First Bad Version

https://leetcode.com/problems/first-bad-version/

Question

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.

Input: n = 5, bad = 4
Output: 4
Explanation:
call isBadVersion(3) -> false
call isBadVersion(5) -> true
call isBadVersion(4) -> true
Then 4 is the first bad version.

Answer

# The isBadVersion API is already defined for you.
# @param version, an integer
# @return an integer
# def isBadVersion(version):

class Solution:
    def firstBadVersion(self, n):
        """
        :type n: int
        :rtype: int
        """
        l, r = 0, n
        while l < r:
            mid = l + (r - l) // 2
            if isBadVersion(mid):
                r = mid
            else:
                l = mid + 1
        return l
        

First, we initialize left = 1 and right = n to include all possible values. Then we notice that we don't even need to design the condition function. It's already given by the isBadVersion API. Finding the first bad version is equivalent to finding the minimal k satisfying isBadVersion(k) is True. Our template can fit in very nicely:

In Python, we can use both l + r // 2 or l + (right - l) // 2.