Winner of the Optimal One-to-Three Stone Game

### Problem Alice and Bob alternate taking the first 1,2,or 3 remaining stones, with Alice first. Each player adds the values taken to a score initially 0; stone values may be negative. All stones must eventually be taken. Assuming optimal play to maximize final score advantage, return "Alice","Bob",or "Tie" according to the final comparison. ```cpp class Solution { public: string stoneGameIII(vector<int>& stoneValue); }; ``` ### Examples **Example 1:** ```text Input: stoneValue = [2,2,2,7] Output: "Bob" Explanation: Taking three gives Alice6 and Bob7. Taking two lets Bob take the last two for9; taking one lets Bob take the remaining11. Alice's best option still loses. ``` **Example 2:** ```text Input: stoneValue = [-1,-1] Output: "Tie" Explanation: Alice takes one-1 and Bob must take the other, tying at-1. Taking both would make Alice lose-2 to0. ``` ### Constraints - stoneValue has length 1 to 50000. - Every stone value lies in `[-1000,1000]`. ### Contract considerations Only the winner label is returned; the optimal move sequence need not be unique. ```hint Read the boundary condition Both players respond optimally and all stones must be taken. Include negative values and each of the three possible result labels. ``` ### Boundary reminders Only the winner label is returned; the optimal move sequence need not be unique.