数据结构之线性表——链表的顺序存储（数组描述）

1 线性表定义

线性表(list)是零个或多个数据元素的集合，线性表中的数据元素之间是有顺序的，线性表中的数据元素个数是有限的，线性表中数据元素的类型必须相同。

2 线性表数学定义

线性表（linear list）也称为有序表（order list）。每一个实例都是元素的一个有序集合。每一个实例的形式为（e1,e2,e3,...,en-1），其中n为又穷自然数，ei是线性表的元素，i是元素ei的索引，n是线性表的大小。元素可以被看做原子，它们本身的结构与线性表的结构无关。当n = 0时，线性表为空；当n>0时，e0是线性表的第0个元素，en-1是线性表的最后一个元素。

3 线性表的性质

e0为线性表的第一个元素，只有一个后继， en为线性表的最后一个元素，只有一个前驱。除e0和en外的其它元素ei，既有前驱，又有后继线性表能够逐项访问和顺序存取。

4线性表顺序存储的设计与实现

（1）顺序表节点的定义

//用数组来模拟线性表typedef struct _tag_SeqList{intcapacity;intlength;int**node; }TSeqList;

（2）顺序表的创建（返回链表）

//链表 创建SeqList* SeqList_Create(int capacity) //O(1){intret;TSeqList*tmp = NULL;tmp = (TSeqList *)malloc(sizeof(TSeqList));if (tmp == NULL){ret = 1;printf("func SeqList_Create() err :%d \n", ret);return NULL;}memset(tmp, 0, sizeof(TSeqList));tmp->capacity = capacity;tmp->length = 0;tmp->node = (int **)malloc(sizeof(void *) * capacity);if (tmp->node == NULL){ret = 2;printf("func SeqList_Create() malloc err :%d \n", ret);return NULL;}memset(tmp->node, 0, sizeof(void *) * capacity);return tmp;}

（3）顺序表的创建（传入句柄）

//链表 创建int SeqList_Create2(int capacity, SeqList**handle){intret = 0;TSeqList*tmp = NULL;tmp = (TSeqList *)malloc(sizeof(TSeqList));if (tmp == NULL){ret = 1;printf("func SeqList_Create2() err :%d \n", ret);return ret;}memset(tmp, 0, sizeof(TSeqList));tmp->capacity = capacity;tmp->length = 0;tmp->node = (int **)malloc(sizeof(void *) * capacity);if (tmp->node == NULL){ret = 2;printf("func SeqList_Create2() malloc err :%d \n", ret);return ret;}*handle = tmp;return ret;}

（4）顺序表的销毁

//链表 销毁void SeqList_Destroy(SeqList* list)  //O(1){TSeqList*tmp = NULL;if (list == NULL){return;}tmp = (TSeqList *)list;if (tmp->node != NULL){free(tmp->node);}free(tmp);return;}

（5）顺序表清空

////链表 清空void SeqList_Clear(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return;}tmp = (TSeqList *)list;tmp->length = 0;memset(tmp->node, 0, (tmp->capacity * sizeof(void *)));return;}

（6）顺序表的长度

//链表 长度int SeqList_Length(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return -1;}tmp = (TSeqList *)list;return tmp->length;}

（7）顺序表的容量

//链表 容量 int SeqList_Capacity(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return -1;}tmp = (TSeqList *)list;return tmp->capacity;}

（8）顺序表在某一个位置插入元素

//链表 在某一个位置 插入元素int SeqList_Insert(SeqList* list, SeqListNode* node, int pos)  //O(n){TSeqList*tList = NULL;int i = 0;if (list == NULL || node == NULL){return -1;}tList = (TSeqList *)list;//如果满了 if (tList->length >= tList->capacity){return -2;}//pos位置的容错处理if (pos > tList->length){pos = tList->length;}for (i = tList->length; i>pos; i--)  //n{tList->node[i] = tList->node[i - 1];}tList->node[i] = (int*)node; //oktList->length++;return 0;}

（9）顺序表获取某一个位置的节点

//获取某一个位置的链表结点SeqListNode* SeqList_Get(SeqList* list, int pos)  //O(1){TSeqList*tList = NULL;SeqListNode *tmp = NULL;tList = (TSeqList *)list;if (list == NULL || pos<0 || pos >= tList->length){return NULL;}tmp = tList->node[pos];return tmp;}

（10）顺序表删除某一个位置的节点

//删除某一个位置的结点SeqListNode* SeqList_Delete(SeqList* list, int pos)  ////O(n){inti = 0;TSeqList*tList = NULL;SeqListNode *tmp = NULL;tList = (TSeqList *)list;if (list == NULL || pos <0 || pos >= tList->length){return NULL;}tmp = tList->node[pos];// pos = 3for (i = pos + 1; i<tList->length; i++){tList->node[i - 1] = tList->node[i];}tList->length--;return tmp;}

5 代码实现以及测试案例

//SeqList.h#ifndef  __MY_SEQLIST_H__ #define __MY_SEQLIST_H__typedef void SeqList;typedef void SeqListNode;//链表 创建SeqList* SeqList_Create(int capacity);//链表 销毁void SeqList_Destroy(SeqList* list);////链表 清空void SeqList_Clear(SeqList* list);//链表 长度int SeqList_Length(SeqList* list);//链表 容量 int SeqList_Capacity(SeqList* list);//链表 在某一个位置 插入元素int SeqList_Insert(SeqList* list, SeqListNode* node, int pos);

