Find Minimum in Rotated Sorted Array

Medium~25 min

Suppose an array of length n sorted in ascending order is rotated between 1 and n times. For example, the array [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[n-1]] by 1 position results in [a[n-1], a[0], a[1], ..., 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.

Examples

Example 1
Input: nums = [3, 4, 5, 1, 2]
Output: 1
Explanation: The original sorted array was [1, 2, 3, 4, 5] and it was rotated 3 times.
Example 2
Input: nums = [4, 5, 6, 7, 0, 1, 2]
Output: 0
Explanation: The original sorted array was [0, 1, 2, 4, 5, 6, 7] and it was rotated 4 times.
Example 3
Input: nums = [11, 13, 15, 17]
Output: 11
Explanation: The array was not rotated (or rotated n times), so the minimum is the first element.

Constraints

  • n == nums.length
  • 1 <= n <= 5000
  • -5000 <= nums[i] <= 5000
  • All values in nums are unique
  • nums is sorted and rotated between 1 and n times
  • Expected time complexity: O(log n)
Code
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Output

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