Recognize a Rotation of Nondecreasing Values

### Problem Return whether `nums` can be obtained by rotating a nondecreasing array by some number of positions, including zero. Duplicate values are allowed. A rotation of A has entries `B[i] = A[(i+x) % A.length]` for one common shift x. ```cpp class Solution { public: bool check(vector<int>& nums); }; ``` ### Examples **Example 1:** ```text nums = [4,4,1,2,4] Output: true Explanation: It is a rotation of [1,2,4,4,4]. ``` **Example 2:** ```text nums = [3,1,4,2] Output: false Explanation: Circular traversal contains two descending transitions: 3 to 1 and 4 to 2. ``` ### Constraints - `1 <= nums.length <= 100`. - `1 <= nums[i] <= 100`. ### Clarifying Questions Nondecreasing allows equality. Include the last-to-first edge when analyzing the array circularly. ```hint Inspect the structure What does the supplied rotation definition permit when values are equal or the shift is zero? ``` ### Reasoning checkpoints - Establish both directions of the claimed rotation test. - Handle duplicate values and the circular boundary without changing the nondecreasing requirement. ### Optional extensions How would you return a valid rotation shift rather than just a Boolean?