约瑟夫（Josephus）问题

来源：互联网发布：开票软件显示frm000012 编辑：程序博客网时间：2024/05/17 05:50

//所谓约瑟夫（Josephus）问题指的是假设有n个人围坐一圈，先由某个位置start的人站起来，并
//从后一个人开始报数，数到m的人就要站出来，然后从这个人的下一个人重新开始报数，再数到

//m的人站出来，一次重复下去，知道所有的人都站出来为止，则站出来的人的次序如何？

方法一：

#include<iostream>using namespace std;void Josephus(int n,int start,int m);//n人数，start开始位置int main(){int n,start,m;cin>>n;cin>>start;cin>>m;Josephus(n,start,m);cout<<endl;return 0;}void Josephus(int n,int start,int m){int *Array=new int [n];int i,count=n;for(i=0;i<n;i++)Array[i]=i+1;start--;//由于数组从0下标开始,方便输出，所以start-1while(count>1)//被除数不能为0{cout<<Array[start]<<"";for(i=start;i<count-1;i++)Array[i]=Array[i+1];start=(start-1+m)%(--count);//因为位置变了座椅start-1}cout<<Array[start]<<endl;}

方法二：

CircList.h

template<class T>struct CircLinkNode{T data;CircLinkNode *link;CircLinkNode(CircLinkNode<T>*next=0){link=next;}CircLinkNode(T x,CircLinkNode<T>*next=0){data=x;link=next;}bool operator ==(T x){return data==x?true:false;}bool operator !=(T x){return data!=x?true:false;}};template<class T>class CircList{private:CircLinkNode<T>*first,*tail;public:CircList();CircList(const T x);CircList(CircList<T>&L){first=L.first;tail=L.tail;}~CircList();int Length()const;bool IsEmpty(){return first->link==first?true:false;}CircList<T>*getHead()const;void setHead(CircList<T>*p);CircLinkNode<T>*Search(T x);CircLinkNode<T>*Locate(int i);T *getData(int i);bool Insert(int i,T x);bool Remove(int i,T&x);void Create(int n);void Output();void Josephus(int n,int start,int m);};template<class T>CircList<T>::CircList(){first=tail=new CircLinkNode<T>;first->link=first;}template<class T>CircList<T>::CircList(const T x){first=new CircLinkNode<T>;CircLinkNode<T>*p=new CircLinkNode<T>(x);first->link=p;p->link=first;tail=p;}template<class T>CircList<T>::~CircList(){CircLinkNode<T>*p;while(first->link!=first){p=first->link;first->link=p->link;delete p;}delete first;}template<class T>CircLinkNode<T>*CircList<T>::Search(T x){CircLinkNode<T>*current=first->link;while(current->link!=first&¤t!=x)current=current->link;if(current!=first)return current;return 0;}template<class T>void CircList<T>::Create(int n){int data=0;delete first;CircLinkNode<T>*current=first=tail=new CircLinkNode<T>;for(int i=0;i<n;i++){CircLinkNode<T>*p=new CircLinkNode<T>;p->data=++data;p->link=first;current->link=p;current=p;tail=p;}}template<class T>void CircList<T>::Output(){CircLinkNode<T>*current=first->link;while(current!=first){cout<<current->data<<"";current=current->link;}}template<class T>void CircList<T>::Josephus(int n,int start,int m){Create(n);int i;if(IsEmpty())return;first=first->link;tail->link=first;//构成没有表头的循环链for(i=1;i<start;i++){first=first->link;tail=tail->link;}while(!IsEmpty()){cout<<first->data<<"";tail->link=tail->link->link;delete first;first=tail->link;for(i=1;i<m;i++){first=first->link;tail=tail->link;}}cout<<first->data<<endl;}

#include"CircList.h"#include<iostream>using namespace std;void Josephus(int n,int start,int m);int main(){CircList<int>cl;int number,start,m;cout<<"input the number:";cin>>number;cout<<"input the start:";cin>>start;cout<<"input the m:";cin>>m;cl.Josephus(number,start,m);return 0;}

0 0