Leetcode Q 69. Sqrt(x) - 为什么添加 () 超出时间限制，at -> int mid = (first + (last - first)) / 2;

Question

这段代码工作正常：//我使用二分搜索来查找它

class Solution {
public:
    int mySqrt(int x) {
        //base cases
        if( x==0){
            return x;
        }

        long long int first = 1, last = x;
        while(first <= last){
            int mid = first + (last - first) / 2;
            if(mid == x/mid){
                return mid;
            }
            else if(mid >( x /mid)){
                last = mid -1;
            }
            else{
                first = mid + 1;
            }
        }
        return last;
    }
};

但是如果我更换

int mid = first + (last - first) / 2;

至

int mid = (first + (last - first)) / 2;

那么就超出了时间限制，为什么呢？

Answer 1

first + (last - first) / 2

(1) 和

(first + (last - first)) / 2

(2) 不相等。您可能需要

(first + last) / 2

(3)。

first + (last - first) / 2 = (1)
first / 2 + last / 2 =
(first + last) / 2           (3)