1406.Stone Game III

1406.Stone Game III === ###### tags: `Hard`,`Array`,`Math`,`DP` [1406. Stone Game III](https://leetcode.com/problems/stone-game-iii/) ### 題目描述 Alice and Bob continue their games with piles of stones. There are several stones **arranged in a row**, and each stone has an associated value which is an integer given in the array `stoneValue`. Alice and Bob take turns, with Alice starting first. On each player's turn, that player can take `1`, `2`, or `3` stones from the **first** remaining stones in the row. The score of each player is the sum of the values of the stones taken. The score of each player is `0` initially. The objective of the game is to end with the highest score, and the winner is the player with the highest score and there could be a tie. The game continues until all the stones have been taken. Assume Alice and Bob **play optimally**. Return `"Alice"` *if Alice will win*, `"Bob"` *if Bob will win, or* `"Tie"` *if they will end the game with the same score*. ### 範例 **Example 1:** ``` Input: values = [1,2,3,7] Output: "Bob" Explanation: Alice will always lose. Her best move will be to take three piles and the score become 6. Now the score of Bob is 7 and Bob wins. ``` **Example 2:** ``` Input: values = [1,2,3,-9] Output: "Alice" Explanation: Alice must choose all the three piles at the first move to win and leave Bob with negative score. If Alice chooses one pile her score will be 1 and the next move Bob's score becomes 5. In the next move, Alice will take the pile with value = -9 and lose. If Alice chooses two piles her score will be 3 and the next move Bob's score becomes 3. In the next move, Alice will take the pile with value = -9 and also lose. Remember that both play optimally so here Alice will choose the scenario that makes her win. ``` **Example 3:** ``` Input: values = [1,2,3,6] Output: "Tie" Explanation: Alice cannot win this game. She can end the game in a draw if she decided to choose all the first three piles, otherwise she will lose. ``` **Constraints**: * 1 <= `stoneValue.length` <= 5 * 10^4^ * -1000 <= `stoneValue[i]` <= 1000 ### 解答 ### Reference [回到題目列表](https://hackmd.io/@Marsgoat/leetcode_every_day)