mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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162 lines
16 KiB
JSON
162 lines
16 KiB
JSON
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"questionId": "1522",
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"title": "Stone Game III",
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"content": "<p>Alice and Bob continue their games with piles of stones. There are several stones <strong>arranged in a row</strong>, and each stone has an associated value which is an integer given in the array <code>stoneValue</code>.</p>\n\n<p>Alice and Bob take turns, with Alice starting first. On each player's turn, that player can take <code>1</code>, <code>2</code>, or <code>3</code> stones from the <strong>first</strong> remaining stones in the row.</p>\n\n<p>The score of each player is the sum of the values of the stones taken. The score of each player is <code>0</code> initially.</p>\n\n<p>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.</p>\n\n<p>Assume Alice and Bob <strong>play optimally</strong>.</p>\n\n<p>Return <code>"Alice"</code><em> if Alice will win, </em><code>"Bob"</code><em> if Bob will win, or </em><code>"Tie"</code><em> if they will end the game with the same score</em>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> values = [1,2,3,7]\n<strong>Output:</strong> "Bob"\n<strong>Explanation:</strong> 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.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> values = [1,2,3,-9]\n<strong>Output:</strong> "Alice"\n<strong>Explanation:</strong> Alice must choose all the three piles at the first move to win and leave Bob with negative score.\nIf 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.\nIf 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.\nRemember that both play optimally so here Alice will choose the scenario that makes her win.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> values = [1,2,3,6]\n<strong>Output:</strong> "Tie"\n<strong>Explanation:</strong> 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.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= stoneValue.length <= 5 * 10<sup>4</sup></code></li>\n\t<li><code>-1000 <= stoneValue[i] <= 1000</code></li>\n</ul>\n",
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"The game can be mapped to minmax game. Alice tries to maximize the total score and Bob tries to minimize it.",
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"Use dynamic programming to simulate the game. If the total score was 0 the game is \"Tie\", and if it has positive value then \"Alice\" wins, otherwise \"Bob\" wins."
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