mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-10 18:48:13 +08:00
193 lines
21 KiB
JSON
193 lines
21 KiB
JSON
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"title": "期望个数统计",
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"content": "English description is not available for the problem. Please switch to Chinese.",
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"translatedTitle": "期望个数统计",
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"translatedContent": "<p>某互联网公司一年一度的春招开始了，一共有 <code>n</code> 名面试者入选。每名面试者都会提交一份简历，公司会根据提供的简历资料产生一个预估的能力值，数值越大代表越有可能通过面试。</p>\n\n<p>小 A 和小 B 负责审核面试者，他们均有所有面试者的简历，并且将各自根据面试者能力值从大到小的顺序浏览。由于简历事先被打乱过，能力值相同的简历的出现顺序是从它们的全排列中<strong>等可能</strong>地取一个。现在给定 <code>n</code> 名面试者的能力值 <code>scores</code>，设 <code>X</code> 代表小 A 和小 B 的浏览顺序中出现在同一位置的简历数，求 <code>X</code> 的期望。</p>\n\n<p>提示：离散的非负随机变量的期望计算公式为 <img alt=\"1\" src=\"https://pic.leetcode.cn/1694957445-AweiqF-svg.svg\" style=\"width: 190px; height: 49px;\" />。在本题中，由于 <code>X</code> 的取值为 0 到 <code>n</code> 之间，期望计算公式可以是 <img alt=\"2\" src=\"https://pic.leetcode.cn/1694957449-DuBtfQ-svg1.svg\" style=\"width: 190px; height: 49px;\" />。</p>\n\n<p><strong>示例 1：</strong></p>\n\n<blockquote>\n<p>输入：<code>scores = [1,2,3]</code></p>\n\n<p>输出：<code>3</code></p>\n\n<p>解释：由于面试者能力值互不相同，小 A 和小 B 的浏览顺序一定是相同的。<code>X</code>的期望是 3 。</p>\n</blockquote>\n\n<p><strong>示例 2：</strong></p>\n\n<blockquote>\n<p>输入：<code>scores = [1,1]</code></p>\n\n<p>输出：<code>1</code></p>\n\n<p>解释：设两位面试者的编号为 0, 1。由于他们的能力值都是 1，小 A 和小 B 的浏览顺序都为从全排列 <code>[[0,1],[1,0]]</code> 中等可能地取一个。如果小 A 和小 B 的浏览顺序都是 <code>[0,1]</code> 或者 <code>[1,0]</code> ，那么出现在同一位置的简历数为 2 ，否则是 0 。所以 <code>X</code> 的期望是 (2+0+2+0) * 1/4 = 1</p>\n</blockquote>\n\n<p><strong>示例 3：</strong></p>\n\n<blockquote>\n<p>输入：<code>scores = [1,1,2]</code></p>\n\n<p>输出：<code>2</code></p>\n</blockquote>\n\n<p><strong>限制：</strong></p>\n\n<ul>\n\t<li><code>1 <= scores.length <= 10^5</code></li>\n\t<li><code>0 <= scores[i] <= 10^6</code></li>\n</ul>\n",
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