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"categoryTitle": "Algorithms",
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"title": "Prime Subtraction Operation",
"titleSlug": "prime-subtraction-operation",
"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> of length <code>n</code>.</p>\n\n<p>You can perform the following operation as many times as you want:</p>\n\n<ul>\n\t<li>Pick an index <code>i</code> that you haven&rsquo;t picked before, and pick a prime <code>p</code> <strong>strictly less than</strong> <code>nums[i]</code>, then subtract <code>p</code> from <code>nums[i]</code>.</li>\n</ul>\n\n<p>Return <em>true if you can make <code>nums</code> a strictly increasing array using the above operation and false otherwise.</em></p>\n\n<p>A <strong>strictly increasing array</strong> is an array whose each element is strictly greater than its preceding element.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,9,6,10]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> In the first operation: Pick i = 0 and p = 3, and then subtract 3 from nums[0], so that nums becomes [1,9,6,10].\nIn the second operation: i = 1, p = 7, subtract 7 from nums[1], so nums becomes equal to [1,2,6,10].\nAfter the second operation, nums is sorted in strictly increasing order, so the answer is true.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [6,8,11,12]\n<strong>Output:</strong> true\n<strong>Explanation: </strong>Initially nums is sorted in strictly increasing order, so we don&#39;t need to make any operations.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,8,3]\n<strong>Output:</strong> false\n<strong>Explanation:</strong> It can be proven that there is no way to perform operations to make nums sorted in strictly increasing order, so the answer is false.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code><font face=\"monospace\">nums.length == n</font></code></li>\n</ul>\n",
"translatedTitle": "质数减法运算",
"translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>nums</code> ,数组长度为 <code>n</code> 。</p>\n\n<p>你可以执行无限次下述运算:</p>\n\n<ul>\n\t<li>选择一个之前未选过的下标 <code>i</code> ,并选择一个 <strong>严格小于</strong> <code>nums[i]</code> 的质数 <code>p</code> ,从 <code>nums[i]</code> 中减去 <code>p</code> 。</li>\n</ul>\n\n<p>如果你能通过上述运算使得 <code>nums</code> 成为严格递增数组,则返回 <code>true</code> ;否则返回 <code>false</code> 。</p>\n\n<p><strong>严格递增数组</strong> 中的每个元素都严格大于其前面的元素。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [4,9,6,10]\n<strong>输出:</strong>true\n<strong>解释:</strong>\n在第一次运算中选择 i = 0 和 p = 3 ,然后从 nums[0] 减去 3 nums 变为 [1,9,6,10] 。\n在第二次运算中选择 i = 1 和 p = 7 ,然后从 nums[1] 减去 7 nums 变为 [1,2,6,10] 。\n第二次运算后nums 按严格递增顺序排序,因此答案为 true 。</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [6,8,11,12]\n<strong>输出:</strong>true\n<strong>解释:</strong>nums 从一开始就按严格递增顺序排序,因此不需要执行任何运算。</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [5,8,3]\n<strong>输出:</strong>false\n<strong>解释:</strong>可以证明,执行运算无法使 nums 按严格递增顺序排序,因此答案是 false 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>\n\t<li><code>nums.length == n</code></li>\n</ul>\n",
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"Think about if we have many primes to subtract from nums[i]. Which prime is more optimal?",
"The most optimal prime to subtract from nums[i] is the one that makes nums[i] the smallest as possible and greater than nums[i-1]."
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