278. First Bad Version

題目原文

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.

Example:

Given n = 5, and version = 4 is the first bad version.

call isBadVersion(3) -> false
call isBadVersion(5) -> true
call isBadVersion(4) -> true

Then 4 is the first bad version. 

解題思路

1. 線性搜尋法，Time Complexity O(n)

2. 二元搜尋法，Time Complexity O(logn)

3. 假設今天數值很大且每筆資料搜尋花費1秒，當資料為2^31 = 2147483648筆，那麼線性搜尋法Worst Case花費2147483648秒，相對二元搜尋法只需花費log(2147483648) = 9.33192986558秒。

4. 這就是為什麼資料結構和演算法如此重要。

程式解答

Linear Search [Time Limit Exceeded]

// Forward declaration of isBadVersion API.
bool isBadVersion(int version);

class Solution 
{
public:
    int firstBadVersion(int n) 
    {
        for (int i = 1; i <= n; i++)
            if (isBadVersion(i))
                return i;
    }
};

Binary Search

// Forward declaration of isBadVersion API.
bool isBadVersion(int version);

class Solution 
{
public:
    int firstBadVersion(int n) 
    {
        int left = 1;
        int mid = 0;
        int right = n;
        
        while (left < right)
        {
            mid = left + (right - left) / 2;
            if (isBadVersion(mid))
                right = mid;
            else
                left = mid + 1;
        }
        return left;
    }
};