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 havenversions[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 APIbool isBadVersion(version)which will return whetherversionis bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

Example:

Given n = 5, and version = 4 is the first bad version.


call isBadVersion(3) -
>
 false
call isBadVersion(5) -
>
 true
call isBadVersion(4) -
>
 true

Then 4 is the first bad version.

Analysis

Since we need to check current index and its immediate right (or left) neighbor, so intuition is to consider using Template #2, or Template #3. But actually using Template #1 also works, the low is the index we need.

How to prove / check if the result would be right as first bad version?

A helpful tip to quickly prove the correctness of your binary search algorithm during an interview. We just need to test an input of size 2. Check if it reduces the search space to a single element (which must be the answer) for both of the scenarios above. If not, your algorithm will never terminate.

Initialization:

In our case, we indicate leftleft and rightright as the boundary of our search space (both inclusive). This is why we initialize left = 1 and right = n.

Example

F T

Solution

Using Binary Search Template #1

public class Solution extends VersionControl {
    public int firstBadVersion(int n) {
        int lo = 1;
        int hi = n;

        while (lo <= hi) {
            int mid = lo + (hi - lo) / 2;
            if (isBadVersion(mid)) {
                hi = mid - 1;
            }
            else {
                lo = mid + 1;
            }
        }

        return lo;
    }
}

Using Binary Search Template #2

public int firstBadVersion(int n) {
    int left = 1;
    int right = n;
    while (left < right) {
        int mid = left + (right - left) / 2;
        if (isBadVersion(mid)) {
            right = mid;
        } else {
            left = mid + 1;
        }
    }
    return left;
}

Using Binary Search Template #3

/* 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 left = 1, right = n;
        while (left + 1 < right) {
            int mid = left + (right - left) / 2;
            if (isBadVersion(mid)) {
                right = mid;
            } else {
                left = mid;
            }
        }
        // left + 1 == right or left + 1 > right
        if (isBadVersion(left) ) {
            return left;
        } else if (isBadVersion(right)) {
            return right;
        }
        return -1;
    }
}