# 33. Search in Rotated Sorted Array

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

# Solution

Approach 1: binary search -- there's a case where the array is rotated less than a half, and another case where it's rotated more than a half.

# Code (Python)

Approach 1:

class Solution:
    def search(self, nums, target):
        """
        :type nums: List[int]
        :type target: int
        :rtype: int
        """
        if not nums:
            return -1
        left, right = 0, len(nums) - 1
        while left < right:
            mid = (left + right) // 2
            for index in (left, mid, right):
                if target == nums[index]:
                    return index
            if nums[mid] > nums[right]:
                # example: [4,5,6,7,0,1,2]
                if nums[left] < target < nums[mid]:
                    right = mid - 1
                else:
                    left = mid + 1
            else:
                # example: [5,0,1,2,3]
                if nums[mid] < target < nums[right]:
                    left = mid + 1
                else:
                    right = mid - 1
        return left if nums[left] == target else -1

# Code (C++)

Approach 1:

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