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{
"data": {
"question": {
"questionId": "1307",
"questionFrontendId": "1201",
"categoryTitle": "Algorithms",
"boundTopicId": 28485,
"title": "Ugly Number III",
"titleSlug": "ugly-number-iii",
"content": "<p>An <strong>ugly number</strong> is a positive integer that is divisible by <code>a</code>, <code>b</code>, or <code>c</code>.</p>\n\n<p>Given four integers <code>n</code>, <code>a</code>, <code>b</code>, and <code>c</code>, return the <code>n<sup>th</sup></code> <strong>ugly number</strong>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3, a = 2, b = 3, c = 5\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The ugly numbers are 2, 3, 4, 5, 6, 8, 9, 10... The 3<sup>rd</sup> is 4.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 4, a = 2, b = 3, c = 4\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The ugly numbers are 2, 3, 4, 6, 8, 9, 10, 12... The 4<sup>th</sup> is 6.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, a = 2, b = 11, c = 13\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> The ugly numbers are 2, 4, 6, 8, 10, 11, 12, 13... The 5<sup>th</sup> is 10.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, a, b, c &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= a * b * c &lt;= 10<sup>18</sup></code></li>\n\t<li>It is guaranteed that the result will be in range <code>[1, 2 * 10<sup>9</sup>]</code>.</li>\n</ul>\n",
"translatedTitle": "丑数 III",
"translatedContent": "<p>丑数是可以被&nbsp;<code>a</code>&nbsp;<strong>或</strong>&nbsp;<code>b</code>&nbsp;<strong>或</strong> <code>c</code>&nbsp;整除的 <strong>正整数</strong> 。</p>\n\n<p>给你四个整数:<code>n</code> 、<code>a</code> 、<code>b</code> 、<code>c</code> ,请你设计一个算法来找出第&nbsp;<code>n</code>&nbsp;个丑数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 3, a = 2, b = 3, c = 5\n<strong>输出:</strong>4\n<strong>解释:</strong>丑数序列为 2, 3, 4, 5, 6, 8, 9, 10... 其中第 3 个是 4。</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 4, a = 2, b = 3, c = 4\n<strong>输出:</strong>6\n<strong>解释:</strong>丑数序列为 2, 3, 4, 6, 8, 9, 10, 12... 其中第 4 个是 6。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>n = 5, a = 2, b = 11, c = 13\n<strong>输出:</strong>10\n<strong>解释:</strong>丑数序列为 2, 4, 6, 8, 10, 11, 12, 13... 其中第 5 个是 10。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n, a, b, c &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= a * b * c &lt;= 10<sup>18</sup></code></li>\n\t<li>本题结果在&nbsp;<code>[1,&nbsp;2 * 10<sup>9</sup>]</code>&nbsp;的范围内</li>\n</ul>\n",
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"Write a function f(k) to determine how many ugly numbers smaller than k. As f(k) is non-decreasing, try binary search.",
"Find all ugly numbers in [1, LCM(a, b, c)] (LCM is Least Common Multiple). Use inclusion-exclusion principle to expand the result."
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