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：2016.12.191．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{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<iostream>#include<iomanip>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;}parision = zzj1.movement = 0;parision = zzj2.movement = 0;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;}parision = zzj1.movement = 0;parision = zzj2.movement = 0;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;}parision = zzj1.movement = 0;parision = zzj2.movement = 0;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;}parision = zzj1.movement = 0;parision = zzj2.movement = 0;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。