一、线性表的定义
线性表（linear list）是数据结构的一种，一个线性表是n个具有相同特性的数据元素的有限序列。数据元素是一个抽象的符号，其具体含义在不同的情况下一般不同。在稍复杂的线性表中，一个数据元素可由多个数据项（item） 组成，此种情况下常把数据元素称为记录（record） ，含有大量记录的线性表又称文件（file）。线性表中的个数n定义为线性表的长度，n=0时称为空表。
线性表的逻辑结构简单，便于实现和操作。因此，线性表这种数据结构在实际应用中是广泛采用的一种数据结构。
二、线性表的特征
1．集合中必存在唯一的一个“第一元素”。
2．集合中必存在唯一的一个 “最后元素” 。
3．除最后一个元素之外，均有唯一的后继(后件)。
4．除第一个元素之外，均有唯一的前驱(前件)。
三、线性表的具体实现
对于线性表的学习，我们可以先从相应的函数入手，通过模块化的学习将相应知识点融会贯通，最后写出完整的代码。
1.构建结构体与相应功能函数
a.用于储存数据的结构体：
typedef struct SequentialList {
int actualLength;
int data[LIST_MAX_LENGTH]; //The maximum length is fixed.
} *SequentialListPtr;
b.打印顺序表函数
void outputList(SequentialListPtr paraList) {
for(int i = 0; i < paraList->actualLength; i ++) {
printf("%d ", paraList->data[i]);
}// Of for i
printf("\r\n");
}// Of outputList
c.打印顺序表元素地址函数
void outputMemory(SequentialListPtr paraListPtr) {
printf("The address of the structure: %ld\r\n", paraListPtr);
printf("The address of actualLength: %ld\r\n", ¶ListPtr->actualLength);
printf("The address of data: %ld\r\n", ¶ListPtr->data);
printf("The address of actual data: %ld\r\n", ¶ListPtr->data[0]);
printf("The address of second data: %ld\r\n", ¶ListPtr->data[1]);
}// Of outputMemory
d.初始化顺序表函数
SequentialListPtr sequentialListInit(int paraData[], int paraLength) {
SequentialListPtr resultPtr = (SequentialListPtr)malloc(sizeof(struct SequentialList));
for (int i = 0; i < paraLength; i ++) {
resultPtr->data[i] = paraData[i];
}// Of for i
resultPtr->actualLength = paraLength;
return resultPtr;
}//Of sequentialListInit 以循环来初始化顺序表
e.顺序表的插入函数
void sequentialListInsert(SequentialListPtr paraListPtr, int paraPosition, int paraValue) {
// Step 1. Space check.
if (paraListPtr->actualLength >= LIST_MAX_LENGTH) {
printf("Cannot insert element: list full.\r\n");
return;
}//Of if
// Step 2. Position check.
if (paraPosition < 0) {
printf("Cannot insert element: negative position unsupported.");
return;
}//Of if
if (paraPosition > paraListPtr->actualLength) {
printf("Cannot insert element: the position %d is bigger than the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return;
}//Of if
// Step 3. Move the remaining part.
for (int i = paraListPtr->actualLength; i > paraPosition; i --) {
paraListPtr->data[i] = paraListPtr->data[i - 1];
}//Of for i
// Step 4. Insert.
paraListPtr->data[paraPosition] = paraValue;
// Step 5. Update the length.
paraListPtr->actualLength ++;
}
f.测试插入结果函数
void sequentialInsertTest() {
int i;
int tempArray[5] = {3, 5, 2, 7, 4};
printf("---- sequentialInsertTest begins. ----\r\n");
// Initialize.
