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59 lines
2.8 KiB
HTML
59 lines
2.8 KiB
HTML
<p>Alice and Bob take turns playing a game, with <strong>Alice</strong><strong> starting first</strong>.</p>
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<p>You are given a string <code>num</code> of <strong>even length</strong> consisting of digits and <code>'?'</code> characters. On each turn, a player will do the following if there is still at least one <code>'?'</code> in <code>num</code>:</p>
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<ol>
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<li>Choose an index <code>i</code> where <code>num[i] == '?'</code>.</li>
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<li>Replace <code>num[i]</code> with any digit between <code>'0'</code> and <code>'9'</code>.</li>
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</ol>
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<p>The game ends when there are no more <code>'?'</code> characters in <code>num</code>.</p>
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<p>For Bob to win, the sum of the digits in the first half of <code>num</code> must be <strong>equal</strong> to the sum of the digits in the second half. For Alice to win, the sums must <strong>not be equal</strong>.</p>
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<ul>
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<li>For example, if the game ended with <code>num = "243801"</code>, then Bob wins because <code>2+4+3 = 8+0+1</code>. If the game ended with <code>num = "243803"</code>, then Alice wins because <code>2+4+3 != 8+0+3</code>.</li>
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</ul>
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<p>Assuming Alice and Bob play <strong>optimally</strong>, return <code>true</code> <em>if Alice will win and </em><code>false</code> <em>if Bob will win</em>.</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> num = "5023"
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<strong>Output:</strong> false
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<strong>Explanation:</strong> There are no moves to be made.
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The sum of the first half is equal to the sum of the second half: 5 + 0 = 2 + 3.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> num = "25??"
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<strong>Output:</strong> true
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<strong>Explanation: </strong>Alice can replace one of the '?'s with '9' and it will be impossible for Bob to make the sums equal.
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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> num = "?3295???"
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<strong>Output:</strong> false
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<strong>Explanation:</strong> It can be proven that Bob will always win. One possible outcome is:
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- Alice replaces the first '?' with '9'. num = "93295???".
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- Bob replaces one of the '?' in the right half with '9'. num = "932959??".
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- Alice replaces one of the '?' in the right half with '2'. num = "9329592?".
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- Bob replaces the last '?' in the right half with '7'. num = "93295927".
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Bob wins because 9 + 3 + 2 + 9 = 5 + 9 + 2 + 7.
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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>2 <= num.length <= 10<sup>5</sup></code></li>
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<li><code>num.length</code> is <strong>even</strong>.</li>
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<li><code>num</code> consists of only digits and <code>'?'</code>.</li>
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</ul>
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