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 returns whether version is bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

Solution:

You could start from the beginning and do a linear search thorugh your product versions one by one until you land on the bad one however if consider that you have a 2500 product versions, if it takes one minute to search and test one version, it would therefore take you almost 2 days to arrive to answer in the worst-case scenario that the first bad version is at n-2 position. Time Complexity : O(N)

We can do better with the Binary Search Algorithm

/* The isBadVersion API is defined in the parent class VersionControl.
      boolean isBadVersion(int version); */

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

Time Complexity: O(logN)