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60 lines
2.9 KiB
HTML
60 lines
2.9 KiB
HTML
<p>Alice and Bob take turns playing a game, with <strong>Alice starting first</strong>.</p>
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<p>There are <code>n</code> stones arranged in a row. On each player's turn, while the number of stones is <strong>more than one</strong>, they will do the following:</p>
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<ol>
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<li>Choose an integer <code>x > 1</code>, and <strong>remove</strong> the leftmost <code>x</code> stones from the row.</li>
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<li>Add the <strong>sum</strong> of the <strong>removed</strong> stones' values to the player's score.</li>
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<li>Place a <strong>new stone</strong>, whose value is equal to that sum, on the left side of the row.</li>
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</ol>
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<p>The game stops when <strong>only</strong> <strong>one</strong> stone is left in the row.</p>
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<p>The <strong>score difference</strong> between Alice and Bob is <code>(Alice's score - Bob's score)</code>. Alice's goal is to <strong>maximize</strong> the score difference, and Bob's goal is the <strong>minimize</strong> the score difference.</p>
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<p>Given an integer array <code>stones</code> of length <code>n</code> where <code>stones[i]</code> represents the value of the <code>i<sup>th</sup></code> stone <strong>from the left</strong>, return <em>the <strong>score difference</strong> between Alice and Bob if they both play <strong>optimally</strong>.</em></p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> stones = [-1,2,-3,4,-5]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong>
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- Alice removes the first 4 stones, adds (-1) + 2 + (-3) + 4 = 2 to her score, and places a stone of
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value 2 on the left. stones = [2,-5].
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- Bob removes the first 2 stones, adds 2 + (-5) = -3 to his score, and places a stone of value -3 on
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the left. stones = [-3].
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The difference between their scores is 2 - (-3) = 5.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> stones = [7,-6,5,10,5,-2,-6]
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<strong>Output:</strong> 13
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<strong>Explanation:</strong>
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- Alice removes all stones, adds 7 + (-6) + 5 + 10 + 5 + (-2) + (-6) = 13 to her score, and places a
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stone of value 13 on the left. stones = [13].
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The difference between their scores is 13 - 0 = 13.
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</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> stones = [-10,-12]
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<strong>Output:</strong> -22
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<strong>Explanation:</strong>
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- Alice can only make one move, which is to remove both stones. She adds (-10) + (-12) = -22 to her
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score and places a stone of value -22 on the left. stones = [-22].
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The difference between their scores is (-22) - 0 = -22.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == stones.length</code></li>
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<li><code>2 <= n <= 10<sup>5</sup></code></li>
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<li><code>-10<sup>4</sup> <= stones[i] <= 10<sup>4</sup></code></li>
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</ul> |