//获取某一个位置元素

SeqListNode* SeqList_Get(SeqList* list, int pos);//删除某一个位置的结点SeqListNode* SeqList_Delete(SeqList* list, int pos);#endif  //__MY_SEQLIST_H__

//SeqList.cpp#define  _CRT_SECURE_NO_WARNINGS #include "seqlist.h"#include <stdlib.h>#include <string.h>#include <stdio.h>//用数组来模拟线性表typedef struct _tag_SeqList{intcapacity;intlength;int**node; }TSeqList;//链表 创建SeqList* SeqList_Create(int capacity) //O(1){intret;TSeqList*tmp = NULL;tmp = (TSeqList *)malloc(sizeof(TSeqList));if (tmp == NULL){ret = 1;printf("func SeqList_Create() err :%d \n", ret);return NULL;}memset(tmp, 0, sizeof(TSeqList));tmp->capacity = capacity;tmp->length = 0;tmp->node = (int **)malloc(sizeof(void *) * capacity);if (tmp->node == NULL){ret = 2;printf("func SeqList_Create() malloc err :%d \n", ret);return NULL;}memset(tmp->node, 0, sizeof(void *) * capacity);return tmp;}//链表 创建int SeqList_Create2(int capacity, SeqList**handle){intret = 0;TSeqList*tmp = NULL;tmp = (TSeqList *)malloc(sizeof(TSeqList));if (tmp == NULL){ret = 1;printf("func SeqList_Create2() err :%d \n", ret);return ret;}memset(tmp, 0, sizeof(TSeqList));tmp->capacity = capacity;tmp->length = 0;tmp->node = (int **)malloc(sizeof(void *) * capacity);if (tmp->node == NULL){ret = 2;printf("func SeqList_Create2() malloc err :%d \n", ret);return ret;}*handle = tmp;return ret;}//链表 销毁void SeqList_Destroy(SeqList* list)  //O(1){TSeqList*tmp = NULL;if (list == NULL){return;}tmp = (TSeqList *)list;if (tmp->node != NULL){free(tmp->node);}free(tmp);return;}////链表 清空void SeqList_Clear(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return;}tmp = (TSeqList *)list;tmp->length = 0;memset(tmp->node, 0, (tmp->capacity * sizeof(void *)));return;}//链表 长度int SeqList_Length(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return -1;}tmp = (TSeqList *)list;return tmp->length;}//链表 容量 int SeqList_Capacity(SeqList* list) //O(1){TSeqList*tmp = NULL;if (list == NULL){return -1;}tmp = (TSeqList *)list;return tmp->capacity;}//链表 在某一个位置 插入元素int SeqList_Insert(SeqList* list, SeqListNode* node, int pos)  //O(n){TSeqList*tList = NULL;int i = 0;if (list == NULL || node == NULL){return -1;}tList = (TSeqList *)list;//如果满了 if (tList->length >= tList->capacity){return -2;}//pos位置的容错处理if (pos > tList->length){pos = tList->length;}for (i = tList->length; i>pos; i--)  //n{tList->node[i] = tList->node[i - 1];}tList->node[i] = (int*)node; //oktList->length++;return 0;}//获取某一个位置的链表结点SeqListNode* SeqList_Get(SeqList* list, int pos)  //O(1){TSeqList*tList = NULL;SeqListNode *tmp = NULL;tList = (TSeqList *)list;if (list == NULL || pos<0 || pos >= tList->length){return NULL;}tmp = tList->node[pos];return tmp;}//删除某一个位置的结点SeqListNode* SeqList_Delete(SeqList* list, int pos)  ////O(n){inti = 0;TSeqList*tList = NULL;SeqListNode *tmp = NULL;tList = (TSeqList *)list;if (list == NULL || pos <0 || pos >= tList->length){return NULL;}tmp = tList->node[pos];// pos = 3for (i = pos + 1; i<tList->length; i++){tList->node[i - 1] = tList->node[i];}tList->length--;return tmp;}

//test.cpp#define  _CRT_SECURE_NO_WARNINGS #include <stdlib.h>#include <string.h>#include <stdio.h>#include "seqlist.h"typedef struct _Teacher{char name[32];int age ;}Teacher;void main(){intret = 0, i = 0;SeqList *list;Teacher t1, t2, t3;t1.age = 31;t2.age = 32;t3.age = 33;list = SeqList_Create(10);//思考1: 如何实现 链表的api(链表的算法) 和 具体的数据分离//思考2: 链表库(业务逻辑)  测试程序的业务逻辑  结点的生命周期 归谁管?ret = SeqList_Insert(list, (SeqListNode *)&t1, 0);  //头插法ret = SeqList_Insert(list, (SeqListNode *)&t2, 0);  //头插法ret = SeqList_Insert(list, (SeqListNode *)&t3, 0);  //头插法//遍历链表for (i=0; i<SeqList_Length(list); i++ ){Teacher *tmp = (Teacher *)SeqList_Get(list, i); //获取链表结点if (tmp == NULL){printf("func SeqList_Get() err:%d \n ", ret);return ;}printf("age:%d \n", tmp->age);}//销毁链表while (SeqList_Length(list) > 0){Teacher *tmp  =  (Teacher *)SeqList_Delete(list, 0);//if (tmp == NULL){printf("func SeqList_Get() err:%d \n ", ret);return ;}printf("age:%d \n", tmp->age);}SeqList_Destroy(list);system("pause");return ;}