约瑟夫环问题

问题描述：假设有N个小孩按照序号1，2，，，N围坐成一圈，从第一个小孩开始报数，每次报到n的人退出，接着从下一个人重新开始从1开始报数，下一次再报到n的人退出，求最后一个留下的人；

数组实现：

public class huan {



    /**

     * @param args

     */

    public static void main(String[] args) {

        String[] s = new String[]{"0a","1b","2c","3d","4e","5f","6g","7h","8i","9j","10k","11l","12m","13n","14o","15p"};

        int k = 3;

        while(s.length != 0){

            int i = 1;

            while(i <= 2){

                if(++k > s.length-1) {//循环n次的时候，每次递增时进行下表越界判断   或者k=k%(s.length)

                    k = 0;

                }

                if(s[k] != null) {

                    i++;

                }

            }

            System.out.print(s[k] + ' ');

            s[k] = null;

        }

    }

}

输出：5f 7h 9j 11l 13n 15p 1b 3d 6g 10k 14o 2c 8i 0a 12m 4e 

 

循环链表实现：

package com.iteye.ljmdbc7a;



import java.util.Scanner;



/**

 * 循环列表的Java实现，解决约瑟夫环问题

 * @author LIU

 *

 */

public class LinkedList

{

    //定义结点，必须是static

    static class Node

    {

        int data;

        Node next;

        Node(int arg1)

        {

            this.data = arg1;

        }

    }

    public static void main(String[] args)

    {

        int n = 0,m = 0;//定义总人数n，和出圈数字m

        //输入n和m

        System.out.println("输入总人数n，出圈数字m");

        Scanner scanner = new Scanner(System.in);

        n = scanner.nextInt();

        m = scanner.nextInt();

        

        //初始化循环列表,头结点first和尾结点p

        Node first = new Node(1);

        first.next = first;

        Node p = first;

        for(int i=2; i<=n; i++)

        {

            Node temp = new Node(i);

            temp.next = p;

            p.next = temp;

            p = p.next;

        }

        p.next = first;//尾接头形成循环链表（p为尾结点）

        

        //执行出圈操作

        System.out.println("出圈顺序为:");

        while(p != p.next)

        {

            //下面for循环后，p是第m个结点的前一个结点

            for(int i=1; i<m; i++)

                p = p.next;

            //删除第m个结点

            System.out.print(p.next.data+" ");

            p.next = p.next.next;

        }

        System.out.print("\n幸运者是:"+p.data);

    }

    

}