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"questionFrontendId": "837",
"categoryTitle": "Algorithms",
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"title": "New 21 Game",
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"content": "<p>Alice plays the following game, loosely based on the card game <strong>&quot;21&quot;</strong>.</p>\n\n<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>\n\n<p>Alice stops drawing numbers when she gets <code>k</code> <strong>or more points</strong>.</p>\n\n<p>Return the probability that Alice has <code>n</code> or fewer points.</p>\n\n<p>Answers within <code>10<sup>-5</sup></code> of the actual answer are considered accepted.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 10, k = 1, maxPts = 10\n<strong>Output:</strong> 1.00000\n<strong>Explanation:</strong> Alice gets a single card, then stops.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 6, k = 1, maxPts = 10\n<strong>Output:</strong> 0.60000\n<strong>Explanation:</strong> Alice gets a single card, then stops.\nIn 6 out of 10 possibilities, she is at or below 6 points.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 21, k = 17, maxPts = 10\n<strong>Output:</strong> 0.73278\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= k &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= maxPts &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
"translatedTitle": "新 21 点",
"translatedContent": "<p>爱丽丝参与一个大致基于纸牌游戏 <strong>“21点”</strong> 规则的游戏,描述如下:</p>\n\n<p>爱丽丝以 <code>0</code> 分开始,并在她的得分少于 <code>k</code> 分时抽取数字。 抽取时,她从 <code>[1, maxPts]</code> 的范围中随机获得一个整数作为分数进行累计,其中 <code>maxPts</code> 是一个整数。 每次抽取都是独立的,其结果具有相同的概率。</p>\n\n<p>当爱丽丝获得 <code>k</code> 分 <strong>或更多分</strong> 时,她就停止抽取数字。</p>\n\n<p>爱丽丝的分数不超过 <code>n</code> 的概率是多少?</p>\n\n<p>与实际答案误差不超过&nbsp;<code>10<sup>-5</sup></code> 的答案将被视为正确答案。</p>\n&nbsp;\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 10, k = 1, maxPts = 10\n<strong>输出:</strong>1.00000\n<strong>解释:</strong>爱丽丝得到一张牌,然后停止。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 6, k = 1, maxPts = 10\n<strong>输出:</strong>0.60000\n<strong>解释:</strong>爱丽丝得到一张牌,然后停止。 在 10 种可能性中的 6 种情况下,她的得分不超过 6 分。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 21, k = 17, maxPts = 10\n<strong>输出:</strong>0.73278\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= k &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= maxPts &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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