33. Search in Rotated Sorted Array(二分查找)

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


法1：将数组一分为二，其中一定有一个是有序的，另一个可能是有序，也能是部分有序。此时有序部分用二分法查找。无序部分再一分为二，其中一个一定有序，另一个可能有序，可能无序。就这样循环.

class Solution {
public:
    int search(vector<int>& nums, int target) {
        if(nums.size()==0) return -1;
        return bt_search(nums, 0,nums.size()-1,target);
    }
   
    int bt_search(vector<int>& a, int low, int high, int target) {
        int mid = low + (high - low) / 2;
        if(a[low]==target) return low;
        if(a[high]==target) return high;
        if(low>=high) return -1;



        if (a[low] < a[mid]) {
            if (a[low]  <target && target<  a[mid]) {    
                return bt_search(a, low+1, mid-1, target);
            }
            else {
                return bt_search(a,mid, high, target);
            }
        } else {
            if (a[mid] <target && target <a[high]) {    
                return bt_search(a, mid+1, high-1, target);
            }
            else {
                return bt_search(a,low, mid, target);
            }
        }
        return -1;
    }
};


从左向右，如果左边的点比右边的点小，说明这两个点之间是有序的。
　　　　　如果左边的点比右边的点大，说明中间有个旋转点，所以一分为二后，肯定有一半是有序的。所以还可以用二分法。
　　　　　　　　不过先要判断左边有序还是右边有序，如果左边有序，则直接将目标与左边的边界比较，就知道目标在不在左边，
　　　　　　　　如果不在左边肯定在右边。

 1 class Solution {
 2     public int search(int[] a, int target) {
 3         int n = a.length;
 4         int lo = 0;
 5         int hi = n - 1;
 6         while(lo<=hi){
 7             int mid = lo+(hi-lo)/2;
 8             if(a[mid]== target)
 9                 return mid;
10             
11             if(a[lo]<=a[mid]){//左半边有序
12                 if(a[lo]<=target && target<=a[mid])//目标值在左半边
13                     hi = mid - 1;
14                 else
15                     lo = mid + 1; 
16             }
17             else{//右半边有序
18                 if(a[mid]<=target && target<=a[hi])
19                     lo = mid + 1;
20                 else
21                     hi = mid - 1;
22             }
23         }
24         return -1;  
25         
26     }
27 }