LC033 - Search in Rotated Sorted Array

Problem

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]] (0-indexed). For example, [0,1,2,4,5,6,7] might be rotated at pivot index 3 and become [4,5,6,7,0,1,2].

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

Input: nums = [4,5,6,7,0,1,2], target = 0

Output: 4

Solution

Do a binary search. Time complexity is $O(\log n)$, no extra space used.

def search(self, nums: List[int], target: int) -> int:
	left = 0
	right = len(nums) - 1

	while left <= right:
		mid = (left + right) // 2
		if target == nums[mid]:
			return mid

	# left section
	if nums[left] <= nums[mid]:
		if target > nums[mid] or target < nums[left]:
			left = mid + 1
		else:
		# search left
			right = mid - 1

	# right section
	else:
		if target < nums[mid] or target > nums[right]:
			right = mid - 1
		else:
		# search right
			left = mid + 1
	
	# if not found
	return -1