LeetCode 33. Search in Rotated Sorted Array

Description:Suppose an array sorted in ascending order is rotated at some pivot unknown to you beforehand.

(i.e., [0,1,2,4,5,6,7] might become [4,5,6,7,0,1,2]).

You are given a target value to search. If found in the array return its index, otherwise return -1.

You may assume no duplicate exists in the array.

Your algorithm’s runtime complexity must be in the order of O(log n).

Example 1:

Input: nums = [4,5,6,7,0,1,2], target = 0
Output: 4
Example 2:

Input: nums = [4,5,6,7,0,1,2], target = 3
Output: -1

解題思路：題目的大概意思是，一個遞增序列（不含重複數據）切成2半，前一半放到後面去組成新的序列，該序列有個特點，只有在分界點上遞減，其他都是遞增的。現在給定一個目標，找出該目標所在的位置，找不到返回-1。因爲要求時間複雜度爲O(log n)，所有得使用二分法，當前數組可以使用二分法。如果mid的數據等於target，則立即返回mid。如果left到mid的數據是連續遞增的，並且target在這個範圍內，則在該範圍內繼續使用二分法，如果不在該範圍內，則在mid到right使用二分法。如果left到mid數據不是連續遞增的，說明在mid到right是連續遞增的，如果target在mid到right範圍內，則繼續使用二分法，否則，在left到mid的範圍內使用二分法。最後都找不到的話，返回-1。

參考代碼：

int bin_search(int left, int right, vector<int> nums, int target) {
    //遞歸用if
    while (left <= right) {
        int mid = (left + right) / 2;
        if (target == nums[mid])
            return mid;
        if (nums[mid] >= nums[left] && target >= nums[left] && target < nums[mid]) {
            //return bin_search(left, mid - 1, nums, target);
            right = mid - 1;
        }
        else if (nums[mid] >= nums[left] && (target <= nums[left] || (target > nums[mid]))) {
            //return bin_search(mid + 1, right, nums, target);
            left = mid + 1;
        }
        else if (nums[mid] <= nums[left] && (target > nums[mid]) && target <= nums[right]) {
            //return bin_search(mid + 1, right, nums, target);
            left = mid + 1;
        }
        else {
            //return bin_search(left, mid-1, nums, target);
            right = mid - 1;
        }
        
    }
    return -1;
}
int MySolution::search(vector<int>& nums, int target) {
    return bin_search(0, nums.size() - 1, nums, target);
}

總結：最後發現遞歸和循環效率相差很大，這裏給出測試結果
使用循環二分查找：
Runtime: 4 ms, faster than 81.73% of C++ online submissions for Search in Rotated Sorted Array.
Memory Usage: 8.9 MB, less than 43.37% of C++ online submissions for Search in Rotated Sorted Array.

使用遞歸二分查找：
Runtime: 8 ms, faster than 15.65% of C++ online submissions for Search in Rotated Sorted Array.
Memory Usage: 10.7 MB, less than 6.03% of C++ online submissions for Search in Rotated Sorted Array.