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42 lines
1.7 KiB
HTML
42 lines
1.7 KiB
HTML
<p>You are given an array of integers <code>nums</code> represents the numbers written on a chalkboard.</p>
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<p>Alice and Bob take turns erasing exactly one number from the chalkboard, with Alice starting first. If erasing a number causes the bitwise XOR of all the elements of the chalkboard to become <code>0</code>, then that player loses. The bitwise XOR of one element is that element itself, and the bitwise XOR of no elements is <code>0</code>.</p>
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<p>Also, if any player starts their turn with the bitwise XOR of all the elements of the chalkboard equal to <code>0</code>, then that player wins.</p>
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<p>Return <code>true</code> <em>if and only if Alice wins the game, assuming both players play optimally</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> nums = [1,1,2]
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<strong>Output:</strong> false
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<strong>Explanation:</strong>
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Alice has two choices: erase 1 or erase 2.
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If she erases 1, the nums array becomes [1, 2]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 2 = 3. Now Bob can remove any element he wants, because Alice will be the one to erase the last element and she will lose.
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If Alice erases 2 first, now nums become [1, 1]. The bitwise XOR of all the elements of the chalkboard is 1 XOR 1 = 0. Alice will lose.
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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> nums = [0,1]
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<strong>Output:</strong> true
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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> nums = [1,2,3]
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<strong>Output:</strong> true
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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 <= nums.length <= 1000</code></li>
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<li><code>0 <= nums[i] < 2<sup>16</sup></code></li>
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</ul>
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