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# 面试题62

0,1,,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。求出这个圆圈里剩下的最后一个数字。

例如，0、1、2、3、4这5个数字组成一个圆圈，从数字0开始每次删除第3个数字，则删除的前4个数字依次是2、0、4、1，因此最后剩下的数字是3。

```
示例 1：

输入: n = 5, m = 3
输出: 3

示例 2：

输入: n = 10, m = 17
输出: 2
```

## 限制：

* 1 <= n <= 10^5
* 1 <= m <= 10^6

## Solutions

1. **Josephus problem**
2. reference: <https://blog.csdn.net/u011500062/article/details/72855826>
3. suppose the index(after the dead one) of the winner in the current round is `x`, since the dead one in the previous round is removed, all indexes after are moved forward(with modulo) `m` steps, thus the index of the winner in the previous round is `(x + m) % (size of previous round)`.

```cpp
class Solution {
public:
    int lastRemaining(int n, int m) {
        int index = 0;
        // prev round has size 2.
        for (int num = 2; num <= n; num++)
            index = (index + m) % num; 

        return index;
    }
};
```