:orphan:

Find Minimum in Rotated Sorted Array
====================================

.. highlight:: none

Problem
-------
https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/

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.

.. highlight:: python

Pattern
-------
Array, Binary Search

Approaches
----------

.. tab-set::

    .. tab-item:: Binary Search

        **Code**

        .. literalinclude:: ../problems/medium/find-minimum-in-rotated-sorted-array/find_minimum_in_rotated_sorted_array__binary_search.py
            :language: python
            :lines: 12-

        **Test**

        >>> from find_minimum_in_rotated_sorted_array__binary_search import findMin
        >>> findMin([3, 4, 5, 1, 2])
        1
        >>> findMin([4, 5, 6, 7, 0, 1, 2])
        0
        >>> findMin([11, 13, 15, 17])
        11

        .. autofunction:: find_minimum_in_rotated_sorted_array__binary_search.findMin