Josephus环的四种解法(约瑟夫环)基于java详解

public class 模拟 {
  public static void main(String[] args) {
    Scanner in=new Scanner(System.in);

    //总人数
    int n=in.nextInt();
    // 数到m的那个人出列
    int m=in.nextInt();
    // 初始化为0 都没有出去
    int [] arr=new int[n];

    //剩下的人数
    int peopleLeft=n;
    //初始化下标
    int index=0;
    // 下标计算器
    int count=0;
    // >0 出循环为负
    while (peopleLeft>1){
      if(arr[index]==0){
        // count为计步器 不是下标指向
        count++;
        if(count==m){
          arr[index]=1;
          count=0;
          peopleLeft--;
        }
      }
      index++;
      if(index==arr.length){
        index=0;
      }
    }
    for (int i = 0; i < arr.length; i++) {
      if(arr[i]==0){
        System.out.println(i+1);
      }
    }
  }
}

/**
   * 递归式:
   * f(1)=0; 第一个位置永远为0
   * f(i)=f(i)+m%n;
   */
  public static int yuesefu(int n,int m){
    if(n==1){
      return 0;
    }else {
      return (yuesefu(n-1,m) + m) % n;
    }
  }
  public static void main(String[] args) {
    System.out.println(yuesefu(41,3)+1);
    vailCode(41,3);
  }

  //逆推验证代码
  public static void vailCode(int a,int b){
    System.out.print(b);
    int reslut;
    for (int i = a; i >=2 ; i--) {
       reslut=2;
      for (int j = i; j <=a ; j++) {
        reslut=(reslut+b)%j;
      }
      System.out.printf("->%d",reslut+1);
    }
  }

public class CircularLinkedList {
  public static void main(String[] args) {
    /**
     * 节点类
     */
    class Node{
      private int data=1;
      private Node next;
      Node(){
        next=null;
      }
    }

    Node head,temp;
    head=new Node();
    head.data=1;

    int a=41;
    int b=3;
    // 临时节点
    temp=head;
    for (int i = 0; i < a; i++) {
      Node new_node=new Node();
      new_node.data=i+1;
      temp.next=new_node;
      temp=new_node;
    }
    temp.next=head.next;
    while (head.next!=head){
      for (int i = 0; i < b-1; i++) {
        head=head.next;
      }
      System.out.print("->"+(head.data+1));
      head.next=head.next.next;
    }
    System.out.println(head.data);
  }
}

public static void main(String[] args) {
    int a=41;
    int b=3;
    LinkedList<Integer> list = new LinkedList<>();
    for (int i = 0; i < a; i++) {
      list.add(i+1);
    }
    while (list.size()>1){
      for (int i = 0; i < b-1; i++) {
        list.add(list.remove());
      }
      System.out.print("->"+list.getFirst());
      list.remove();//remve head
    }
    System.out.println(list.getFirst());
  }