Find a Strictly Increasing Subsequence with Limited Numeric Steps

### Problem Choose a subsequence of `nums` that is strictly increasing and whose neighboring retained values differ by at most k. Return its maximum length, retaining original index order while permitting skipped positions. ```cpp class Solution { public: int lengthOfLIS(vector<int>& nums, int k); }; ``` ### Examples **Example 1:** ```text Input: nums = [1,3,2,4], k = 2 Output: 3 Explanation: Both [1,3,4] and [1,2,4] work. All four values are not increasing. ``` **Example 2:** ```text Input: nums = [2,2,3], k = 1 Output: 2 Explanation: Equal 2 values cannot extend a strictly increasing subsequence, but either occurrence can precede 3. ``` ### Constraints - `1 <= nums.length <= 100000`. - `1 <= nums[i], k <= 100000`. ### Clarifying Questions - May equal values appear consecutively in the selected subsequence? No; increase is strict. - Can positions be skipped? Yes, while keeping their original order. - Is a gap equal to `k` allowed? Yes. - Is the bound on adjacent selected values or all pairs? Adjacent selected values. ```hint Check the boundary Check repeated values and a numeric gap exactly equal to `k`. ```