二换一

a、b、c三个物品，两个可以换另一个，三个可以换一个奖品，求最多能换多少个奖品

class Solution {
public:
    int numberofprize(int a, int b, int c) {
        int lo = 0, hi = 1E9;
        int ret = 0;

        auto check = [&](int val) {
            int tmp = 0;
            int x = a, y = b, z = c;
            x -= val, y -= val, z -= val;
            if (x >= 0) tmp += x, x = 0;
            if (y >= 0) tmp += y, y = 0;
            if (z >= 0) tmp += z, z = 0;
            return tmp / 2 >= -(x + y + z);
        };

        while (lo <= hi) {
            int mid = (lo + hi) >> 1;
            if (check(mid)) {
                ret = mid;
                lo = mid + 1;
            }
            else {
                hi = mid - 1;
            }
        }
        return ret;
    }
};