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39 lines
2.2 KiB
HTML
39 lines
2.2 KiB
HTML
<p>You are given <strong>two identical</strong> eggs and you have access to a building with <code>n</code> floors labeled from <code>1</code> to <code>n</code>.</p>
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<p>You know that there exists a floor <code>f</code> where <code>0 <= f <= n</code> such that any egg dropped at a floor <strong>higher</strong> than <code>f</code> will <strong>break</strong>, and any egg dropped <strong>at or below</strong> floor <code>f</code> will <strong>not break</strong>.</p>
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<p>In each move, you may take an <strong>unbroken</strong> egg and drop it from any floor <code>x</code> (where <code>1 <= x <= n</code>). If the egg breaks, you can no longer use it. However, if the egg does not break, you may <strong>reuse</strong> it in future moves.</p>
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<p>Return <em>the <strong>minimum number of moves</strong> that you need to determine <strong>with certainty</strong> what the value of </em><code>f</code> is.</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 = 2
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> We can drop the first egg from floor 1 and the second egg from floor 2.
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If the first egg breaks, we know that f = 0.
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If the second egg breaks but the first egg didn't, we know that f = 1.
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Otherwise, if both eggs survive, we know that f = 2.
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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> n = 100
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<strong>Output:</strong> 14
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<strong>Explanation:</strong> One optimal strategy is:
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- Drop the 1st egg at floor 9. If it breaks, we know f is between 0 and 8. Drop the 2nd egg starting from floor 1 and going up one at a time to find f within 8 more drops. Total drops is 1 + 8 = 9.
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- If the 1st egg does not break, drop the 1st egg again at floor 22. If it breaks, we know f is between 9 and 21. Drop the 2nd egg starting from floor 10 and going up one at a time to find f within 12 more drops. Total drops is 2 + 12 = 14.
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- If the 1st egg does not break again, follow a similar process dropping the 1st egg from floors 34, 45, 55, 64, 72, 79, 85, 90, 94, 97, 99, and 100.
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Regardless of the outcome, it takes at most 14 drops to determine f.
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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 <= 1000</code></li>
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</ul>
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