剑指offer | 约瑟夫环问题

约瑟夫环问题

0，1，2，...，n-1这n个数字排成一个圆圈，从数字0开始每次从这个圆圈里删除第m个数字，求最后一个数字

使用环形链表模拟圆圈

public class LastNumberInCircle {

    public int lastRemaining(int n, int m) {
        if (n < 1 || m <= 0) {
            throw new RuntimeException("invalid parameters");
        }

        if (n == 1) {
            return n;
        }

        List list = new LinkedList<>();
        for (int i = 0; i < n; i++) {
            list.add(i);
        }

        int start = 0;
        while (list.size() > 1) {
            start = start + m;
            start = start % list.size() - 1;
            if (start < 0) {
                list.remove(list.size() - 1);
                start = 0;
            } else {
                list.remove(start);
            }
        }
        return list.get(0);
    }
}

公式法

public class LastNumberInCircle {

    // 使用公式
    public int lastRemaining2(int n, int m) {
        if (n < 1 || m <= 0) {
            throw new RuntimeException("invalid parameters");
        }

        if (n == 1) {
            return n;
        }

        int last = 0;
        for (int i = 2; i <= n; i++) {
            last = (last + m) % i;
        }
        return last;
    }
}