mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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190 lines
21 KiB
JSON
190 lines
21 KiB
JSON
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"categoryTitle": "Algorithms",
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"title": "Count Distinct Numbers on Board",
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"content": "<p>You are given a positive integer <code>n</code>, that is initially placed on a board. Every day, for <code>10<sup>9</sup></code> days, you perform the following procedure:</p>\n\n<ul>\n\t<li>For each number <code>x</code> present on the board, find all numbers <code>1 <= i <= n</code> such that <code>x % i == 1</code>.</li>\n\t<li>Then, place those numbers on the board.</li>\n</ul>\n\n<p>Return<em> the number of <strong>distinct</strong> integers present on the board after</em> <code>10<sup>9</sup></code> <em>days have elapsed</em>.</p>\n\n<p><strong>Note:</strong></p>\n\n<ul>\n\t<li>Once a number is placed on the board, it will remain on it until the end.</li>\n\t<li><code>%</code> stands for the modulo operation. For example, <code>14 % 3</code> is <code>2</code>.</li>\n</ul>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> Initially, 5 is present on the board. \nThe next day, 2 and 4 will be added since 5 % 2 == 1 and 5 % 4 == 1. \nAfter that day, 3 will be added to the board because 4 % 3 == 1. \nAt the end of a billion days, the distinct numbers on the board will be 2, 3, 4, and 5. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> \nSince 3 % 2 == 1, 2 will be added to the board. \nAfter a billion days, the only two distinct numbers on the board are 2 and 3. \n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 100</code></li>\n</ul>\n",
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"translatedTitle": "统计桌é<C592>¢ä¸Šçš„ä¸<C3A4>å<EFBFBD>Œæ•°å—",
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"translatedContent": "<p>ç»™ä½ ä¸€ä¸ªæ£æ•´æ•° <code>n</code> ，开始时，它放在桌é<C592>¢ä¸Šã€‚在 <code>10<sup>9</sup></code> 天内，æ¯<C3A6>天都è¦<C3A8>执行下述æ¥éª¤ï¼š</p>\n\n<ul>\n\t<li>对于出现在桌é<C592>¢ä¸Šçš„æ¯<C3A6>ä¸ªæ•°å— <code>x</code> ，找出符å<C2A6>ˆ <code>1 <= i <= n</code> 且满足 <code>x % i == 1</code> çš„æ‰€æœ‰æ•°å— <code>i</code> 。</li>\n\t<li>然å<C2B6>Žï¼Œå°†è¿™äº›æ•°å—放在桌é<C592>¢ä¸Šã€‚</li>\n</ul>\n\n<p>返回在 <code>10<sup>9</sup></code> 天之å<E280B9>Žï¼Œå‡ºçŽ°åœ¨æ¡Œé<C592>¢ä¸Šçš„ <strong>ä¸<C3A4>å<EFBFBD>Œ</strong> 整数的数目。</p>\n\n<p><strong>注æ„<C3A6>：</strong></p>\n\n<ul>\n\t<li>一旦数å—放在桌é<C592>¢ä¸Šï¼Œåˆ™ä¼šä¸€ç›´ä¿<C3A4>留直到结æ<E2809C>Ÿã€‚</li>\n\t<li><code>%</code> 表示å<C2BA>–ä½™è¿<C3A8>算。例如，<code>14 % 3</code> ç‰äºŽ <code>2</code> 。</li>\n</ul>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 5\n<strong>输出：</strong>4\n<strong>解释：</strong>最开始，5 在桌é<C592>¢ä¸Šã€‚ \n第二天，2 å’Œ 4 也出现在桌é<C592>¢ä¸Šï¼Œå› 为 5 % 2 == 1 且 5 % 4 == 1 。 \nå†<C3A5>过一天 3 也出现在桌é<C592>¢ä¸Šï¼Œå› 为 4 % 3 == 1 。 \n在å<C2A8><C3A5>亿天结æ<E2809C>Ÿæ—¶ï¼Œæ¡Œé<C592>¢ä¸Šçš„ä¸<C3A4>å<EFBFBD>Œæ•°å—有 2 ã€<C3A3>3 ã€<C3A3>4 ã€<C3A3>5 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 3 \n<strong>输出：</strong>2\n<strong>解释：</strong> \nå› ä¸º 3 % 2 == 1 ，2 也出现在桌é<C592>¢ä¸Šã€‚ \n在å<C2A8><C3A5>亿天结æ<E2809C>Ÿæ—¶ï¼Œæ¡Œé<C592>¢ä¸Šçš„ä¸<C3A4>å<EFBFBD>Œæ•°å—å<E28094>ªæœ‰ä¸¤ä¸ªï¼š2 å’Œ 3 。 \n</pre>\n\n<p> </p>\n\n<p><strong>æ<><C3A6>示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 100</code></li>\n</ul>\n",
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"For n > 2, n % (n - 1) == 1 thus n - 1 will be added on the board the next day.",
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"As the operations are performed for so long time, all the numbers lesser than n except 1 will be added to the board.",
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