Leetcode 278. 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 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. 

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解题思路：

使用binary search, 即半分法。 保证算法复杂度为O(logn)。

注意： mid 没有直接写成 (left + right) / 2, 是因为可能会有溢出。写成left + (right - left) / 2, 虽然从数学公式上来看一样，但实际计算时有差异，不会有溢出。

也要注意是让你找第一个还是最后一个bad version

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Java code:

1. 

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

2. 九章算法模板写法（2016.1.14）

/* 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 start = 0;
        int end = n;
        int mid;
        while(start + 1 < end) {
            mid = start + (end - start) / 2;
            if(isBadVersion(mid)){
                end = mid;
            } else {
                start = mid;  
            }
        }
        if(isBadVersion(start)){
            return start;
        }
        return end;
    }
}

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3. 20160525 做题：

掌握原理，用最简单的例子去试边界情况。

（1）

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

public class Solution extends VersionControl {
    public int firstBadVersion(int n) {
        //use binary search 
        int left = 1;
        int right = n;
        while(left <= right) {
            int mid = left + (right - left) / 2;
            if(!isBadVersion(mid)) {
                left = mid + 1;
            }else {
                right = mid - 1;
            }
        }
        return left;
    }
}

(2)

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

public class Solution extends VersionControl {
    public int firstBadVersion(int n) {
        //use binary search 
        int left = 1;
        int right = n;
        while(left < right - 1) {  //when left neighours right, terminate
            int mid = left + (right - left) / 2;
            if(!isBadVersion(mid)) {
                left = mid + 1;
            }else {
                right = mid;
            }
        }
        if(isBadVersion(left)) {
            return left;
        }
        return right;
    }
}

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Reference:

1. http://www.cnblogs.com/yuzhangcmu/p/4161837.html

2. http://bookshadow.com/weblog/2015/09/07/leetcode-first-bad-version/

3. http://www.jiuzhang.com/solutions/first-bad-version/