題目

There is an integer array nums sorted in ascending order (with distinct values).

Prior to being passed to your function, nums is possibly rotated at an unknown pivot index k (1 <= k < nums.length) such that the resulting array is [nums[k], nums[k+1], ..., nums[n-1], nums[0], nums[1], ..., nums[k-1]]

Given the array nums after the possible rotation and an integer target, return the index of target if it is in nums, or -1 if it is not in nums.

You must write an algorithm with O(log n) runtime complexity.

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

Example 3:

Input: nums = [1], target = 0
Output: -1

Constraints:

• 1 <= nums.length <= 5000
• -10^4 <= nums[i] <= 10^4
• All values of nums are unique.
• nums is an ascending array that is possibly rotated.
• -10^4 <= target <= 10^4

思路

兩次二分查詢，第一次查詢陣列反轉的邊界，將陣列分隔為左右兩個陣列。在根據目標值的大小判斷是使用左陣列還是右陣列後，再進行一次二分查詢找出目標值的位置。

程式碼

python版本：

class Solution:
    def search(self, nums: List[int], target: int) -> int:
        l, r = 0, len(nums)
        while l < r:
            mid = (l+r)//2
            if nums[mid] >= nums[0]:
                l = mid+1
            else:
                r = mid
        if target >= nums[0]:
            l = 0
        else:
            r = len(nums)
        while l < r:
            mid = (l+r)//2
            if nums[mid] > target:
                r = mid
            elif nums[mid] < target:
                l = mid+1
            else:
                return mid
        return -1