约瑟夫问题解答

2024年1月10日 177次阅读

问题：
编号为1,2，····n的n个人按顺时针做成一圈，一开始任选一个正整数作为报数的上限值m，从第一个人开始按顺时针方向自1开始顺时针报数，报到m时停止，这个人出列。从他在顺时针方向上的下一个人开始重新报数，如此下去，直至所有人出列。

下面是用STL中的list

#include <iostream>
#include <list>
#include <algorithm>
using namespace std;

int main()
{
    int i, m = 6,n=20;
    list<int> ilist;
    //下面是用链表解决约瑟夫环问题
    for (i = 1; i <= 20; i++)
        ilist.push_back(i);
    cout << "size= " << ilist.size() << endl;

    list<int> ::iterator ite;
    for (ite = ilist.begin(); ite != ilist.end(); ++ite)
        cout << *ite << ' ';
    cout << endl;
    //m %= n;这是错误的
    list<int>::iterator pit= ilist.begin();

    while (!ilist.empty())
    {
        int i = 1;
        for (; i < m; i++)
            if (++pit == ilist.end())
                pit = ilist.begin();
        printf("%d ", *pit);
        if((pit=ilist.erase())==ilist.end()) 
                     pit = ilist.begin();
       //cout << *(pit)<<endl;
       }

      system("pause");
}

//用自己的循环链表解决

#include < iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <climits>
using namespace std;

struct node {
    int data;
    node* next;
    node() { data = 0; next = nullptr; }
    node(int x) { data = x; next = nullptr; }
};

//下面是约瑟夫问题（循环链表的操作）
node* node_creat(int n)
{
    node* pRet = nullptr;
    if (n != 0)
    {
        int n_idx = 1;
        node* p_node = nullptr;
        p_node=new node[n];
        if (NULL==p_node )
        {
            return nullptr;
        }

        pRet=p_node;
        while (n_idx < n)
        {
            p_node->data = n_idx;
            p_node->next = p_node + 1;
            p_node = p_node->next;
            n_idx++;
        }
        p_node->data = n;
        p_node->next = pRet;
    }
    return pRet;
}
void Josephus()
{
    node* pList = NULL, *pIter = NULL;
    int n = 20, m = 6;

    pList = node_creat(n);

    pIter = pList;
    m %= n;
    while (pIter != pIter->next)
    {
        int i = 1;
        for (; i < m - 1; i++)
        {
            pIter = pIter->next;
        }
        //输出第m个节点
        printf("%d ", pIter->next->data);

        pIter->next = pIter->next->next;
        pIter = pIter->next;
    }
    printf("%d\n", pIter->data);
    delete []pList;//不要忘记释放内存

}

int main() {
    Josephus();

}
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