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278 First Bad Version ​

题目 ​

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

Example 2:

Input: n = 1, bad = 1
Output: 1

 

Constraints:

  • 1 <= bad <= n <= 231 - 1
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    • 解法 ​

    注意 isBadVersion 的调用时机要越少越好

    py
    # leetcode submit region begin(Prohibit modification and deletion)
# The isBadVersion API is already defined for you.
# def isBadVersion(version: int) -> bool:

class Solution:
    # def __init__(self, bad: int):
    #     self.bad = bad

    # def isBadVersion(self, n: int):
    #     if n >= self.bad:
    #         return  True
    #     return False

    def firstBadVersion(self, n: int) -> int:
        start = 1
        end = n
        while start < end:
            mid = (start + end) // 2
            if isBadVersion(mid):
                end = mid
            else:
                start = mid + 1
        return end

        
# leetcode submit region end(Prohibit modification and deletion)

Solution(1).firstBadVersion(1)

    复杂度分析 ​

    • 时间复杂度O(Log N)
    • 空间复杂度O(1)