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Find Minimum in Rotated Sorted Array

Medium
Binary Search

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 1

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

Example 2

Input: nums = [4,5,6,7,0,1,2]
Output: 0
Explanation: The original 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 original array was [11,13,15,17] and it was rotated 4 times (full rotation).

Constraints

  • •n == nums.length
  • •1 <= n <= 5000
  • •-5000 <= nums[i] <= 5000
  • •All the integers of nums are unique.
  • •nums is sorted and rotated between 1 and n times.
Show Hints (3)
Hint 1: The minimum element is the only element that is smaller than its previous element (the rotation point).
Hint 2: Compare the middle element with the rightmost element to determine which half contains the minimum.
Hint 3: If nums[mid] > nums[right], the minimum is in the right half. Otherwise, it is in the left half (including mid).
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