mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
190 lines
21 KiB
JSON
190 lines
21 KiB
JSON
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"questionId": "1362",
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"questionFrontendId": "1227",
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"categoryTitle": "Algorithms",
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"boundTopicId": 37657,
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"title": "Airplane Seat Assignment Probability",
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"titleSlug": "airplane-seat-assignment-probability",
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"content": "<p><code>n</code> passengers board an airplane with exactly <code>n</code> seats. The first passenger has lost the ticket and picks a seat randomly. But after that, the rest of the passengers will:</p>\n\n<ul>\n\t<li>Take their own seat if it is still available, and</li>\n\t<li>Pick other seats randomly when they find their seat occupied</li>\n</ul>\n\n<p>Return <em>the probability that the </em><code>n<sup>th</sup></code><em> person gets his own seat</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 1.00000\n<strong>Explanation: </strong>The first person can only get the first seat.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 0.50000\n<strong>Explanation: </strong>The second person has a probability of 0.5 to get the second seat (when first person gets the first seat).\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n</ul>\n",
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"translatedTitle": "飞机座位分配概率",
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"translatedContent": "<p>有 <code>n</code> 位乘客即将登机，飞机正好有 <code>n</code> 个座位。第一位乘客的票丢了，他随便选了一个座位坐下。</p>\n\n<p>剩下的乘客将会：</p>\n\n<ul>\n\t<li>\n\t<p>如果他们自己的座位还空着，就坐到自己的座位上，</p>\n\t</li>\n\t<li>当他们自己的座位被占用时，随机选择其他座位</li>\n</ul>\n\n<p>第 <code>n</code> 位乘客坐在自己的座位上的概率是多少？</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 1\n<strong>输出：</strong>1.00000\n<strong>解释：</strong>第一个人只会坐在自己的位置上。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入:</strong> n = 2\n<strong>输出:</strong> 0.50000\n<strong>解释：</strong>在第一个人选好座位坐下后，第二个人坐在自己的座位上的概率是 0.5。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 10^5</code></li>\n</ul>\n",
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"Let f(n) denote the probability of the n-th person getting correct seat in n-person case, then:\r\n\r\nf(1) = 1 (base case, trivial)\r\nf(2) = 1/2 (also trivial)",
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"Try to calculate f(3), f(4), and f(5) using the base cases. What if the value of them?\r\nf(i) for i >= 2 will also be 1/2.",
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"Try to proof why f(i) = 1/2 for i >= 2."
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