数据结构1-2 约瑟夫环问题

Posted 2021-01-20 robotpaul

这里放出两种不同的代码，一个是老师给的（较为复杂），还有一个是自己写的。

自己写的：

#include<iostream>
using namespace std;
struct Node {
    int data;            //数据单元
    Node *link;            //指向下一个结点
};
class Josephus
{
private:
    Node *head, *current;        //head是头结点，current指向当前结点
    int sum;//存储链表中元素的个数
public:
    Josephus();                //无参构造函数，全部初始化为空
    Josephus(int Snumber, int strnumber);//有参构造函数，Snumber为总数，strnumber为开始序号
    ~Josephus();//析构函数
    void del(Node *&p);
    void select(int num);//num为间隔数
    void print();
};
Josephus::Josephus()
{
    current = NULL;
    head = NULL;
    sum = 0;
}
Josephus::Josephus(int Snumber, int strnumber)
{
    sum = Snumber;
    head = new Node;
    head->data = strnumber;
    current = head;
    int dt = strnumber + 1;
    for (int i = 1; i < Snumber; i++)
    {
        Node *p;
        p = new Node;
        p->data = dt;
        current->link = p;
        current = p;
        dt++;
    }
    current->link = head;

}
void Josephus::del(Node *&p)
{
    Node *d = p->link;
    p->link = p->link->link;
    delete d;
}
void Josephus::select(int num)
{
    int sont = 1;
    Node *p = head;
    while (sum!= 1)
    {
        if (sont % (num-1)  == 0)
        {
            del(p);
            sum--;
            head = p;
        }
        sont++;
        p = p->link;
    }
    
    
}
void Josephus::print()
{
    cout << "剩下的序号有：" << endl;
    Node *p = head;
    for (int i = 0; i < sum; i++)
    {
        cout << p->data << " ";
        p = p->link;
    }
    cout << endl;
}
Josephus::~Josephus()
{
    /*Node *p = head->link;
    while (p!=head)
    {
        Node *de = p;
        p = p->link;
        delete de;
    }*/
    head = NULL;
    current = NULL;
}

测试代码：

#include"LinkList.h"
int  main()
{
    int Snum, stnum,num;
    cout << "请输入总数以及开始序号:";
    cin >> Snum >> stnum;
    Josephus A(Snum, stnum);
    A.print();
    cout << "请输入间隔数:";
    cin >> num;
    A.select(num);
    A.print();
    system("pause");
    return 0;
}

