First Bad Version

You are a product manager and currently leading a team to develop a new product. Unfortunately, the latest version of your product fails the quality check. Since each version is developed based on the previous version, all the versions after a bad version are also bad.

Suppose you have n versions [1, 2, ..., n] and you want to find out the first bad one, which causes all the following ones to be bad.

You are given an API bool isBadVersion(version) which will return whether version is bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

二分搜索法

复杂度

时间 O(logN) 空间 O(1)

思路

因为一个版本是错误，其后面的所有版本都是错误的，所以我们可以用二分搜索，当取中点时，如果中点是错误版本，说明后面都是错误的，那第一个错误版本肯定在前面。如果中点不是错误版本，说明第一个错误版本肯定在后面。

注意

• 这里直接使用min <= max的二分模板，因为我们其实要找的是好和坏的分界点，即这个点既不是好也不是坏，所以是找不到的，按照模板的特点，最后退出循环时，max指向小于目标的点，min指向大于目标的点，这里第一个坏的version较大，所以返回min

代码

public class Solution extends VersionControl {
    public int firstBadVersion(int n) {
        int min = 1, max = n, mid = 0;
        while(min <= max){
            mid = min + (max - min) / 2;
            if(isBadVersion(mid)){
                max = mid - 1;
            } else {
                min = mid + 1;
            }
        }
        return min;
    }
}