Choose Exam Questions with Forced Skips

### Problem An exam contains questions in a fixed order. `questions[i] = [points, brainpower]` describes question `i`. Solving it earns `points` but prevents solving the next `brainpower` questions. You may instead skip it voluntarily and consider the following question. Return the largest total score you can earn while following these rules. ```cpp class Solution { public: long long mostPoints(vector<vector<int>>& questions); }; ``` ### Examples **Example 1:** ```text questions = [[5,1],[6,1],[4,1]] Output: 9 Explanation: Solve indices 0 and 2 for 5+4 points. ``` **Example 2:** ```text questions = [[2,3],[9,1],[3,1]] Output: 9 Explanation: Skipping index 0 and solving index 1 is best. ``` ### Constraints - `1 <= questions.length <= 10^5`. - Every row has two integers, each in `[1,10^5]`. ### Clarifying Questions The next candidate after solving i is i+brainpower+1. Forced skips beyond the end simply finish the exam. ```hint Inspect the structure What is the best score available from a suffix when its first question is either skipped or solved? ``` ### Reasoning checkpoints - Respect the forced skip after every solved question and distinguish it from a voluntary skip. - Prove that the chosen score is maximal over every valid sequence of solve-or-skip decisions. - Handle skips beyond the final question and scores that exceed 32-bit range. ### Optional extensions How could you also return one optimal set of solved question indices?