其实原理很简单，就是通过循环链表不断循环然后删除就OK

标准代码：

//Circle.h
#include<iostream>
using namespace std;
template<class T>
struct Node   //结点结构
{
    T data;   //结点数据
    Node*link;
    Node() { link = NULL; }
    Node(T e, Node*next = NULL)
    {
        data = e;
        link = next;
    }
};
template<class T>
class CircleLinkList
{     //不带表头结点的循环链表类
private:
    Node<T> *current, *front; //current指向某结点，front指向current前驱
public:
    CircleLinkList() :current(NULL), front(NULL) {} //构建空循环链表
    CircleLinkList(T *d, int  mSize); //利用d数组元素构建循环链表
    ~CircleLinkList();            //析构函数
    bool InsertAfter(const T&x);    //在current所指结点之后插入x
    bool RemoveCurrent(T&x);    //删除current所指结点
    void movenext(int n = 1);    //current后移n次
    T GetCurrentData() { return current->data; }
    bool toLocatioin(T &t);//让current指向t结点，若没有则current不移动
    void Output() const;    //输出循环链表
};  
class Joseph //    约瑟夫环类
{
private:
    int numOfBoy;  //圈中人数
    int startPosition;  //报数起始点
    int interval;     //报数间隔
public:
    Joseph(int boys, int start, int m) :
        numOfBoy(boys), startPosition(start), interval(m) {}//构造函数
    void setNumOfBoy(int num) { numOfBoy = num; }//重置圈中人数
    void setStartPosition(int start) { startPosition = start; }//重置起始点
    void setInterval(int inter) { interval = inter; }//重置报数间隔
    int GetWinner();//求得最终优胜者编号
    void print();   //输出约瑟夫环
};
template<class T>
CircleLinkList<T>::CircleLinkList(T *d, int  mSize)
{    //构造函数,将d数组中的mSize个元素创建循环链表
//采用前插法创建。
    int i;
    Node<T> *p;
    current = new Node<T>;
    current->data = d[mSize - 1];
    front = current;
    for (i = mSize - 2; i >= 0; i--)
    {
        p = new Node<T>(d[i], current);
        current = p;
    }
    front->link = current;
}
template<class T>
CircleLinkList<T>::~CircleLinkList()    //析构函数
{
    while (current != front)//销毁循环链表
    {
        Node<T> *r = current;
        current = current->link;
        delete r;
    }
    delete current;
}
template<class T>
bool CircleLinkList<T>::InsertAfter(const T&x)
//在current所指结点之后插入x,current指向x结点
{
    Node<T> *s = new Node<T>(x);
    if (!s)return false;
    if (!current)  //原循环链表为空
        current = front = s->link = s;
    else //原循环链表非空
    {
        s->link = current->link;
        current->link = s;
        front = current;
        current = s;
    }
    return true;
}
template<class T>
bool CircleLinkList<T>::RemoveCurrent(T&x) //删除current所指结点
{
    if (!current)//循环链表为空
        return false;
    x = current->data;
    if (current == front)//链表中只有一个元素
    {
        delete current;
        current = front = NULL;
    }
    else
    {
        front->link = current->link;//修改链表指针
        delete current;
        current = front->link;
    }
    return true;
}
template<class T>
void CircleLinkList<T>::Output() const     //输出循环链表
{
    if (!current)//循环链表为空
        return;
    Node<T> *p = current;
    do
    {
        cout << p->data << "  ";
        p = p->link;
    } while (p != current);
    cout << endl;
}
template<class T>
void CircleLinkList<T>::movenext(int k)    //current后移k次
{
    for (int i = 1; i <= k; i++)
    {
        front = current; // front后移
        current = current->link; //current后移
    }
}
template<class T>
bool CircleLinkList<T>::toLocatioin(T &t)
//将current指向元素为t的结点，若没有则current不移动
{
    if (!current)//循环链表为空
        return false;
    Node<T> *current1 = current, *front1 = front;
    while (current1->data != t) //寻找元素t
    {
        front1 = current1;
        current1 = current1->link;
        if (current1 == current)// 已寻找一圈没有元素为t的结点
            return false;
    }
    current = current1; //current指向元素为t的结点
    front = front1;
    return true;
}
int Joseph::GetWinner()//获得最终优胜者
{
    CircleLinkList<int> boys;
    for (int i = 0; i < numOfBoy; i++)//创建循环链表,编号依次为1~numOfBoy
    {
        int temp = i + 1;
        boys.InsertAfter(temp);
    }
    boys.toLocatioin(startPosition);   //找到报数起点
    cout << endl << "依次出列的小孩是：" << endl;
    for (int i = 1; i < numOfBoy; i++)   //numOfBoy-1个小孩出圈
    {
        int x;
        boys.movenext(interval - 1);  //报数
        boys.RemoveCurrent(x); //出圈
        cout << x << "  ";  //输出出圈编号
    }
    return boys.GetCurrentData();  //返回优胜者编号
}
void Joseph::print()   //输出约瑟夫环
{
    cout << "圈中人数:" << numOfBoy << endl;
    cout << "报数起始点:" << startPosition << endl;
    cout << "报数间隔:" << interval << endl;
}

测试代码

//测试代码.cpp
#include"Circle.h"
int main()
{
    int total, interv, startboy;
    cout << "请分别输入人数，起始号码和间隔数"<<endl;
    cin >> total >> startboy >> interv;
    Joseph jose(total, startboy, interv);
    jose.print();
    cout << "优胜者编号为： " << jose.GetWinner() << endl;
    system("pause");
    return 0;
}