Description Link to heading

153. Find Minimum in Rotated Sorted Array (Medium)

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.

Solution Link to heading

The array after rotating is like the follow picture: Jyqb9sOfLdkolgc

We can use binary search ,int left = 0, right = nums.size(), n = nums.size(), if nusm[mid] <= nums[n - 1], mid >= k; otherwise, mid < k.

It also works for special cases.

Code Link to heading 

class Solution {
  public:
    int findMin(vector<int> &nums) {
        int n = nums.size();
        int left = 0, right = nums.size();
        while (left < right) {
            int mid = left + (right - left) / 2;
            if (nums[mid] <= nums[n - 1]) { // it means `mid >= k`
                right = mid;
            } else { // it means `mid < k`
                left = mid + 1;
            }
        }
        return nums[left % n];
    }
};