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43 lines
1.5 KiB
HTML
43 lines
1.5 KiB
HTML
<p>Alice plays the following game, loosely based on the card game <strong>"21"</strong>.</p>
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<p>Alice starts with <code>0</code> points and draws numbers while she has less than <code>k</code> points. During each draw, she gains an integer number of points randomly from the range <code>[1, maxPts]</code>, where <code>maxPts</code> is an integer. Each draw is independent and the outcomes have equal probabilities.</p>
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<p>Alice stops drawing numbers when she gets <code>k</code> <strong>or more points</strong>.</p>
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<p>Return the probability that Alice has <code>n</code> or fewer points.</p>
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<p>Answers within <code>10<sup>-5</sup></code> of the actual answer are considered accepted.</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> n = 10, k = 1, maxPts = 10
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<strong>Output:</strong> 1.00000
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<strong>Explanation:</strong> Alice gets a single card, then stops.
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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> n = 6, k = 1, maxPts = 10
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<strong>Output:</strong> 0.60000
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<strong>Explanation:</strong> Alice gets a single card, then stops.
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In 6 out of 10 possibilities, she is at or below 6 points.
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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> n = 21, k = 17, maxPts = 10
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<strong>Output:</strong> 0.73278
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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>0 <= k <= n <= 10<sup>4</sup></code></li>
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<li><code>1 <= maxPts <= 10<sup>4</sup></code></li>
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</ul>
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