链表实现排序算法

数据结构

实

验

报

告

实验名称：实验三排序

学生姓名：

班级：

班内序号：15

学号：

日期：2016.12.19

1．实验要求

题目2

使用链表实现下面各种排序算法，并进行比较。

排序算法：

1、插入排序

2、冒泡排序

3、快速排序

4、简单选择排序

5、其他

要求：

1、测试数据分成三类：正序、逆序、随机数据

2、对于这三类数据，比较上述排序算法中关键字的比较次数和移动

次数（其中关键字交换计为3次移动）。

3、对于这三类数据，比较上述排序算法中不同算法的执行时间，精

确到微秒（选作）

4、对2和3的结果进行分析，验证上述各种算法的时间复杂度

编写测试main()函数测试线性表的正确性

2. 程序分析

2.1 存储结构

我使用了线性表的链式存储结构，通过建立双向循环链表进行顺序存取。每个节点分为data、next、previor。data域称为数据域，数据通过node结构存储待排序的信息；next为指针域，用来储存直接后继的地址；prior为指针域，用来储存直接前继的地址；

struct Node

{

int data;

struct Node*next;

struct Node*previor;

};

2.2 程序流程(或程序结构、或类关系图等表明程序构成的内容，一般为流程

{

private:

Node* partion(Node*first,Node*end); //快速排序一趟

public:

Node*front;

int comparision; //比较次数

int movement; //移动次数

LinkList() //无参构造

{

front = new Node;

front->next = NULL;

front->previor = NULL;

comparision = movement = 0;

}

LinkList(int a[],int n); //构造函数:建立双向链表

void insertsort(); //插入排序

void bubblesort(); //冒泡排序

void Qsort(Node*x,Node*y); //快速排序

void selectsort(); //简单选择排序

void show(); //显示排序结果

~LinkList(); //析构函数

};

2.3 关键算法分析

构造函数：通过使用头插法建立双向链表，其关键是多设一个指针变量用于储存上一个末节点的地址，这样才能使节点指向其上一个节点。在这

次排序实验中，使用双向循环链表更方便进行遍历操作。LinkList::LinkList(int a[],int n)

{

front = new Node;

front->next = NULL;

front->previor = NULL;

comparision = movement = 0;

Node*x = new Node;

Node*s = new Node;

s->data = a[n - 1];

s->next = front;

s->previor = front;

front->next = s;

front->previor = s;

x = s;

for (int i = n - 2; i >= 0; i--)

{

Node*s = new Node;

s->data = a[i];

s->next = front->next;

s->previor = front;

front->next = s;

x->previor = s;

x = s;

}

}

插入排序函数：将front头节点当作哨兵。从第二个有效节点开始进行插入，进行边查找，边后移的操作。

void LinkList::insertsort()

{

Node*p = front->next;

Node*s = p->next;

while (s!=front)

{

if (s->data < p->data)

{

comparision++;

front->data = s->data;

movement++;

Node*x = p;

Node*y = s;

while (front->data < x->data)

{

comparision++;

y->data = x->data;

movement++;

x = x->previor;

y = y->previor;

}

y->data = front->data;

movement++;

}

comparision++;

p = p->next;

s = s->next;

}

}

冒泡排序函数：每一次内循环边比较边交换，将无序区中最大的数放入有序区中，并记录无序元素的范围。当无序元素指向front时即整体排序完

成。

void LinkList::bubblesort()

{

Node*s = front->previor; //初始化无序元素位置while (s != front)

{

Node*p = s; //本次无序元素位置

s = front;

Node*x = front->next;

Node*y = x->next;

while (x != p)

{

if (x->data > y->data)

{

comparision++;

front->data = x->data;

x->data = y->data;

y->data = front->data;

movement = movement + 3;

s = x; //更新无序元素位置}

comparision++;

x = x->next;

y = y->next;

}

}

}

快速排序函数：快速排序函数是个递归调用函数，关键在一次快速排序函数的编写。选择第一个元素作为分区的轴值，将待排序元素分成左

右两个区域，左区的元素都比轴值小，右边的都更大。

然后反复进行此操作，即可完成排序。而结束递归的关键便是

左右分界节点有了直接前后继关系的时候。

void LinkList::Qsort(Node*x,Node*y)

{

if (x->previor != y)

{

Node*pivot = partion(x, y);

Qsort(x, pivot->previor);

Qsort(pivot->next, y);

}

}

Node* LinkList::partion(Node*first, Node*end)

{

int basic = first->data;

while (first != end)

