Java | Josephu（約瑟夫）問題

Josephu問題

/*
 * Josephu問題：
 *  設編號爲1，2，...，n的n個人圍坐一圈，約定編號爲k（1 <= k <= n）的人從1開始報數，數到m的那個人出列，它的下一位
 *  又從1開始報數，數到m的那個人又出列，依此類推，直到所有人出列爲止，由此產生一個出隊編號的序列。
 *
 * 用一個不帶頭結點的循環鏈表來處理Josephu問題：
 *  構建一個單項的環形鏈表思路：
 *      1. 先創建第一個節點，讓first指向該節點，並形成環形
 *      2. 後面當我們每創建一個新的節點，就把該節點加入到已有的環形鏈表中即可
 *  遍歷環形鏈表
 *      1. 先讓一個輔助指針（變量）curBoy，指向first節點
 *      2. 然後通過一個while循環遍歷該環形鏈表即可
 * 舉例：
 *  n = 5，即有5個人
 *  k = 1，從第一個人開始報數
 *  m = 2，數2下
 *  出圈的順序：2 -> 4 -> 1 -> 5 -> 3
 */

Boy類

class Boy{
    private int id;
    private Boy next;

    public Boy(int id) {
        this.id = id;
    }

    public Boy(Boy boy) {
        this.id = boy.id;
    }

    public int getId() {
        return id;
    }

    public void setId(int id) {
        this.id = id;
    }

    public Boy getNext() {
        return next;
    }

    public void setNext(Boy next) {
        this.next = next;
    }

    @Override
    public String toString() {
        return "Boy{" +
                "id=" + id +
                '}';
    }
}

CircleSingleLinkedList類

class CircleSingleLinkedList{
    private Boy first = null;
    // 添加小孩節點，構建成一個環形鏈表
    public void addBoys(int nums){
        if (nums < 1)
            throw new RuntimeException("小孩數量有誤！");
        Boy boy = null;
        Boy curBoy = null;
        for (int i = 1; i <= nums; i++) {
            boy = new Boy(i);
            if (first == null){
                first = new Boy(boy);
                first.setNext(first);
                continue;
            }
            curBoy = first;
            while (curBoy.getNext().getId() != first.getId()){
                curBoy = curBoy.getNext();
            }
            curBoy.setNext(boy);
            boy.setNext(first);
        }
    }
    // 遍歷當前的環形鏈表
    public void showBoy(){
        Boy curBoy = first;
        System.out.println(first);
        while (curBoy.getNext() != null){
            curBoy = curBoy.getNext();
            if (curBoy.getId() == first.getId())
                return;
            System.out.println(curBoy);
        }
    }
    // 根據用戶的輸入，計算出小孩出圈的順序
    public void countBoy(int startId,int countNum,int nums){
        addBoys(nums);
//        showBoy();
        Boy curBoy = first;
        int count = 1;  // flag = 0時用於記錄是否開始遊戲，flag = 1時用於記錄是否到達countNum
        boolean startGame = false;   // 判斷是否開始遊戲，即第一次循環到編號startId的小孩
        while (curBoy.getNext() != null){
            curBoy = curBoy.getNext();
            if (curBoy.getNext().getId() == first.getId())
                break;
        }
        while (curBoy.getNext() != curBoy){
            if (!startGame && count == startId){
                count = 1;
                startGame = true;
            }
            if (startGame && count == countNum){
                System.out.println(curBoy.getNext() + "出圈");
                curBoy.setNext(curBoy.getNext().getNext());
                count = 1;
            }
            curBoy = curBoy.getNext();
            count ++;
        }
        System.out.println(curBoy + "出圈");
    }
}

代碼測試

@Test
public void test(){
    CircleSingleLinkedList circleSingleLinkedList = new CircleSingleLinkedList();
    circleSingleLinkedList.countBoy(1,2,5);
}

結果輸出

Boy{id=2}出圈
Boy{id=4}出圈
Boy{id=1}出圈
Boy{id=5}出圈
Boy{id=3}出圈