数据结构-实验六

查找和排序的实现

实验内容：

（1）编程实现两种查找方法：折半查找和二叉排序树。若查找成功，返回元素在有序数组中的位置和查找次数；若查找失败，返回出错标志和查找次数；

（2）在9种排序算法（直接插入排序、折半插入排序、希尔排序、冒泡排序、快速排序、简单选择排序、堆排序、归并排序和基数排序）中选择5种排序算法进行编程实现。

#include<iostream>
using namespace std;
typedef int KeyType;
typedef int InfoType;
typedef struct
{
    KeyType key;
    InfoType otherinfo;
} ElemType;
typedef struct
{
    ElemType R[20];
    int length;
} SSTable;
typedef struct BSTNode
{
    ElemType data;
    struct BSTNode* lchild, * rchild;
} BSTNode,*BSTree; //BSTNode为节点，BSTree为结构体指针

//创建二叉排序树
int Search_Bin(SSTable ST,KeyType key)//折半查找
{
    int low=0;
    int high=ST.length-1;
    int mid;
    int locate;
    int count=0;
    while(low<=high)
    {
        mid=(low+high)/2;
        count++;
        if(key==ST.R[mid].key)
        {
            break;
        }
        else if(key<ST.R[mid].key)
        {
            high=mid-1;
        }
        else
        {
            low=mid+1;
        }
    }
    locate=mid+1;
    if(ST.R[mid].key==key)
    {
        cout<<"查找成功"<<" "<<"一共查找了"<<count+1<<"次"<<endl;
        cout<<"查找的位置为"<<locate<<endl;
    }
    else
    {
        cout<<"查找失败"<<" "<<"一共查找了"<<count<<"次"<<endl;
    }
}

void CreateBSTree(BSTree& T,KeyType e)
{
    if (!T)
    {
        BSTree S;
        S = new BSTNode;
        S->data.key = e;
        S->lchild = NULL;
        S->rchild = NULL;
        T = S;
    }
    else if (e<T->data.key)
    {
        CreateBSTree(T->lchild,e);
    }
    else if (e>T->data.key)
    {
        CreateBSTree(T->rchild,e);
    }
}
void InOrderTraverse(BSTree T)//中序遍历的递归算法
{
    if(T)
    {
        InOrderTraverse(T->lchild);
        cout<<T->data.key<< "  ";
        InOrderTraverse(T->rchild);
    }
}

int count1 = 0,count2=0;
//二叉排序树的查找
BSTree SearchBST(BSTree T, KeyType key)
{
    if ((!T) || key == T->data.key)
    {
        count2++;
        return T;
    }
    else if(key<T->data.key)
    {
        return SearchBST(T->lchild,key);
    }
    else
    {
        return SearchBST(T->rchild, key);
    }
}


int main()
{
    cout<<"折半查找算法"<<endl;
    SSTable ST;
    int i,n1,k,key1;
    cout<<"输入表的长度:";
    cin>>ST.length;
    cout<<"请输入一个有序的数列"<<endl;
    for(i=0; i<ST.length; i++)
    {
        cin>>ST.R[i].key;
    }
    for(int i=0; i<2; i++)
    {
        cout<<"请输入要查找的数字:";
        cin>>key1;
        cout<<endl;
        Search_Bin(ST,key1);
    }
    cout<<endl;
    cout<<endl;
    cout<<"二叉排序树查找"<<endl;
    BSTree T =NULL;
    int n2;
    cout << "请输入结点总数：";
    cin >> n2;
    //int a[666];
    cout << "请分别输入各个结点：";
    int e;
    for (int i = 0; i < n2; i++)
    {
        cin >> e;
        CreateBSTree(T,e);
    }
    cout<<"输出二叉排序树的结果："<<endl;
    InOrderTraverse(T);
    cout<<endl;
    for(int i=0; i<2; i++)
    {
        cout << "请输入要查找的元素:";
        int key;
        cin >> key;
        BSTree address = SearchBST(T, key);
        if (!address)
        {
            cout << "该元素不存在，比较次数为：" << count1-5;
        }
        else
        {
            cout <<"查找成功，比较次数为" <<count2<< "次"<<endl;
        }
    }
    return 0;

}

#include <iostream>
using namespace std;
typedef int KeyType;
typedef int InfoType;
typedef struct
{
    KeyType key;
    InfoType otherinfo;
} ElemType;
typedef struct BSTNode
{
    ElemType data;
    struct BSTNode* lchild, * rchild;
} BSTNode,*BSTree; //BSTNode为节点，BSTree为结构体指针

//创建二叉排序树
void CreateBSTree(BSTree& T,KeyType e)
{
    if (!T)
    {
        BSTree S;
        S = new BSTNode;
        S->data.key = e;
        S->lchild = NULL;
        S->rchild = NULL;
        T = S;
    }
    else if (e<T->data.key)
    {
        CreateBSTree(T->lchild,e);
    }
    else if (e>T->data.key)
    {
        CreateBSTree(T->rchild,e);
    }
}
void InOrderTraverse(BSTree T)//中序遍历的递归算法
{
    if(T)
    {
        InOrderTraverse(T->lchild);
        cout<<T->data.key<< "  ";
        InOrderTraverse(T->rchild);
    }
}

