Josephus问题

n 个小孩围成一圈做游戏，游戏将决出一个胜利者。假定一个数 m ,从第 s 个小孩起顺时针计数，每数到第 m 个小孩时该小孩离开；接着又从下一个小孩开始数数，数到第 m 个小孩时该小孩也离开；如此不断反复进行，最后剩下的一个小孩便是胜利者。

对于一定的n、m 和 s,究竟谁是胜利者呢？

链表：

#include <iostream>#include <iomanip>using namespace std;struct Jose         //小孩结点{    int code;//小孩编号    Jose* pNext;//指向下一个小孩结点};int main(){    //赋初值    int nBoyNum,nInterval;    int i,j;    cout <<"please input the number of boys,\n"  //小孩数         <<"interval of counting:\n";  //数小孩个数    cin >>nBoyNum >>nInterval;    Jose *pHead,*pNew,*pTmp;    pHead = NULL;    for (i=0; i<nBoyNum; i++)    {        //创建新节点        pNew = new Jose;        if (pNew==NULL)        {            cout << "Can not new Jose!";            return -1;        }        pNew->code = i+1;        pNew->pNext = NULL;        if (pHead == NULL)            pHead = pNew;//插入到链表的头部        else        {            //找到尾结点            pTmp = pHead;            while (pTmp->pNext != NULL)                pTmp = pTmp->pNext;            pTmp->pNext = pNew;        }    }    pNew->pNext = pHead; // 构成循环链表    cout<<"The all Boys:";    pTmp = pHead;    while(pTmp->pNext != pHead)    {        cout<<pTmp->code<<",";        pTmp = pTmp->pNext;    }    cout<<pTmp->code<<endl;    Jose *pPrev,*pCur;    pCur = pPrev = pHead;    cout << "The leaving Boy:";    while (pCur->pNext != pCur)    {        for(j=0; j<nInterval-1; j++)        {            pPrev = pCur;            pCur = pCur->pNext;        }        // 删除        cout << pCur->code<<",";        pHead = pCur->pNext;        pPrev->pNext = pHead;        delete pCur;        pCur = pHead;    }    cout << "\nThe winner is "<<pCur->code<<endl;    return 0;}

// josephus problem procedural solving//当s=1的时候，i=1,i不小于s,所以不符合;#include<iostream>using namespace std;//-------------------------------------struct Jose // 小孩结点{    int code;            // 小孩编号    Jose* pNext;    // 指向下一个小孩结点};//-----------------------------------//-------------------------------------bool   GetValue(int &n,int &s, int &m);Jose*  CreateRing(Jose* pHead, int n, int s); // 创建循环链表Jose*  CountBoys(Jose *pHead, int m); // 数m个小孩Jose*  Process(Jose *pHead, int m);   // 排除n-1个小孩//-------------------------------------//-------------------------------------int main(){    int n, s, m;    Jose *pHead = NULL;    if (!GetValue(n,s,m))        return 0;    pHead = CreateRing(pHead, n, s);    pHead = Process(pHead,m);    cout<<"\nThe winner is "<<pHead->code<<"\n";    delete pHead;    return 1;}//------------------------------------bool GetValue(int &n, int &s, int &m){    cout <<"please input boyNumber, startPosition, intervalNumber:\n";    cin>>n>>s>>m;    if (n>=2 && s>=1 && s<=n && m>=1 && m<=n)        return true;    cerr<<"failed in bad boyNumber or startPosition or intervalNumber.\n";    //发给它的内容立即输出;    return false;    /*else    {        cout<<"failed in bad boyNumber or startPosition or intervalNumber.\n";        return false;    }*/}//------------------------------------Jose* CreateRing(Jose *pHead, int n,int s){    Jose *pCur,*pPrev;    for(int i=1; i<=n; i++)    {        // 创建新节点        pCur = new Jose;        pCur->code = i;        pCur->pNext = NULL;        // 将新节点加入链表        if (pHead == NULL)        {            pHead = pCur;            pPrev = pCur;        }        else        {            pPrev->pNext = pCur;            pPrev = pCur;        }    }//------------------------    pCur->pNext = pHead;  //构成循环链表    cout<<"There are "<<n<<" boys.\n";    pPrev = CountBoys(pHead,s);    pHead = pPrev->pNext;    return pHead;}//------------------------------------Jose * CountBoys(Jose* pHead, int m){    Jose *pCur,*pPrev;    if (pHead->pNext == pHead)        return pHead;    pCur  = pHead;    for(int i=1; i<m; i++)    {        pPrev = pCur;        pCur = pCur->pNext;    }    return pPrev;}//------------------------------------Jose* Process(Jose *pHead, int m){    Jose *pCur,*pPrev;    cout<<"Boys leaved in order:\n";    while(pHead->pNext != pHead)    {        pPrev = CountBoys(pHead, m);        pCur  = pPrev->pNext;        pHead = pCur->pNext;        static int line=0;        cout<<"  "<<pCur->code;        if(!(++line%10))            cout<<endl;        pPrev->pNext = pHead; //小孩脱链        delete pCur;    }    return pHead;}//====================================