{

while ((first != end) && (end->data >= basic))

{

end = end->previor;

comparision++;

}

comparision++;

first->data = end->data;

movement++;

while ((first != end) && (first->data <= basic))

{

first = first->next;

comparision++;

}

comparision++;

end->data = first->data;

movement++;

}

first->data = basic;

movement++;

return first;

}

简单选择排序函数：是将待排序中最小的元素放置序列最前面，其关键是先

通过循环比较确定最小元素的位置，再进行数据交换，

从而大大减少了元素交换的次数。

void LinkList::selectsort()

{

Node*s = front->next;

while (s != front->previor)

{

Node*p = s->next;

Node*record = s;

while (p != front)

{

Node*x = record;

if (p->data < x->data)

{

comparision++;

record = p;

}

comparision++;

p = p->next;

}

if (record != s)

{

int a = record->data;

record->data = s->data;

s->data = a;

movement = movement + 3;

}

s = s->next;

}

}

3.程序运行结果分析

4.总结

本次实验进行了使用链表存储结构实现插入排序、冒泡排序、快速排序、简单选择排序的编程。这使我对不同的排序方法有了更加深刻的理解和认识。

从中也体会到不同的排序方式所耗费的时间复杂度实在是大相径庭，这警示我们，编写一个时间复杂度小的排序函数在进行排序操作时，起着至关重要的作用。

完整代码如下：

#include

#include

using namespace std;

struct Node

{

int data;

struct Node*next;

struct Node*previor;

};

class LinkList

{

private:

Node* partion(Node*first,Node*end); //快速排序一趟

public:

Node*front;

int comparision; //比较次数

int movement; //移动次数

LinkList() //无参构造

{

front = new Node;

front->next = NULL;

front->previor = NULL;

comparision = movement = 0;

}

LinkList(int a[],int n); //构造函数:建立双向链表void insertsort(); //插入排序

void bubblesort(); //冒泡排序

void Qsort(Node*x,Node*y); //快速排序

void selectsort(); //简单选择排序

void show(); //显示排序结果

~LinkList(); //析构函数

};

LinkList::LinkList(int a[],int n)

{

front = new Node;

front->next = NULL;

front->previor = NULL;

comparision = movement = 0;

Node*x = new Node;

Node*s = new Node;

s->data = a[n - 1];

s->next = front;

s->previor = front;

front->next = s;

front->previor = s;

x = s;

for (int i = n - 2; i >= 0; i--)

{

Node*s = new Node;

s->data = a[i];

s->next = front->next;

s->previor = front;

front->next = s;

x->previor = s;

x = s;

}

}

Node* LinkList::partion(Node*first, Node*end)

{

int basic = first->data;

while (first != end)

{

while ((first != end) && (end->data >= basic))

{

end = end->previor;

comparision++;

}

comparision++;

first->data = end->data;

movement++;

while ((first != end) && (first->data <= basic))

{

first = first->next;

comparision++;

}

comparision++;

end->data = first->data;

movement++;

}

first->data = basic;

movement++;

return first;

}

void LinkList::insertsort()

{

Node*p = front->next;

Node*s = p->next;

while (s!=front)

{

if (s->data < p->data)

{

comparision++;

front->data = s->data;

movement++;

Node*x = p;

Node*y = s;

while (front->data < x->data)

{

comparision++;

y->data = x->data;

movement++;

x = x->previor;

y = y->previor;

}

y->data = front->data;

movement++;

}

comparision++;

p = p->next;

s = s->next;

}

}

void LinkList::bubblesort()

{

Node*s = front->previor; //初始化无序元素位置while (s != front)

{

Node*p = s; //本次无序元素位置s = front;

Node*x = front->next;

Node*y = x->next;

while (x != p)

{

if (x->data > y->data)

{

comparision++;

front->data = x->data;

x->data = y->data;

y->data = front->data;

movement = movement + 3;

s = x; //更新无序元素位置}

comparision++;

x = x->next;

y = y->next;

}

}

}

void LinkList::Qsort(Node*x,Node*y)

{

if (x->previor != y)

{

Node*pivot = partion(x, y);

Qsort(x, pivot->previor);

Qsort(pivot->next, y);

}

}

void LinkList::selectsort()

{

Node*s = front->next;

while (s != front->previor)

{

Node*p = s->next;

Node*record = s;

while (p != front)

{

Node*x = record;

if (p->data < x->data)

{

comparision++;

record = p;

}

comparision++;

p = p->next;

}

if (record != s)