SequentialListPtr tempList = sequentialListInit(tempArray, 5);
printf("After initialization, the list is: ");
outputList(tempList);
// Insert to the first.
printf("Now insert to the first, the list is: ");
sequentialListInsert(tempList, 0, 8);
outputList(tempList);
// Insert to the last.
printf("Now insert to the last, the list is: ");
sequentialListInsert(tempList, 6, 9);
outputList(tempList);
// Insert beyond the tail.
printf("Now insert beyond the tail. \r\n");
sequentialListInsert(tempList, 8, 9);
printf("The list is:");
outputList(tempList);
// Insert to position 3.
for (i = 0; i < 5; i ++) {
printf("Inserting %d.\r\n", (i + 10));
sequentialListInsert(tempList, 0, (i + 10));
outputList(tempList);
}//Of for i
printf("---- sequentialInsertTest ends. ----\r\n");
}
g.顺序表的删除函数
int sequentialListDelete(SequentialListPtr paraListPtr, int paraPosition) {
// Step 1. Position check.
if (paraPosition < 0) {
printf("Invalid position: %d.\r\n", paraPosition);
return -1;
}//Of if
if (paraPosition >= paraListPtr->actualLength) {
printf("Cannot delete element: the position %d is beyond the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return -1;
}//Of if
// Step 2. Move the remaining part.
int resultValue = paraListPtr->data[paraPosition];
for (int i = paraPosition; i < paraListPtr->actualLength; i ++) {
paraListPtr->data[i] = paraListPtr->data[i + 1];
}//Of for i
// Step 3. Update the length.
paraListPtr->actualLength --;
// Step 4. Return the value.
return resultValue;
}
h.测试删除结果函数
void sequentialDeleteTest() {
int tempArray[5] = {3, 5, 2, 7, 4};
printf("---- sequentialDeleteTest begins. ----\r\n");
// Initialize.
SequentialListPtr tempList = sequentialListInit(tempArray, 5);
printf("After initialization, the list is: ");
outputList(tempList);
// Delete the first.
printf("Now delete the first, the list is: ");
sequentialListDelete(tempList, 0);
outputList(tempList);
// Delete to the last.
printf("Now delete the last, the list is: ");
sequentialListDelete(tempList, 3);
outputList(tempList);
// Delete the second.
printf("Now delete the second, the list is: ");
sequentialListDelete(tempList, 1);
outputList(tempList);
// Delete the second.
printf("Now delete the 5th, the list is: ");
sequentialListDelete(tempList, 5);
outputList(tempList);
// Delete the second.
printf("Now delete the (-6)th, the list is: ");
sequentialListDelete(tempList, -6);
outputList(tempList);
printf("---- sequentialDeleteTest ends. ----\r\n");
outputMemory(tempList);
}
i.定位特定数据函数
int locateElement(SequentialListPtr paraListPtr, int paraValue) {
for (int i = 0; i < paraListPtr->actualLength; i ++) {
if (paraListPtr->data[i] == paraValue) {
return i;
}// Of if
}//Of for i
return -1;
}
j.获得特定位置数据值的函数
int getElement(SequentialListPtr paraListPtr, int paraPosition) {
// Step 1. Position check.
if (paraPosition < 0) {
printf("Invalid position: %d.\r\n", paraPosition);
return -1;
}//Of if
if (paraPosition >= paraListPtr->actualLength) {
printf("Cannot delete element: the position %d is beyond the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return -1;
}//Of if
return paraListPtr->data[paraPosition];
}
顺序表的基本操作已经完成，现在只需要理清其中的关系并将其连接起来
以下为顺序表函数的相应关系图：
2.明确主函数
void main() {
sequentialInsertTest();
sequentialDeleteTest();
}// Of main
以上便为构造顺序表以及实现其相关功能的操作，完整代码如下：
#include <stdio.h>
#include <malloc.h>
#define LIST_MAX_LENGTH 10
/**
* Linear list of integers. The key is data.
*/
typedef struct SequentialList {
int actualLength;
int data[LIST_MAX_LENGTH]; //The maximum length is fixed.
} *SequentialListPtr;
/**
* Output the list.
