二分查找为什么不能使用(left+right)/2？

AI摘要：二分查找中，使用(left+right)/2计算中间值可能导致整数溢出，当left和right都很大时，其和可能超出int范围。应改用left + (right - left)/2来避免溢出问题。

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刚刚在刷力扣时，刷到了一个简单地二分查找问题。
但当我提交时发现，超出了时间限制。
经过检查发现是中值出现了问题，mid = (left+right)/2;

若使用(left+right)/2，因为java中int数据类型是32位的，数值超过32位就会被反转。eg：2147483647+1 = -2147483648。
所以，我们不应使用此方法。而是应该使用left + (right - left)/2 <= right
因为根据定义得left < right
所以，right - left > 0且 <= right。并且left + (right - left) = right
因此，left + (right - left)/2 <= right;

    /** 
 * Forward declaration of guess API.
 * @param  num   your guess
 * @return          -1 if num is higher than the picked number
 *                  1 if num is lower than the picked number
 *               otherwise return 0
 * int guess(int num);
 */

//二分查找
public class Solution extends GuessGame {
    public int guessNumber(int n) {
        int left = 1;
        int right = n;
        while(left <= right){
            int mid = left + (right - left)/2 <= right;
            //int mid = (left+right)/2;
            int result = guess(mid);
            if(result == 0){
                return mid;
            }
            else if(result == -1){
                right = mid - 1;
            }
            else if(result == 1){
                left = mid + 1;
            }
        }
        return -1;
    }
}