definition
Queue: A linear list that only allows insertion at one end and deletion at the other .
A queue is a first-in, first- out linear list. The end that allows insertion is called the tail of the queue, and the end that allows deletion is called the head of the queue.
As shown below:
circular queue
The linear table has sequential storage and chain storage, and the stack is a linear table, so there are two storage methods. Similarly, the queue, as a special linear table, also exists in these two storage methods.
Insufficient queue order storage
Assuming that there is a queue with n elements, an array larger than n needs to be established for the sequential storage queue, and all elements of the queue are stored in the first n elements of the array, and the end of the array subscript 0 is the head of the queue. The so-called queue operation is actually adding an element to the end of the queue without moving any elements, so the complexity of the family is O(1).
Unlike the stack, the queue elements are dequeued at the head of the queue, that is, the position with the subscript 0, which means that all elements in the queue have to move forward, that is, the position with the subscript 0 is not Empty, the time complexity is O(n).
Their specific implementation is the same as the sequential storage structure of the linear table, and is no longer cumbersome.
but
If you do not limit the condition that the elements of the queue must be stored in the first n elements of the array, the performance of dequeuing will be greatly increased, as shown in the figure
In order to avoid that when there is only one element, the overlapping of the queue head and the queue tail makes processing troublesome, two pointers are introduced, front points to the head element of the queue, and rear points to the next position of the rear element, so that when front is equal to rear, it means empty. queue.
In this way, another problem arises. If there is an element at the end of the queue, where does rear point to when a new element is inserted? Moreover, when there is only an element at the end of the queue, adding it backwards will cause an array out-of-bounds error, but in fact the previous position may be empty. We call this phenomenon false overflow .
Circular queue definition
The way to solve the false overflow is to start from the beginning when the back is full, that is, a loop that is connected end to end. We call this head-to- tail sequential storage structure of the queue a circular queue.
Subscripts 2, 3, and 4 already have elements, and when a new element is inserted, the position with subscript 0 is stored. As shown in the figure:
But it was previously agreed that when front==rear, it means that the queue is empty. In the above method, when front==rear also means that the queue is full, how to deal with it?
We require that when the queue is full, there is still a free unit in the array, as shown in the figure:
This results in the following formula:
Queue full condition (rear+1) %QueueSize==front
Queue length formula: (rear-front+QueueSize)%QueueSize
Chained storage of queues
The chained storage structure of the queue is actually a singly linked list of a linear table, but it can only go in and out of the head. We call it a chain queue for short.
When the queue is empty, both front and rear point to the head node:
Enqueue operation
- Follow the last element to point to the new element;
- Point the tail pointer to the new element.
Dequeue operation
- Change the successor of the head node to the next node;
- If there is only one element left in addition to the head node, point rear to the head node.
In general, when you can determine the maximum queue length, it is recommended to use a circular queue, and if you cannot estimate the length of the queue, use a chain queue.
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