int count = 0,count2=0;
//二叉排序树的查找
BSTree SearchBST(BSTree T, KeyType key)
{
    if ((!T))
    {
        return T;
    }
    if( key == T->data.key)
    {
        count2=count2+2;
        return T;
    }
    count=count+1;
    if(key<T->data.key)
    {
        return SearchBST(T->lchild,key);
    }
    else
    {
        return SearchBST(T->rchild, key);
    }
}

int main()
{
    BSTree T =NULL;
    int n2;
    cout << "请输入结点总数：";
    cin >> n2;
    //int a[666];
    cout << "请分别输入各个结点：";
    int e;
    for (int i = 0; i < n2; i++)
    {
        cin >> e;
        CreateBSTree(T,e);
    }
    cout<<"输出二叉排序树的结果："<<endl;
    InOrderTraverse(T);
    cout<<endl;
    while(1)
    {
        cout << "请输入要查找的元素:";
        int key;
        cin >> key;
        BSTree address = SearchBST(T, key);
        if (!address)
        {
            cout << "该元素不存在，比较次数为：" << count;
        }
        else
        {
            cout <<"查找成功，比较次数为" <<count2<< "次"<<endl;
        }

    }

}

 

#include<iostream>
#include<cstdlib>
#include<cmath>
using namespace std;
#define MAXSIZE 20
typedef int KeyType;
typedef int InfoType;
typedef struct
{
    KeyType key;
    InfoType otherinfo;
} RedType;
typedef struct
{
    RedType r[MAXSIZE+1];
    int length;
} SqList;

void InsertSort(SqList &L)//直接插入排序法
{
    int i,j;
    for(i=2; i<=L.length; i++)
        if(L.r[i].key<L.r[i-1].key)
        {
            L.r[0]=L.r[i];
            L.r[i]=L.r[i-1];
            for( j=i-2; L.r[0].key<L.r[j].key; --j)
                L.r[j+1]=L.r[j];
            L.r[j+1]=L.r[0];
        }
}

void BInsertSort(SqList &L)//折半插入排序法
{
    int i,j,low,high,m;
    for(i=2; i<=L.length; i++)
    {
        L.r[0]=L.r[i];
        low=1;
        high=i-1;
        while(low<=high)
        {
            m=(low+high)/2;
            if(L.r[0].key<L.r[m].key)high=m-1;
            else low=m+1;
        }
        for(j=i-1; j>=high+1; --j)L.r[j+1]=L.r[j];
        L.r[high+1]=L.r[0];
    }
}


void BubbleSort(SqList &L)//冒泡排序
{
    int m,flag,i,j;
    RedType t;
    m=L.length-1;
    flag=1;
    while((m>0)&&(flag==1))
    {
        flag=0;
        for(j=1; j<=m; j++)
        {
            if(L.r[j].key>L.r[j+1].key)
            {
                flag=1;
                t=L.r[j];
                L.r[j]=L.r[j+1];
                L.r[j+1]=t;
            }
        }
        --m;
    }
}


int Partition(SqList &L,int low,int high)//快速排序
{
    int pivotkey;
    L.r[0]=L.r[low];
    pivotkey=L.r[low].key;
    while(low<high)
    {
        while(low<high&&L.r[high].key>=pivotkey)--high;
        L.r[low]=L.r[high];
        while(low<high&&L.r[low].key<=pivotkey)++low;
        L.r[high]=L.r[low];
    }
    L.r[low]=L.r[0];
    return low;
}
void QSort(SqList &L,int low,int high)
{
    int pivotkey;
    if(low<high)
    {
        pivotkey=Partition(L,low,high);
        QSort(L,low,pivotkey-1);
        QSort(L,pivotkey+1,high);
    }
}

void QuickSort(SqList &L)
{
    QSort(L,1,L.length);
}

void SelectSort(SqList &L)//选择排序
{
    int i,j,k;
    RedType t;
    for(i=1; i<L.length; i++)
    {

        k=i;
        for(j=i+1; j<=L.length; ++j)
            if(L.r[j].key<L.r[k].key)k=j;
        if(k!=i)
        {

            t=L.r[i];
            L.r[i]=L.r[k];
            L.r[k]=t;
        }
    }
}

void print(SqList &L)
{
    int i;
    for(i=1; i<=L.length; i++)
    {
        cout<<L.r[i].key<<" ";
    }
    cout<<endl;
}
int main()
{
    SqList L;
    int a;
    int n,i;
    while(1)
    {
        cout<<"请输入一个数，表示线性表长度"<<endl;
        cin>>n;
        L.length=n;
        cout<<"请输入线性表元素"<<endl;
        for(i=1; i<=n; i++)
        {
            cin>>L.r[i].key;
        }
        cout<<"请输入一个数字,1表示直接插入,2表示折半插入,3表示冒泡排序,4表示快速排序,5表示选择排序"<<endl;
        cin>>a;
        if(a==1)
        {
            cout<<"直接插入排序法结果；"<<endl;
            InsertSort(L);
            for(i=1; i<=L.length; i++)
                cout<<L.r[i].key<<" ";
            cout<<endl;
        }
        if(a==2)
        {
            cout<<"折半插入排序法结果: "<<endl;
            BInsertSort(L);
            print(L);
        }
        if(a==3)
        {
            cout<<"冒泡排序法结果: "<<endl;
            BubbleSort(L);
            print(L);
        }
        if(a==4)
        {
            cout<<"快速排序法结果: "<<endl;
            QuickSort(L);
            print(L);
        }
        if(a==5)
        {
            cout<<"选择排序法结果: "<<endl;
            SelectSort(L);
            print(L);
        }
    }
    return 0;
}