue," and the operation of removing elements from the front is termed "dequeue."
The common operations on a queue are shown in the table below. Note that method names may vary across different programming languages. Here, we use the same naming convention as that used for stacks.
To implement a queue, we need a data structure that allows adding elements at one end and removing them at the other. Both linked lists and arrays meet this requirement.
As shown in the figure below, we can consider the "head node" and "tail node" of a linked list as the "front" and "rear" of the queue, respectively. It is stipulated that nodes can only be added at the rear and removed at the front.
Deleting the first element in an array has a time complexity of $O(n)$, which would make the dequeue operation inefficient. However, this problem can be cleverly avoided as follows.
We use a variable `front` to indicate the index of the front element and maintain a variable `size` to record the queue's length. Define `rear = front + size`, which points to the position immediately following the tail element.
With this design, **the effective interval of elements in the array is `[front, rear - 1]`**. The implementation methods for various operations are shown in the figure below.
- Enqueue operation: Assign the input element to the `rear` index and increase `size` by 1.
- Dequeue operation: Simply increase `front` by 1 and decrease `size` by 1.
Both enqueue and dequeue operations only require a single operation, each with a time complexity of $O(1)$.
You might notice a problem: as enqueue and dequeue operations are continuously performed, both `front` and `rear` move to the right and **will eventually reach the end of the array and can't move further**. To resolve this, we can treat the array as a "circular array" where connecting the end of the array back to its beginning.
In a circular array, `front` or `rear` needs to loop back to the start of the array upon reaching the end. This cyclical pattern can be achieved with a "modulo operation" as shown in the code below:
The above implementation of the queue still has its limitations: its length is fixed. However, this issue is not difficult to resolve. We can replace the array with a dynamic array that can expand itself if needed. Interested readers can try to implement this themselves.
- **Amazon orders**: After shoppers place orders, these orders join a queue, and the system processes them in order. During events like Singles' Day, a massive number of orders are generated in a short time, making high concurrency a key challenge for engineers.
- **Various to-do lists**: Any scenario requiring a "first-come, first-served" functionality, such as a printer's task queue or a restaurant's food delivery queue, can effectively maintain the order of processing with a queue.