{

int a = record->data;

record->data = s->data;

s->data = a;

movement = movement + 3;

}

s = s->next;

}

}

void LinkList::show()

{

Node*x = new Node;

x = front->next;

while (x != front)

{

cout << x->data << setw(4);

x = x->next;

}

cout << endl << "比较次数：" << comparision << endl;

cout << "移动次数：" << movement << endl;

cout << endl;

}

LinkList:: ~LinkList()

{

Node*p = front;

while (p!=front)

{

Node*a = p;

p = p->next;

delete a;

}

delete p;

}

void showmenu();

int main()

{

showmenu();

cin.get();

cin.get();

return 0;

}

void showmenu()

{

int jay1[7] = { 2,6,7,9,15,24,29 };

int jay2[7] = { 54,40,38,37,29,24,12 };

int jay3[7] = { 16,45,81,1,4,69,100 };

LinkList zzj1(jay1, 7);

LinkList zzj2(jay2, 7);

LinkList zzj3(jay3, 7);

cout << "正序数据："; zzj1.show();

cout << "逆序数据："; zzj2.show();

cout << "乱序数据："; zzj3.show();

int choice;

cout << "请选择所要操作的内容：\n"

"1.插入排序 2.冒泡排序\n"

"3.快速排序 4.简单选择排序\n"

"5.退出\n";

cin >> choice;

int count = 0;

Node*x, *y, *z;

while (choice != 5)

{

switch (choice)

{

case 1:

if (count != 0)

{

x = zzj1.front->next;

y = zzj2.front->next;

z = zzj3.front->next;

for (int i = 0; i < 7; i++)

{

x->data = jay1[i];

y->data = jay2[i];

z->data = jay3[i];

x = x->next;

y = y->next;

z = z->next;

}

https://www.360docs.net/doc/7f4206695.html,parision = zzj1.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj2.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj3.movement = 0;

}

cout << "插入排序：\n";

zzj1.insertsort();

zzj2.insertsort();

zzj3.insertsort();

zzj1.show();

zzj2.show();

zzj3.show();

count = 1;

break;

case 2:

if (count != 0)

{

x = zzj1.front->next;

y = zzj2.front->next;

z = zzj3.front->next;

for (int i = 0; i < 7; i++)

{

x->data = jay1[i];

y->data = jay2[i];

z->data = jay3[i];

x = x->next;

y = y->next;

z = z->next;

}

https://www.360docs.net/doc/7f4206695.html,parision = zzj1.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj2.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj3.movement = 0;

}

zzj1.bubblesort();

zzj2.bubblesort();

zzj3.bubblesort();

cout << "冒泡排序：\n";

zzj1.show();

zzj2.show();

zzj3.show();

count = 1;

break;

case 3:

if (count != 0)

{

x = zzj1.front->next;

y = zzj2.front->next;

z = zzj3.front->next;

for (int i = 0; i < 7; i++)

{

x->data = jay1[i];

y->data = jay2[i];

z->data = jay3[i];

x = x->next;

y = y->next;

z = z->next;

}

https://www.360docs.net/doc/7f4206695.html,parision = zzj1.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj2.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj3.movement = 0;

}

x = zzj1.front;

y = zzj2.front;

z = zzj3.front;

zzj1.Qsort(x->next, x->previor);

zzj2.Qsort(y->next, y->previor);

zzj3.Qsort(z->next, z->previor);

cout << "快速排序：\n";

zzj1.show();

zzj2.show();

zzj3.show();

count = 1;

break;

case 4:

if (count != 0)

{

x = zzj1.front->next;

y = zzj2.front->next;

z = zzj3.front->next;

for (int i = 0; i < 7; i++)

{

x->data = jay1[i];

y->data = jay2[i];

z->data = jay3[i];

x = x->next;

y = y->next;

z = z->next;

}

https://www.360docs.net/doc/7f4206695.html,parision = zzj1.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj2.movement = 0;

https://www.360docs.net/doc/7f4206695.html,parision = zzj3.movement = 0;

}

zzj1.selectsort();

zzj2.selectsort();

zzj3.selectsort();

cout << "简单选择排序：\n";

zzj1.show();

zzj2.show();

zzj3.show();

count = 1;

break;

default:cout << "这不是一个选项。\n";

}

cout << "请选择所要操作的内容：\n"

"1.插入排序 2.冒泡排序\n"

"3.快速排序 4.简单选择排序\n"

"5.退出\n";

cin >> choice;

}

cout << "感谢您的使用。\n";

}