Find Minimum in Rotated Sorted Array
01 · 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.
02 · Examples
nums = [3,4,5,1,2]
1
The original array was [1,2,3,4,5] rotated 3 times.
nums = [4,5,6,7,0,1,2]
0
The original array was [0,1,2,4,5,6,7] and it was rotated 4 times.
nums = [11,13,15,17]
11
The original array was [11,13,15,17] and it was rotated 4 times (full rotation).
03 · Constraints
- 01n == nums.length
- 021 <= n <= 5000
- 03-5000 <= nums[i] <= 5000
- 04All the integers of nums are unique.
- 05nums is sorted and rotated between 1 and n times.
04 · Optimal complexity
- Time
- O(log n)
- Space
- O(1)
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