LC 33. Search in Rotated Sorted Array

问题描述

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

参考答案

class Solution {
public:
    int search(vector<int>& nums, int target) {
        if(nums.size() == 0) return -1;
        int l = 0;
        int r = nums.size()-1;
        while(l<r){
            int mid = (l+r)>>1;
            if(nums[l]<=nums[mid]){
                if(target<=nums[mid] && target >= nums[l]) r = mid;
                else l = mid +1;
            }else if(nums[mid]<nums[r]){
                if(target>nums[mid] && target <= nums[r]) l = mid +1;
                else r = mid;
            }
        }
        if(target == nums[l]) return r;
        return -1;
    }
};

答案描述

由于不知道序列是否有序，因此在进行二分搜索的时候，需要先确定在什么区间：

1. 低位< 中位：意味着从 低位 到 中位，一定是有序的。如果循环的连接点，没有过中位，那么中位海拔更低，低位海拔更高，这个时候，有序的数列在，

2. 中位<高位：之间，这一段里面就是有序的，因此可以在这个区间内进行搜索。

宗旨，时刻保持有序。