First Bad Version

Problem

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

Binary Search: O(log n) time

/* The isBadVersion API is defined in the parent class VersionControl.
      boolean isBadVersion(int version); */
public class Solution {
    public int firstBadVersion(int n) {
        int start = 1, end = n;
        while (start < end) {
            int mid = start + (end - start) / 2; //avoid overflow 
            if (isBadVersion(mid)) end = mid;
            else start = mid + 1;
        }
        return end;
    }
}

Analysis

Typical binary search solution
We know if mid is not bad version, all the number from start to mid is not bad version either
Hence we set start = mid + 1 in that situation
Otherwise, we simply set end = mid because we need to return end at the end
If end happens to be the first bad version, start will be keep increased and eventually break the loop