之前实现的顺序栈和链式栈的进栈和出栈操作时间复杂度都是O(1)。而用同样的方式实现队列，进队和出队的复杂度总有一个是O(n) 。
顺序队列的瓶颈
顺序队列
线性表的第一个元素作为队头
线性表的最后一个元素作为队尾
入队的新元素是在线性表的最后，时间复杂度为O(1)；
出队时需要将后续的所有元素向前移动，时间复杂度为O(n)；
顺序队列的优化方案
定义顺序队列的头：
typedef unsigned int TSeqQueueNode;
typedef struct _tag_SeqQueue
{
int capacity;
int length;
int front;
int rear;
TSeqQueueNode* node;
} TSeqQueue;
顺序队列的创建
SeqQueue* SeqQueue_Create(int capacity) // O(1)
{
TSeqQueue* ret = NULL;
if( capacity >= 0 )
{
ret = (TSeqQueue*)malloc(sizeof(TSeqQueue) + sizeof(TSeqQueueNode) * capacity);
}
if( ret != NULL )
{
ret->capacity = capacity;
ret->length = 0;
ret->front = 0;
ret->rear = 0;
ret->node = (TSeqQueueNode*)(ret + 1);
}
return ret;
}
入队列
int SeqQueue_Append(SeqQueue* queue, void* item) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
int ret = (sQueue != NULL) && (item != NULL);
ret = ret && (sQueue->length + 1 <= sQueue->capacity);
if( ret )
{
sQueue->node[sQueue->rear] = (TSeqQueueNode)item;
sQueue->rear = (sQueue->rear + 1) % sQueue->capacity;
sQueue->length++;
}
return ret;
}
出队列
void* SeqQueue_Retrieve(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
void* ret = SeqQueue_Header(queue);
if( ret != NULL )
{
sQueue->front = (sQueue->front + 1) % sQueue->capacity;
sQueue->length--;
}
return ret;
}
void* SeqQueue_Header(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
void* ret = NULL;
if( (sQueue != NULL) && (sQueue->length > 0) )
{
ret = (void*)(sQueue->node[sQueue->front]);
}
return ret;
}
出队列由原来的O(n)变成的O(1)；
完整版seqQueue.c代码：
#include <stdio.h>
#include <malloc.h>
#include "SeqQueue.h"
typedef unsigned int TSeqQueueNode;
typedef struct _tag_SeqQueue
{
int capacity;
int length;
int front;
int rear;
TSeqQueueNode* node;
} TSeqQueue;
SeqQueue* SeqQueue_Create(int capacity) // O(1)
{
TSeqQueue* ret = NULL;
if( capacity >= 0 )
{
ret = (TSeqQueue*)malloc(sizeof(TSeqQueue) + sizeof(TSeqQueueNode) * capacity);
}
if( ret != NULL )
{
ret->capacity = capacity;
ret->length = 0;
ret->front = 0;
ret->rear = 0;
ret->node = (TSeqQueueNode*)(ret + 1);
}
return ret;
}
void SeqQueue_Destroy(SeqQueue* queue) // O(1)
{
free(queue);
}
void SeqQueue_Clear(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
if( sQueue != NULL )
{
sQueue->length = 0;
sQueue->front = 0;
sQueue->rear = 0;
}
}
int SeqQueue_Append(SeqQueue* queue, void* item) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
int ret = (sQueue != NULL) && (item != NULL);
ret = ret && (sQueue->length + 1 <= sQueue->capacity);
if( ret )
{
sQueue->node[sQueue->rear] = (TSeqQueueNode)item;
sQueue->rear = (sQueue->rear + 1) % sQueue->capacity;
sQueue->length++;
}
return ret;
}
void* SeqQueue_Retrieve(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
void* ret = SeqQueue_Header(queue);
if( ret != NULL )
{
sQueue->front = (sQueue->front + 1) % sQueue->capacity;
sQueue->length--;
}
return ret;
}
void* SeqQueue_Header(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
void* ret = NULL;
if( (sQueue != NULL) && (sQueue->length > 0) )
{
ret = (void*)(sQueue->node[sQueue->front]);
}
return ret;
}
