LeetCode-278. First Bad Version

Description

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.

Solution 1(C++)

// Forward declaration of isBadVersion API.
bool isBadVersion(int version);

class Solution {
public:
    int firstBadVersion(int n) {
        int lower = 1, upper = n, mid;
        while(lower < upper) {
            mid = lower + (upper - lower) / 2;
            if(!isBadVersion(mid)) lower = mid + 1;   /* Only one call to API */
            else upper = mid;
        }
        return lower;   /* Because there will alway be a bad version, return lower here */
    }
};

算法分析

这一道题的算法其实也是二分法，但是细节地方不同，而算法的最终效果也与之前不同。所以有必要对于二分法进行专门的文章叙述。

程序分析

略。