Find Minimum in Rotated Sorted Array
Difficulty: Medium
Category: DSA
Topics: Array, Binary Search
Asked at: Facebook, Amazon, Bloomberg, Goldman Sachs, Microsoft, Oracle
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.
```
**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.