*/
void outputList(SequentialListPtr paraList) {
for(int i = 0; i < paraList->actualLength; i ++) {
printf("%d ", paraList->data[i]);
}// Of for i
printf("\r\n");
}// Of outputList
/**
* Output the memeory for the list.
*/
void outputMemory(SequentialListPtr paraListPtr) {
printf("The address of the structure: %ld\r\n", paraListPtr);
printf("The address of actualLength: %ld\r\n", ¶ListPtr->actualLength);
printf("The address of data: %ld\r\n", ¶ListPtr->data);
printf("The address of actual data: %ld\r\n", ¶ListPtr->data[0]);
printf("The address of second data: %ld\r\n", ¶ListPtr->data[1]);
}// Of outputMemory
/**
* Initialize a sequential list. No error checking for this function.
* @param paraListPtr The pointer to the list. It must be a pointer to change the list.
* @param paraValues An int array storing all elements.
*/
SequentialListPtr sequentialListInit(int paraData[], int paraLength) {
SequentialListPtr resultPtr = (SequentialListPtr)malloc(sizeof(struct SequentialList));
for (int i = 0; i < paraLength; i ++) {
resultPtr->data[i] = paraData[i];
}// Of for i
resultPtr->actualLength = paraLength;
return resultPtr;
}//Of sequentialListInit
/**
* Insert an element into a sequential linear list.
* @param paraListPtr The pointer to the list. It must be a pointer to change the list.
* @param paraPosition The position, e.g., 0 stands for inserting at the first position.
* @param paraValue The value to be inserted.
*/
void sequentialListInsert(SequentialListPtr paraListPtr, int paraPosition, int paraValue) {
// Step 1. Space check.
if (paraListPtr->actualLength >= LIST_MAX_LENGTH) {
printf("Cannot insert element: list full.\r\n");
return;
}//Of if
// Step 2. Position check.
if (paraPosition < 0) {
printf("Cannot insert element: negative position unsupported.");
return;
}//Of if
if (paraPosition > paraListPtr->actualLength) {
printf("Cannot insert element: the position %d is bigger than the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return;
}//Of if
// Step 3. Move the remaining part.
for (int i = paraListPtr->actualLength; i > paraPosition; i --) {
paraListPtr->data[i] = paraListPtr->data[i - 1];
}//Of for i
// Step 4. Insert.
paraListPtr->data[paraPosition] = paraValue;
// Step 5. Update the length.
paraListPtr->actualLength ++;
}// Of sequentialListInsert
/**
* Test the insert function.
*/
void sequentialInsertTest() {
int i;
int tempArray[5] = {3, 5, 2, 7, 4};
printf("---- sequentialInsertTest begins. ----\r\n");
// Initialize.
SequentialListPtr tempList = sequentialListInit(tempArray, 5);
printf("After initialization, the list is: ");
outputList(tempList);
// Insert to the first.
printf("Now insert to the first, the list is: ");
sequentialListInsert(tempList, 0, 8);
outputList(tempList);
// Insert to the last.
printf("Now insert to the last, the list is: ");
sequentialListInsert(tempList, 6, 9);
outputList(tempList);
// Insert beyond the tail.
printf("Now insert beyond the tail. \r\n");
sequentialListInsert(tempList, 8, 9);
printf("The list is:");
outputList(tempList);
// Insert to position 3.
for (i = 0; i < 5; i ++) {
printf("Inserting %d.\r\n", (i + 10));
sequentialListInsert(tempList, 0, (i + 10));
outputList(tempList);
}//Of for i
printf("---- sequentialInsertTest ends. ----\r\n");
}// Of sequentialInsertTest
/**
* Delete an element from a sequential linear list.
* @param paraListPtr The pointer to the list. It must be a pointer to change the list.
* @param paraPosition The position, e.g., 0 stands for inserting at the first position.
* @return The deleted value.
