leetcode-problemset/leetcode-cn/originData/minimize-length-of-array-using-operations.json

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            "title": "Minimize Length of Array Using Operations",
            "titleSlug": "minimize-length-of-array-using-operations",
            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> containing <strong>positive</strong> integers.</p>\n\n<p>Your task is to <strong>minimize</strong> the length of <code>nums</code> by performing the following operations <strong>any</strong> number of times (including zero):</p>\n\n<ul>\n\t<li>Select <strong>two</strong> <strong>distinct</strong> indices <code>i</code> and <code>j</code> from <code>nums</code>, such that <code>nums[i] &gt; 0</code> and <code>nums[j] &gt; 0</code>.</li>\n\t<li>Insert the result of <code>nums[i] % nums[j]</code> at the end of <code>nums</code>.</li>\n\t<li>Delete the elements at indices <code>i</code> and <code>j</code> from <code>nums</code>.</li>\n</ul>\n\n<p>Return <em>an integer denoting the <strong>minimum</strong> <strong>length</strong> of </em><code>nums</code><em> after performing the operation any number of times.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,4,3,1]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows:\nOperation 1: Select indices 2 and 1, insert nums[2] % nums[1] at the end and it becomes [1,4,3,1,3], then delete elements at indices 2 and 1.\nnums becomes [1,1,3].\nOperation 2: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [1,1,3,1], then delete elements at indices 1 and 2.\nnums becomes [1,1].\nOperation 3: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [1,1,0], then delete elements at indices 1 and 0.\nnums becomes [0].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length. </pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,5,5,10,5]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows:\nOperation 1: Select indices 0 and 3, insert nums[0] % nums[3] at the end and it becomes [5,5,5,10,5,5], then delete elements at indices 0 and 3.\nnums becomes [5,5,5,5]. \nOperation 2: Select indices 2 and 3, insert nums[2] % nums[3] at the end and it becomes [5,5,5,5,0], then delete elements at indices 2 and 3. \nnums becomes [5,5,0]. \nOperation 3: Select indices 0 and 1, insert nums[0] % nums[1] at the end and it becomes [5,5,0,0], then delete elements at indices 0 and 1.\nnums becomes [0,0].\nThe length of nums cannot be reduced further. Hence, the answer is 2.\nIt can be shown that 2 is the minimum achievable length. </pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,4]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> One way to minimize the length of the array is as follows: \nOperation 1: Select indices 1 and 2, insert nums[1] % nums[2] at the end and it becomes [2,3,4,3], then delete elements at indices 1 and 2.\nnums becomes [2,3].\nOperation 2: Select indices 1 and 0, insert nums[1] % nums[0] at the end and it becomes [2,3,1], then delete elements at indices 1 and 0.\nnums becomes [1].\nThe length of nums cannot be reduced further. Hence, the answer is 1.\nIt can be shown that 1 is the minimum achievable length.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "通过操作使数组长度最小",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;，它只包含 <strong>正</strong>&nbsp;整数。</p>\n\n<p>你的任务是通过进行以下操作&nbsp;<strong>任意次</strong>&nbsp;（可以是 0 次）&nbsp;<strong>最小化</strong>&nbsp;<code>nums</code>&nbsp;的长度：</p>\n\n<ul>\n\t<li>在 <code>nums</code>&nbsp;中选择 <strong>两个不同</strong>&nbsp;的下标&nbsp;<code>i</code>&nbsp;和&nbsp;<code>j</code>&nbsp;，满足&nbsp;<code>nums[i] &gt; 0</code>&nbsp;且&nbsp;<code>nums[j] &gt; 0</code>&nbsp;。</li>\n\t<li>将结果&nbsp;<code>nums[i] % nums[j]</code>&nbsp;插入&nbsp;<code>nums</code>&nbsp;的结尾。</li>\n\t<li>将 <code>nums</code>&nbsp;中下标为&nbsp;<code>i</code>&nbsp;和&nbsp;<code>j</code>&nbsp;的元素删除。</li>\n</ul>\n\n<p>请你返回一个整数，它表示进行任意次操作以后<em>&nbsp;</em><code>nums</code>&nbsp;的 <strong>最小长度</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,4,3,1]\n<b>输出：</b>1\n<b>解释：</b>使数组长度最小的一种方法是：\n操作 1 ：选择下标 2 和 1 ，插入 nums[2] % nums[1] 到数组末尾，得到 [1,4,3,1,3] ，然后删除下标为 2 和 1 的元素。\nnums 变为 [1,1,3] 。\n操作 2 ：选择下标 1 和 2 ，插入 nums[1] % nums[2] 到数组末尾，得到 [1,1,3,1] ，然后删除下标为 1 和 2 的元素。\nnums 变为 [1,1] 。\n操作 3 ：选择下标 1 和 0 ，插入 nums[1] % nums[0] 到数组末尾，得到 [1,1,0] ，然后删除下标为 1 和 0 的元素。\nnums 变为 [0] 。\nnums 的长度无法进一步减小，所以答案为 1 。\n1 是可以得到的最小长度。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [5,5,5,10,5]\n<b>输出：</b>2\n<b>解释：</b>使数组长度最小的一种方法是：\n操作 1 ：选择下标 0 和 3 ，插入 nums[0] % nums[3] 到数组末尾，得到 [5,5,5,10,5,5] ，然后删除下标为 0 和 3 的元素。\nnums 变为 [5,5,5,5] 。\n操作 2 ：选择下标 2 和 3 ，插入 nums[2] % nums[3] 到数组末尾，得到 [5,5,5,5,0] ，然后删除下标为 2 和 3 的元素。\nnums 变为 [5,5,0] 。\n操作 3 ：选择下标 0 和 1 ，插入 nums[0] % nums[1] 到数组末尾，得到 [5,5,0,0] ，然后删除下标为 0 和 1 的元素。\nnums 变为 [0,0] 。\nnums 的长度无法进一步减小，所以答案为 2 。\n2 是可以得到的最小长度。</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,3,4]\n<b>输出：</b>1\n<b>解释：</b>使数组长度最小的一种方法是：\n操作 1 ：选择下标 1 和 2 ，插入 nums[1] % nums[2] 到数组末尾，得到 [2,3,4,3] ，然后删除下标为 1 和 2 的元素。\nnums 变为 [2,3] 。\n操作 2 ：选择下标 1 和 0 ，插入 nums[1] % nums[0] 到数组末尾，得到 [2,3,1] ，然后删除下标为 1 和 0 的元素。\nnums 变为 [1] 。\nnums 的长度无法进一步减小，所以答案为 1 。\n1 是可以得到的最小长度。</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;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "The problem can be solved by considering different cases.",
                "Let the minimum value in <code>nums</code> be <code>x</code>; we can consider the following cases:",
                "If <code>x</code> occurs once: The minimum length of <code>nums</code> achievable in this case is <code>1</code>, since every other value, <code>y</code>, can be paired with <code>x</code>, resulting in deleting <code>x</code> and <code>y</code>, and inserting <code>x % y == x</code>, since <code>x < y</code>. So, only <code>x</code> remains after the operations.",
                "If there is a value <code>y</code> in <code>nums</code> such that <code>y % x</code> is not equal to <code>0</code>: The minimum achievable length in this case is <code>1</code> as well, because inserting <code>y % x</code> creates a new minimum, since <code>y % x < x</code>, returning to the first case.",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.11<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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