LC153 - Find Minimum in Rotated Sorted Array

Problem

Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array nums = [0,1,2,4,5,6,7] might become:

• [4,5,6,7,0,1,2] if it was rotated 4 times.

• [0,1,2,4,5,6,7] if it was rotated 7 times.

Notice that rotating an array [a[0], a[1], a[2], ..., a[n-1]] 1 time results in the array [a[n-1], a[0], a[1], a[2], ..., a[n-2]].

Given the sorted rotated array nums of unique elements, return the minimum element of this array.

You must write an algorithm that runs in O(log n) time.

Example

Input: nums = [3,4,5,1,2]

Output: 1

Explanation: The original array was [1,2,3,4,5] rotated 3 times.

Solution

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

def findMin(self, nums: List[int]) -> int: 
	left = 0
	right = len(nums) - 1
	
	while left < right:
		mid = (left + right) // 2
		if nums[mid] < nums[right]:
			right = mid
		else:
			left = mid + 1

	return nums[left]