*/
int sequentialListDelete(SequentialListPtr paraListPtr, int paraPosition) {
// Step 1. Position check.
if (paraPosition < 0) {
printf("Invalid position: %d.\r\n", paraPosition);
return -1;
}//Of if
if (paraPosition >= paraListPtr->actualLength) {
printf("Cannot delete element: the position %d is beyond the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return -1;
}//Of if
// Step 2. Move the remaining part.
int resultValue = paraListPtr->data[paraPosition];
for (int i = paraPosition; i < paraListPtr->actualLength; i ++) {
paraListPtr->data[i] = paraListPtr->data[i + 1];
}//Of for i
// Step 3. Update the length.
paraListPtr->actualLength --;
// Step 4. Return the value.
return resultValue;
}// Of sequentialListDelete
/**
* Test the delete function.
*/
void sequentialDeleteTest() {
int tempArray[5] = {3, 5, 2, 7, 4};
printf("---- sequentialDeleteTest begins. ----\r\n");
// Initialize.
SequentialListPtr tempList = sequentialListInit(tempArray, 5);
printf("After initialization, the list is: ");
outputList(tempList);
// Delete the first.
printf("Now delete the first, the list is: ");
sequentialListDelete(tempList, 0);
outputList(tempList);
// Delete to the last.
printf("Now delete the last, the list is: ");
sequentialListDelete(tempList, 3);
outputList(tempList);
// Delete the second.
printf("Now delete the second, the list is: ");
sequentialListDelete(tempList, 1);
outputList(tempList);
// Delete the second.
printf("Now delete the 5th, the list is: ");
sequentialListDelete(tempList, 5);
outputList(tempList);
// Delete the second.
printf("Now delete the (-6)th, the list is: ");
sequentialListDelete(tempList, -6);
outputList(tempList);
printf("---- sequentialDeleteTest ends. ----\r\n");
outputMemory(tempList);
}// Of sequentialDeleteTest
/**
* Locate an element in the list.
* @param paraListPtr The pointer to the list.
* @param paraValue the indicated value.
* @return The position of the value, or -1 indicating not exists
*/
int locateElement(SequentialListPtr paraListPtr, int paraValue) {
for (int i = 0; i < paraListPtr->actualLength; i ++) {
if (paraListPtr->data[i] == paraValue) {
return i;
}// Of if
}//Of for i
return -1;
}// Of locateElement
/**
* Get an element in the list.
* @param paraListPtr The pointer to the list.
* @param paraPosition The given position.
* @return The position of the value, or -1 indicating not exists
*/
int getElement(SequentialListPtr paraListPtr, int paraPosition) {
// Step 1. Position check.
if (paraPosition < 0) {
printf("Invalid position: %d.\r\n", paraPosition);
return -1;
}//Of if
if (paraPosition >= paraListPtr->actualLength) {
printf("Cannot delete element: the position %d is beyond the list length %d.\r\n", paraPosition, paraListPtr->actualLength);
return -1;
}//Of if
return paraListPtr->data[paraPosition];
}// Of locateElement
/**
* Clear elements in the list.
* @param paraListPtr The pointer to the list.
* @return The position of the value, or -1 indicating not exists
*/
void clearList(SequentialListPtr paraListPtr) {
paraListPtr->actualLength = 0;
}// Of clearList
/**
The entrance.
*/
void main() {
sequentialInsertTest();
sequentialDeleteTest();
}// Of main
四、反思与总结
对于顺序表的学习，我认为远不止于此，包括申请动态内存时返回值是指针还是其他类型仍需我进行相应的测试，未来也要进行更多功能的拓展，包括对申请内存时的防御性编程以免出错或者便于调试时纠错。
同时我还学会到了很重要的一点：在编写变量名称时最好将其写的长一点复杂一点，以增加变量的标识性与可读性。这对于大项目来说尤为重要，这是一个很好的习惯，我要继续保持。
