数据结构 — 循环链表

单链表的局限

单链表可以用于表示任意的线性关系，但有些线性关系是循环的，即没有队尾元素的

循环链表的定义

将单链表中最后一个数据元素的next指针指向第一个元素

循环链表的操作

  • 创建链表
  • 销毁链表
  • 获取链表长度
  • 清空链表
  • 获取第pos个元素操作
  • 插入元素到位置pos
  • 删除位置pos处的元素

游标的定义

在循环链表中可以定义一个“当前”指针，这个指针通常称为游标，可以通过这个游标来遍历链表中的所有元素。

循环链表的新操作

  • 获取当前游标指向的数据元素
  • 将游标重置指向链表中的第一个数据元素
  • 将游标移动指向到链表中的下一个数据元素
  • 直接指定删除链表中的某个数据元素
CircleListNode* CircleList_DeleteNode(CircleList* list,CircleListNode* node);
CircleListNode* CircleList_Reset(CircleList* list);
CircleListNode* CircleList_Current(CircleList* list);
CircleListNode* CircleList_Next(CircleList* list);

完整代码

CircleList.h

#ifndef _CIRCLELIST_H_
#define _CIRCLELIST_H_

typedef void CircleList;
typedef struct _tag_CircleListNode CircleListNode;
struct _tag_CircleListNode
{
    CircleListNode* next;
};

CircleList* CircleList_Create();
void CircleList_Destroy(CircleList* list);
void CircleList_Clear(CircleList* list);
int CircleList_Length(CircleList* list);
int CircleList_Insert(CircleList* list, CircleListNode* node, int pos);
CircleListNode* CircleList_Get(CircleList* list, int pos);
CircleListNode* CircleList_Delete(CircleList* list, int pos);
CircleListNode* CircleList_DeleteNode(CircleList* list,CircleListNode* node);
CircleListNode* CircleList_Reset(CircleList* list);
CircleListNode* CircleList_Current(CircleList* list);
CircleListNode* CircleList_Next(CircleList* list);

#endif

CircleList.c

#include <stdio.h>
#include <malloc.h>
#include "CircleList.h"

typedef struct _tag_CircleList
{
    CircleListNode header;
    CircleListNode* slider;
    int length;
} TCircleList;

CircleList* CircleList_Create()
{
    TCircleList* ret = (TCircleList*)malloc(sizeof(TCircleList));
    
    if( ret != NULL )
    {
        ret->length = 0;
        ret->header.next = NULL;
        ret->slider = NULL;
    }
    
    return ret;
}

void CircleList_Destroy(CircleList* list)
{
    free(list);
}

void CircleList_Clear(CircleList* list)
{
    TCircleList* sList = (TCircleList*)list;
    
    if( sList != NULL )
    {
        sList->length = 0;
        sList->header.next = NULL;
        sList->slider = NULL;
    }
}

int CircleList_Length(CircleList* list)
{
    TCircleList* sList = (TCircleList*)list;
    int ret = -1;
    
    if( sList != NULL )
    {
        ret = sList->length;
    }
    
    return ret;
}

int CircleList_Insert(CircleList* list, CircleListNode* node, int pos)
{ 
    TCircleList* sList = (TCircleList*)list;
    int ret = (sList != NULL) && (pos >= 0) && (node != NULL);
    int i = 0;
    
    if( ret )
    {
        CircleListNode* current = (CircleListNode*)sList;
        
        for(i=0; (i<pos) && (current->next != NULL); i++)
        {
            current = current->next;
        }
        
        node->next = current->next;
        current->next = node;
        
        if(sList->length == 0)
        {
            sList->slider = node;
            node->next = node;
        } 
        
        sList->length++;
    }
    
    return ret;
}

CircleListNode* CircleList_Get(CircleList* list, int pos)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;
    int i = 0;
    
    if( (sList != NULL) && (0 <= pos) )
    {
        CircleListNode* current = (CircleListNode*)sList;
        
        for(i=0; i<pos; i++)
        {
            current = current->next;
        }
        
        ret = current->next;
    }
    
    return ret;
}

CircleListNode* CircleList_Delete(CircleList* list, int pos)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;
    int i = 0;
    
    if( (sList != NULL) && (0 <= pos) )
    {
        CircleListNode* current = (CircleListNode*)sList;
        CircleListNode* first = sList->header.next;
        CircleListNode* last = (CircleListNode*)CircleList_Get(sList, sList->length-1); 
        for(i=0; i<pos; i++)
        {
            current = current->next;
        }
        
        ret = current->next;
        current->next = ret->next;
        
        sList->length--;
        if(first == ret)
        {
            sList->header.next = ret->next;
            last->next = ret->next; 
        }
        if(sList->slider == ret)
        {
            sList->slider = ret->next; 
        }
        if(sList->length == 0)
        {
            sList->header.next = NULL; 
            sList->slider = NULL;
        }
    }
    
