> For the complete documentation index, see [llms.txt](https://protegejj.gitbook.io/algorithm-practice/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://protegejj.gitbook.io/algorithm-practice/leetcode/binary-search/278-first-bad-version.md).

# 278    First Bad Version

## 278. [First Bad Version](https://leetcode.com/problems/first-bad-version/description/)

## 1. 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 will return whether`version`is bad. Implement a function to find the first bad version. You should minimize the number of calls to the API.

## 2. Implementation

**(1) Binary Search**

思路：这题是关于git bisect的原理，本质是二分法找左边界问题，注意将数据转换成long类型，避免data overflow

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

public class Solution extends VersionControl {
    public int firstBadVersion(int n) {
        long start = 1, end = n, mid = 0;

        while (start + 1 < end) {
            mid = start + (end - start) / 2;

            if (!isBadVersion((int)mid)) {
                start = mid + 1;
            }
            else {
                end = mid;
            }
        }
        return isBadVersion((int)start) ? (int)start : (int)end;
    }
}
```

## 3. Time & Space Complexity

**Binary Search:** 时间复杂度O(logn), 空间复杂度O(1)


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://protegejj.gitbook.io/algorithm-practice/leetcode/binary-search/278-first-bad-version.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.