390 Elimination Game 淘汰游戏

详见：https://leetcode.com/problems/elimination-game/description/

C++：

方法一：

class Solution {
public:
    int lastRemaining(int n) {
        return help(n, true);
    }
    int help(int n, bool left2right)
    {
        if (n == 1)
        {
            return 1;
        }
        if (left2right)
        {
            return 2 * help(n / 2, false);
        }
        else
        {
            return 2 * help(n / 2, true) - 1 + n % 2;
        }
    }
};

方法二：

class Solution {
public:
    int lastRemaining(int n) {
        return n==1?1:2*(1+n/2-lastRemaining(n/2));
    }
};

方法三：

class Solution {
public:
    int lastRemaining(int n) {
        int base = 1, res = 1;
        while (base * 2 <= n)
        {
            res += base;
            base *= 2;
            if (base * 2 > n)
            {
                break;
            }
            if ((n / base) % 2 == 1)
            {
                res += base;
            }
            base *= 2;
        }
        return res;
    }
};

详见：https://www.cnblogs.com/grandyang/p/5860706.html