Choose a Maximum-Score Conflict-Free Team

### Problem Each player has the corresponding entries in `scores` and `ages`. A younger player conflicts with an older player only when the younger player’s score is strictly greater. Equal-age players never conflict. Choose a subset with no conflicting pair and return its maximum total score. ```cpp class Solution { public: int bestTeamScore(vector<int>& scores, vector<int>& ages); }; ``` ### Examples **Example 1:** ```text scores = [5,9,7], ages = [2,3,2] Output: 21 Explanation: Both age-2 scores are at most the age-3 score, so all players can join. ``` **Example 2:** ```text scores = [8,3,4], ages = [1,2,3] Output: 8 Explanation: The younger score-8 player conflicts with both older players; the older pair totals only 7. ``` ### Constraints - Both arrays have equal length in `[1,1000]`. - `1 <= scores[i] <= 10^6`. - `1 <= ages[i] <= 1000`. ### Clarifying Questions Age ties allow arbitrary score differences. A conflict requires a strict score advantage for the younger player. ```hint Inspect the structure Which equal-age or equal-score combinations are permitted by the exact conflict rule? ``` ### Reasoning checkpoints - Show that every selected pair of players obeys the exact age/score conflict rule. - Prove the maximum total without excluding legal equal-age or equal-score combinations. ### Optional extensions How could coordinate compression and a prefix-maximum tree accelerate the quadratic recurrence?