leetcode-problemset/leetcode-cn/originData/ugly-number-iii.json

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            "title": "Ugly Number III",
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            "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>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>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>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>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 <code>n</code> 个丑数。</p>\n\n<p>丑数是可以被 <code>a</code> <strong>或</strong> <code>b</code> <strong>或</strong> <code>c</code> 整除的 <strong>正整数</strong> 。</p>\n\n<p> </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><strong>示例 4：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 1000000000, a = 2, b = 217983653, c = 336916467\n<strong>输出：</strong>1999999984\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n, a, b, c <= 10^9</code></li>\n\t<li><code>1 <= a * b * c <= 10^18</code></li>\n\t<li>本题结果在 <code>[1, 2 * 10^9]</code> 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.",
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