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39 lines
1.4 KiB
HTML
39 lines
1.4 KiB
HTML
<p>Alice and Bob take turns playing a game, with Alice starting first.</p>
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<p>Initially, there are <code>n</code> stones in a pile. On each player's turn, that player makes a <em>move</em> consisting of removing <strong>any</strong> non-zero <strong>square number</strong> of stones in the pile.</p>
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<p>Also, if a player cannot make a move, he/she loses the game.</p>
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<p>Given a positive integer <code>n</code>, return <code>true</code> if and only if Alice wins the game otherwise return <code>false</code>, assuming both players play optimally.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> n = 1
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<strong>Output:</strong> true
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<strong>Explanation: </strong>Alice can remove 1 stone winning the game because Bob doesn't have any moves.</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 2
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<strong>Output:</strong> false
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<strong>Explanation: </strong>Alice can only remove 1 stone, after that Bob removes the last one winning the game (2 -> 1 -> 0).
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 4
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<strong>Output:</strong> true
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<strong>Explanation:</strong> n is already a perfect square, Alice can win with one move, removing 4 stones (4 -> 0).
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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>1 <= n <= 10<sup>5</sup></code></li>
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</ul>
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