Josephus 问题相关

package com.bupt.syc;

import java.util.Iterator;
import java.util.LinkedList;

import org.junit.Test;

public class Josephus {
    // 模拟解法
    public static int JosephusWinner(int M, int N) throws Exception {
        if (N < M) {
            throw new Exception("M should smaller than N");
        }
        int arr[] = new int[N];
        for (int i = 0; i < N; i++) {
            arr[i] = 1;
        }
        int cnt = 0, k = 0, j = 0;
        int num=-1;
        while(cnt<=N-1){
            if(arr[k]==1){
                j+=arr[k];
            }
            if(j==M){
                arr[k]=0;
                cnt++;
            }
        }
        return num;
    }
    //公式法
     //f(1)=0
    //f=(f+m)mod i (i>1)
    public static int JosephusWinner2(int M ,int N){
        int winner=0;
        for(int i=2;i<=N;i++){
            winner=(winner+M)%i;
        }
        return winner;
    }
    public static void JosephusWinner3(int M ,int N){
        LinkedList <Integer> linkedList=new LinkedList<Integer>();
        for(int i=0;i<N;i++){
            linkedList.add(i);
        }
        int num=0;
        while(linkedList.size()>1){
            Iterator iterator=linkedList.iterator();
            while(iterator.hasNext()){
                num++;
                iterator.next();
                if(num==M){
                    iterator.remove();
                    num=0;
                }
            }
        }
        if(linkedList.size()==1){
            System.out.println("winner is :"+linkedList.get(0));
        }
    }
    //题目：有N个人围成一圈，每人有一个编号，从编号为1的人开始，每隔M个出圈，按出圈次序排成一列，其编号刚好按顺序从1到M。 
    //要求：从键盘输入M，N，编程计算并输出这N个人原来在圈中的位置。
    public static void reverseJosephusWinner(int M,int N){
        LinkedList <Integer> linkedList=new LinkedList<Integer>();
        for(int i=0;i<N;i++){
            linkedList.add(0);
        }
        int num=1;
        int cnt=0;
        int index=0;
        while(num<=N){
            if(linkedList.get(index)==0){
                cnt++;
            }
            if(cnt==M&&linkedList.get(index)==0){
                linkedList.set(index, num);
                num++;
                cnt=0;
                for(int i=0;i<N;i++){
                    System.out.print(linkedList.get(i)+" ");
                }
                System.out.println();
            }
            if(index+1>N-1) index=0;
            else index++;
        }
    }
    public static void main(String args[]) {
         JosephusWinner3(5,9);
        reverseJosephusWinner(5,9);
    }
}