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.

题目分析

在一个升序数组中寻找一个target的位置，这个升序数组可能经过了轮换。一开始以为是找出轮换前的位置，后来发现就是找轮转后的位置。利用二分法，先找到最小值得坐标，然后通过坐标转换进行查找。

代码

class Solution {
public:
    int search(int A[], int n, int target) {
        int lo=0,hi=n-1;
        // find the index of the smallest value using binary search.
        // Loop will terminate since mid < hi, and lo or hi will shrink by at least 1.
        // Proof by contradiction that mid < hi: if mid==hi, then lo==hi and loop would have been terminated.
        while(lo<hi){
            int mid=(lo+hi)/2;
            if(A[mid]>A[hi]) lo=mid+1;
            else hi=mid;
        }
        // lo==hi is the index of the smallest value and also the number of places rotated.
        int rot=lo;
        lo=0;hi=n-1;
        // The usual binary search and accounting for rotation.
        while(lo<=hi){
            int mid=(lo+hi)/2;
            int realmid=(mid+rot)%n;
            if(A[realmid]==target)return realmid;
            if(A[realmid]<target)lo=mid+1;
            else hi=mid-1;
        }
        return -1;
    }
};

其实也可以把这个数组转换成原始数组，然后利用二分查找搜索。

Search in Rotated Sorted Array II

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).

Write a function to determine if a given target is in the array.

The array may contain duplicates.

代码

核心还是二分法，判断mid和low的关系，如果mid>low则说明在这个范围内是递增的，反之在mid到high之间的范围是递增的，然后继续二分搜索就行。

class Solution {
public:
    bool search(vector<int>& nums, int target) {
        int left = 0, right =  nums.size()-1, mid;
        
        while(left<=right)
        {
            mid = (left + right) >> 1;
            if(nums[mid] == target) return true;

            // the only difference from the first one, trickly case, just updat left and right
            if( (nums[left] == nums[mid]) && (nums[right] == nums[mid]) ) {++left; --right;}

            else if(nums[left] <= nums[mid])
            {
                if( (nums[left]<=target) && (nums[mid] > target) ) right = mid-1;
                else left = mid + 1; 
            }
            else
            {
                if((nums[mid] < target) &&  (nums[right] >= target) ) left = mid+1;
                else right = mid-1;
            }
        }
        return false;
    }
};