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.

Example 1:

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

Approach 1:

Iterate through array , on finding the first bad version , return that element.

Time : O(n)

Space : O(1)

Approach 2 :

More optimized log(n) approach.

Assuming every good versions as 0’s and bad elements as 1’s , then the array may be imagined as a sorted array. So this is what leads to idea of binary search. On finding the first version which is bad, the low pointer will be at the first bad version. So just return that index position.

Time : O(log(n))

Space : O(1)

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