数据结构和算法(1) ---- Queue 的原理和实现

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`Queue` 的定义和结构

队列(Queue) 是只允许在一端进行插入，在另一端进行删除的线性表
队列是一种先进先出(First In First Out)的线性表，简称 FIFO(First IN First OUT), 允许插入的一端称为队尾, 允许删除的一端称为队列头

队列的基本结构如下图所示：
queue struct

`Queue` 的抽象数据类型

队列也有线性表的各种操作,不同的是插入元素只能在队列尾,删除元素只能在对列头进行:
队列的抽象结构如下所示：

ADT Queue(队列)
Data:同线性表, 元素具有相同的类型，相邻的元素具有前驱和后继关系
Operation:InitQueue(Q*)DestroyQueue(Q*)isEmpty(Q*)isFull(Q*)dequeue(Q*, *e)enqueue(Q*, e)queueSize(Q)
endADT

队列有多种实现方式,比如静态数组,动态数组,单链表,双链表等

静态数组实现`Queue`

静态数组实现队列的基本原理：

建立一个 MAX_SIZE 的数组, 用于存放 Queue 中的元素
建立int类型 queue->rear 代表队列尾, 每次 enqueue 一个元素时，queu->rear 指向最新的元素位置
建立 queue->front 代表队列头, 每次 dequeue 一个元素，从 queue->front 位置处取出数据，并且最后其指向下一个元素位置
当 queue->rear 和 queue->front 相等时,queue->front和queue->rear都重新设置为 0,此时队列为空,表示重新开始存储数据

参考代码如下:

#define MAX_SIZE 100
typedef struct {int data[MAX_SIZE];int front;// queue 尾端的索引int rear;
}Queue;void Queueinit(Queue* queue) {queue->front = -1;queue->rear = -1;
}int isEmpty(Queue* queue) {return (queue->front == -1 && queue->rear == -1);
};int isFull(Queue* queue) {// queue->rear == MAX_SIZE - 1  queue->front = 0//return (queue->rear + 1)%MAX_SIZE == queue->front;if((queue->rear + 1 - queue->front) == MAX_SIZE) {return 1;}return 0;
};void enqueue(Queue* queue,int item) {if(isFull(queue)) {fprintf(stderr,"queue is full. \n");return;}//printf("queue front is %d rear is %d \n",queue->front,queue->rear);if(isEmpty(queue)) {queue->rear = 0;queue->front = 0;} else {queue->rear = (queue->rear+1)%MAX_SIZE;}queue->data[queue->rear] = item;
}int dequeue(Queue* queue) {if(isEmpty(queue)) {fprintf(stderr,"queue is empty. \n");return -1;}int item = queue->data[queue->front];// with no elementif(queue->front == queue->rear) {printf("queue has no element backup to empty\n");queue->front = -1;queue->rear = -1;} else {queue->front = (queue->front +1)%MAX_SIZE;}return item;
}int peek(Queue* queue) {if(isEmpty(queue)) {fprintf(stderr,"queue is empty. \n");return -1;}return queue->data[queue->front];
}int testbasicQueueStaticArray(int agrc, char *argv[]) {{Queue testqueue = {.front = -1,.rear = -1,};Queueinit(&testqueue);for(int i = 0; i < 2000; i++) {enqueue(&testqueue,200+i);dequeue(&testqueue);}enqueue(&testqueue,1001);enqueue(&testqueue,1002);enqueue(&testqueue,1003);printf("dequeue item:%d \n", dequeue(&testqueue));printf("dequeue item:%d \n", dequeue(&testqueue));printf("dequeue item:%d \n", dequeue(&testqueue));printf("dequeue item:%d \n", dequeue(&testqueue));printf("peek queue element: %d queue size:%d\n", peek(&testqueue),QueueSize(&testqueue));}}

单链表实现`Queue`

单链表实现Queue的基本原理：

建立一个单链表，包含指向队列头的指针queue->front 和指向队列尾的指针queue->rear
当enqueue时,首先为新元素分配空间，然后插入到单链表的尾部，用queue->rear指向它
当dequeue时,首先返回queue->front指向的节点内容，然后free掉queue->front节点,queue->front指向顺序的后一个节点

参考代码如下:

struct node {int data;struct node *next;
};typedef struct {struct node *front;struct node *rear;
}Queue;static int empty(Queue* queue){return (queue->front == NULL);
}static void initQueue(Queue* queue) {queue->front = queue->rear = NULL;
}static void push(Queue* queue, int value) {struct node *pnode;pnode = (struct node*)malloc(sizeof(struct node));if(pnode == NULL) {printf("malloc node failed!.\n");exit(1);}pnode->data = value;pnode->next = NULL;if(empty(queue)) {queue->front = pnode;queue->rear = pnode;} else {queue->rear->next= pnode;queue->rear = pnode;}
}static int pop(Queue* queue) {if (empty(queue)){printf("Queue Underflow. Unable to remove.\n");exit(1);}int item;struct node *p = queue->front;item = queue->front->data;queue->front = queue->front->next;if (queue->front == NULL) /* Queue contained only one node */queue->rear = NULL;free(p);return item;
}static int peek(Queue* queue) {if (empty(queue)){printf("Queue Underflow. Unable to remove.\n");exit(1);}return queue->front->data;
}static int queueSize(Queue* queue){struct node *p = queue->front;int count = 0;if(empty(queue)){return 0;}do {p = p->next;count++;}while(p != NULL);return count;
}int testbasicQueueImplsingleLinkedList(int agrc, char *argv[]) {{Queue testqueue;int qsize = 0;initQueue(&testqueue);push(&testqueue, 10);printf("queue size: %d. \n", queueSize(&testqueue));push(&testqueue, 101);push(&testqueue, 102);push(&testqueue, 103);push(&testqueue, 104);printf("queue size: %d. \n", queueSize(&testqueue));printf("pop value: %d queue size: %d. \n", pop(&testqueue), qsize);qsize = queueSize(&testqueue);printf("pop value: %d queue size: %d. \n", pop(&testqueue), qsize);qsize = queueSize(&testqueue);printf("pop value: %d queue size: %d. \n", pop(&testqueue), qsize);qsize = queueSize(&testqueue);printf("pop value: %d queue size: %d. \n", pop(&testqueue), qsize);printf("queue size: %d. \n", queueSize(&testqueue));printf("peek value: %d  \n", peek(&testqueue));printf("queue size: %d. \n", queueSize(&testqueue));}return 1;
}