leetcode-problemset/leetcode-cn/originData/minimum-number-of-operations-to-make-all-array-elements-equal-to-1.json

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            "categoryTitle": "Algorithms",
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            "title": "Minimum Number of Operations to Make All Array Elements Equal to 1",
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            "content": "<p>You are given a <strong>0-indexed</strong>&nbsp;array <code>nums</code> consisiting of <strong>positive</strong> integers. You can do the following operation on the array <strong>any</strong> number of times:</p>\n\n<ul>\n\t<li>Select an index <code>i</code> such that <code>0 &lt;= i &lt; n - 1</code> and replace either of&nbsp;<code>nums[i]</code> or <code>nums[i+1]</code> with their gcd value.</li>\n</ul>\n\n<p>Return <em>the <strong>minimum</strong> number of operations to make all elements of </em><code>nums</code><em> equal to </em><code>1</code>. If it is impossible, return <code>-1</code>.</p>\n\n<p>The gcd of two integers is the greatest common divisor of the two integers.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,6,3,4]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> We can do the following operations:\n- Choose index i = 2 and replace nums[2] with gcd(3,4) = 1. Now we have nums = [2,6,1,4].\n- Choose index i = 1 and replace nums[1] with gcd(6,1) = 1. Now we have nums = [2,1,1,4].\n- Choose index i = 0 and replace nums[0] with gcd(2,1) = 1. Now we have nums = [1,1,1,4].\n- Choose index i = 2 and replace nums[3] with gcd(1,4) = 1. Now we have nums = [1,1,1,1].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,10,6,14]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It can be shown that it is impossible to make all the elements equal to 1.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 50</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n\n<p>&nbsp;</p>\n<p><b>Follow-up:</b></p>\n\n<p>The <code>O(n)</code> time complexity&nbsp;solution works, but could you find an <code>O(1)</code> constant time complexity solution?</p>\n",
            "translatedTitle": "使数组所有元素变成 1 的最少操作次数",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的 <strong>正</strong>&nbsp;整数数组&nbsp;<code>nums</code>&nbsp;。你可以对数组执行以下操作 <strong>任意</strong>&nbsp;次：</p>\n\n<ul>\n\t<li>选择一个满足&nbsp;<code>0 &lt;= i &lt; n - 1</code>&nbsp;的下标 <code>i</code>&nbsp;，将&nbsp;<code>nums[i]</code> 或者&nbsp;<code>nums[i+1]</code>&nbsp;两者之一替换成它们的最大公约数。</li>\n</ul>\n\n<p>请你返回使数组 <code>nums</code>&nbsp;中所有元素都等于 <code>1</code>&nbsp;的 <strong>最少</strong>&nbsp;操作次数。如果无法让数组全部变成 <code>1</code>&nbsp;，请你返回 <code>-1</code>&nbsp;。</p>\n\n<p>两个正整数的最大公约数指的是能整除这两个数的最大正整数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><b>输入：</b>nums = [2,6,3,4]\n<b>输出：</b>4\n<b>解释：</b>我们可以执行以下操作：\n- 选择下标 i = 2 ，将 nums[2] 替换为 gcd(3,4) = 1 ，得到 nums = [2,6,1,4] 。\n- 选择下标 i = 1 ，将 nums[1] 替换为 gcd(6,1) = 1 ，得到 nums = [2,1,1,4] 。\n- 选择下标 i = 0 ，将 nums[0] 替换为 gcd(2,1) = 1 ，得到 nums = [1,1,1,4] 。\n- 选择下标 i = 2 ，将 nums[3] 替换为 gcd(1,4) = 1 ，得到 nums = [1,1,1,1] 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>nums = [2,10,6,14]\n<b>输出：</b>-1\n<b>解释：</b>无法将所有元素都变成 1 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 50</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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