int SeqQueue_Length(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
int ret = -1;
if( sQueue != NULL )
{
ret = sQueue->length;
}
return ret;
}
int SeqQueue_Capacity(SeqQueue* queue) // O(1)
{
TSeqQueue* sQueue = (TSeqQueue*)queue;
int ret = -1;
if( sQueue != NULL )
{
ret = sQueue->capacity;
}
return ret;
}
SeqQueue.c
main.c
#include <stdio.h>
#include <stdlib.h>
#include "SeqQueue.h"
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
int main(int argc, char *argv[])
{
SeqQueue* queue = SeqQueue_Create(6);
int a[10] = {0};
int i = 0;
for(i=0; i<10; i++)
{
a[i] = i + 1;
SeqQueue_Append(queue, a + i);
}
printf("Header: %d\n", *(int*)SeqQueue_Header(queue));
printf("Length: %d\n", SeqQueue_Length(queue));
printf("Capacity: %d\n", SeqQueue_Capacity(queue));
while( SeqQueue_Length(queue) > 0 )
{
printf("Retrieve: %d\n", *(int*)SeqQueue_Retrieve(queue));
}
printf("\n");
for(i=0; i<10; i++)
{
a[i] = i + 1;
SeqQueue_Append(queue, a + i);
printf("Retrieve: %d\n", *(int*)SeqQueue_Retrieve(queue));
}
SeqQueue_Destroy(queue);
return 0;
}
运行结果为：
同样的，我们来实现链式队列；
链式队列的头：
typedef struct _tag_LinkQueue
{
TLinkQueueNode* front;
TLinkQueueNode* rear;
int length;
} TLinkQueue;
节点：
struct _tag_LinkQueueNode
{
TLinkQueueNode* next;
void* item;
};
创建：
LinkQueue* LinkQueue_Create() // O(1)
{
TLinkQueue* ret = (TLinkQueue*)malloc(sizeof(TLinkQueue));
if( ret != NULL )
{
ret->front = NULL;
ret->rear = NULL;
ret->length = 0;
}
return ret;
}
入队列：
int LinkQueue_Append(LinkQueue* queue, void* item) // O(1)
{
TLinkQueue* sQueue = (TLinkQueue*)queue;
TLinkQueueNode* node = (TLinkQueueNode*)malloc(sizeof(TLinkQueueNode));
int ret = (sQueue != NULL ) && (item != NULL) && (node != NULL);
if( ret )
{
node->item = item;
if( sQueue->length > 0 )
{
sQueue->rear->next = node;
sQueue->rear = node;
node->next = NULL;
}
else
{
sQueue->front = node;
sQueue->rear = node;
node->next = NULL;
}
sQueue->length++;
}
if( !ret )
{
free(node);
}
return ret;
}
出队列：
void* LinkQueue_Retrieve(LinkQueue* queue) // O(1)
{
TLinkQueue* sQueue = (TLinkQueue*)queue;
TLinkQueueNode* node = NULL;
void* ret = NULL;
if( (sQueue != NULL) && (sQueue->length > 0) )
{
node = sQueue->front;
sQueue->front = node->next;
ret = node->item;
free(node);
sQueue->length--;
if( sQueue->length == 0 )
{
sQueue->front = NULL;
sQueue->rear = NULL;
}
}
return ret;
}
main.c
#include <stdio.h>
#include <stdlib.h>
#include "LinkQueue.h"
/* run this program using the console pauser or add your own getch, system("pause") or input loop */
int main(int argc, char *argv[])
{
LinkQueue* queue = LinkQueue_Create();
int a[10] = {0};
int i = 0;
for(i=0; i<10; i++)
{
a[i] = i + 1;
LinkQueue_Append(queue, a + i);
}
printf("Header: %d\n", *(int*)LinkQueue_Header(queue));
printf("Length: %d\n", LinkQueue_Length(queue));
// LinkQueue_Clear(queue);
while( LinkQueue_Length(queue) > 0 )
{
printf("Retrieve: %d\n", *(int*)LinkQueue_Retrieve(queue));
}
LinkQueue_Destroy(queue);
return 0;
}
运行结果：
优化后的队列，增加了front，rear后，入队和出队都是O(1)；
原文地址：https://www.cnblogs.com/Liu-Jing/p/9574572.html
时间： 2024-11-01 17:39:45