leetcode-problemset/leetcode-cn/originData/split-the-array-to-make-coprime-products.json

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            "title": "Split the Array to Make Coprime Products",
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            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>\n\n<p>A <strong>split</strong> at an index <code>i</code> where <code>0 &lt;= i &lt;= n - 2</code> is called <strong>valid</strong> if the product of the first <code>i + 1</code> elements and the product of the remaining elements are coprime.</p>\n\n<ul>\n\t<li>For example, if <code>nums = [2, 3, 3]</code>, then a split at the index <code>i = 0</code> is valid because <code>2</code> and <code>9</code> are coprime, while a split at the index <code>i = 1</code> is not valid because <code>6</code> and <code>3</code> are not coprime. A split at the index <code>i = 2</code> is not valid because <code>i == n - 1</code>.</li>\n</ul>\n\n<p>Return <em>the smallest index </em><code>i</code><em> at which the array can be split validly or </em><code>-1</code><em> if there is no such split</em>.</p>\n\n<p>Two values <code>val1</code> and <code>val2</code> are coprime if <code>gcd(val1, val2) == 1</code> where <code>gcd(val1, val2)</code> is the greatest common divisor of <code>val1</code> and <code>val2</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/14/second.PNG\" style=\"width: 450px; height: 211px;\" />\n<pre>\n<strong>Input:</strong> nums = [4,7,8,15,3,5]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.\nThe only valid split is at index 2.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/14/capture.PNG\" style=\"width: 450px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> nums = [4,7,15,8,3,5]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> The table above shows the values of the product of the first i + 1 elements, the remaining elements, and their gcd at each index i.\nThere is no valid split.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
            "translatedTitle": "分割数组使乘积互质",
            "translatedContent": "<p>给你一个长度为 <code>n</code> 的整数数组 <code>nums</code> ，下标从 <strong>0</strong> 开始。</p>\n\n<p>如果在下标 <code>i</code> 处 <strong>分割</strong> 数组，其中 <code>0 &lt;= i &lt;= n - 2</code> ，使前 <code>i + 1</code> 个元素的乘积和剩余元素的乘积互质，则认为该分割 <strong>有效</strong> 。</p>\n\n<ul>\n\t<li>例如，如果 <code>nums = [2, 3, 3]</code> ，那么在下标 <code>i = 0</code> 处的分割有效，因为 <code>2</code> 和 <code>9</code> 互质，而在下标 <code>i = 1</code> 处的分割无效，因为 <code>6</code> 和 <code>3</code> 不互质。在下标 <code>i = 2</code> 处的分割也无效，因为 <code>i == n - 1</code> 。</li>\n</ul>\n\n<p>返回可以有效分割数组的最小下标 <code>i</code> ，如果不存在有效分割，则返回 <code>-1</code> 。</p>\n\n<p>当且仅当 <code>gcd(val1, val2) == 1</code> 成立时，<code>val1</code> 和 <code>val2</code> 这两个值才是互质的，其中 <code>gcd(val1, val2)</code> 表示 <code>val1</code> 和 <code>val2</code> 的最大公约数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/14/second.PNG\" style=\"width: 450px; height: 211px;\" /></p>\n\n<pre>\n<strong>输入：</strong>nums = [4,7,8,15,3,5]\n<strong>输出：</strong>2\n<strong>解释：</strong>上表展示了每个下标 i 处的前 i + 1 个元素的乘积、剩余元素的乘积和它们的最大公约数的值。\n唯一一个有效分割位于下标 2 。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/12/14/capture.PNG\" style=\"width: 450px; height: 215px;\" /></p>\n\n<pre>\n<strong>输入：</strong>nums = [4,7,15,8,3,5]\n<strong>输出：</strong>-1\n<strong>解释：</strong>上表展示了每个下标 i 处的前 i + 1 个元素的乘积、剩余元素的乘积和它们的最大公约数的值。\n不存在有效分割。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == nums.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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