    return ret;
}

CircleListNode* CircleList_DeleteNode(CircleList* list,CircleListNode* node)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;
    int i = 0;
    
    if(sList != NULL)
    {
        CircleListNode* current = (CircleListNode*)sList;
        for(i=0; i<sList->length; i++)
        {
            if(current->next == node)
            {
                ret = current->next;
                break;
            }
            current = current->next;
        }
        if(ret != NULL)
        {
            CircleList_Delete(sList, i);
        }
    }
    
    return ret;
}

CircleListNode* CircleList_Reset(CircleList* list)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;

    if(sList != NULL)
    {
        sList->slider = sList->header.next;
        ret = sList->slider; 
    }
    
    return ret;
}

CircleListNode* CircleList_Current(CircleList* list)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;

    if(sList != NULL)
    {
        ret = sList->slider; 
    }
    
    return ret;
}

CircleListNode* CircleList_Next(CircleList* list)
{
    TCircleList* sList = (TCircleList*)list;
    CircleListNode* ret = NULL;

    if((sList != NULL)&&(sList->slider != NULL))
    {
        ret = sList->slider;
        sList->slider = ret->next;
    }
    
    return ret;
}

main.c

#include <stdio.h>
#include <stdlib.h>
#include "CircleList.h"
struct Value
{
    CircleListNode header;
    int v;
};
int main(int argc, char *argv[])
{
    int i = 0;
    
    CircleList* list = CircleList_Create();
    
    struct Value v1;
    struct Value v2;
    struct Value v3;
    struct Value v4;
    struct Value v5;
    struct Value v6;
    struct Value v7;
    struct Value v8;
    
    v1.v = 1;
    v2.v = 2;
    v3.v = 3;
    v4.v = 4;
    v5.v = 5;
    v6.v = 6;
    v7.v = 7;
    v8.v = 8;
    
    CircleList_Insert(list, (CircleListNode*)&v1, CircleList_Length(list));
    CircleList_Insert(list, (CircleListNode*)&v2, CircleList_Length(list));
    CircleList_Insert(list, (CircleListNode*)&v3, CircleList_Length(list));
    CircleList_Insert(list, (CircleListNode*)&v4, CircleList_Length(list));
    
    CircleList_Insert(list, (CircleListNode*)&v5, CircleList_Length(list)+1);
    CircleList_Delete(list, 0);
    
    for(i=0; i<2*CircleList_Length(list); i++)
    {
        struct Value* pv = (struct Value*)CircleList_Get(list, i);
        printf("%d\n", pv->v);
    }
    
    printf("\n");
    
    while(CircleList_Length(list) > 0)
    {
        struct Value* pv = (struct Value*)CircleList_Delete(list, 0);
        printf("%d\n", pv->v);
    }
    
    CircleList_Destroy(list);
    return 0;
}

约瑟夫问题

n个人围成一个圆圈，首先第1个人从1开始一个人一个人顺时针报数，报到第m个人，令其出列。然后再从下一个人开始从1顺时针报数，报到第m个人，再令其出列，...，如此下去，求出列顺序。

应用代码

main.c

#include <stdio.h>
#include <stdlib.h>
#include "CircleList.h"
typedef struct _tag_Value
{
    CircleListNode header;
    int v;
}Value;
int main(int argc, char *argv[])
{
    int i = 0;
    int n = 0;
    int m = 0;
    
    printf("Please enter: n,m\n");
    scanf("%d,%d",&n,&m);
    
    Value* v = (Value*)malloc(sizeof(Value)*n);
    CircleList* list = CircleList_Create();
    
    for(i=0;i<n;i++)
    {
        v[i].v=i+1;
        CircleList_Insert(list, (CircleListNode*)&v[i], CircleList_Length(list));
    }
    
    for(i=0; i<CircleList_Length(list); i++)
    {
        Value* pv = (Value*)CircleList_Next(list);
        printf("%d\n", pv->v);
    }
    
    printf("\n");
    
    CircleList_Reset(list);
    
    while(CircleList_Length(list)>0)
    {
        Value* pv = NULL;
        for(i=1;i<m;i++)
        {
            CircleList_Next(list);
        }
        pv = (Value*)CircleList_Current(list);
        
        printf("%d\n", pv->v);
        
        CircleList_DeleteNode(list, (CircleListNode*)pv);   
    }
    
    CircleList_Destroy(list);
    return 0;
}

小结

  • 循环链表只是在单链表的基础上做了一个加强
  • 循环链表完全可以取代单链表的使用
  • 循环链表的Next和Current操作可以高效的遍历链表中的所有元素
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