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leetcode-problemset/leetcode-cn/originData/global-and-local-inversions.json
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"categoryTitle": "Algorithms",
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"title": "Global and Local Inversions",
"titleSlug": "global-and-local-inversions",
"content": "<p>You are given an integer array <code>nums</code> of length <code>n</code> which represents a permutation of all the integers in the range <code>[0, n - 1]</code>.</p>\n\n<p>The number of <strong>global inversions</strong> is the number of the different pairs <code>(i, j)</code> where:</p>\n\n<ul>\n\t<li><code>0 &lt;= i &lt; j &lt; n</code></li>\n\t<li><code>nums[i] &gt; nums[j]</code></li>\n</ul>\n\n<p>The number of <strong>local inversions</strong> is the number of indices <code>i</code> where:</p>\n\n<ul>\n\t<li><code>0 &lt;= i &lt; n - 1</code></li>\n\t<li><code>nums[i] &gt; nums[i + 1]</code></li>\n</ul>\n\n<p>Return <code>true</code> <em>if the number of <strong>global inversions</strong> is equal to the number of <strong>local inversions</strong></em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,0,2]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> There is 1 global inversion and 1 local inversion.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,0]\n<strong>Output:</strong> false\n<strong>Explanation:</strong> There are 2 global inversions and 1 local inversion.\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>5</sup></code></li>\n\t<li><code>0 &lt;= nums[i] &lt; n</code></li>\n\t<li>All the integers of <code>nums</code> are <strong>unique</strong>.</li>\n\t<li><code>nums</code> is a permutation of all the numbers in the range <code>[0, n - 1]</code>.</li>\n</ul>\n",
"translatedTitle": "全局倒置与局部倒置",
"translatedContent": "<p>给你一个长度为 <code>n</code> 的整数数组 <code>nums</code> ,表示由范围 <code>[0, n - 1]</code> 内所有整数组成的一个排列。</p>\n\n<p><strong>全局倒置</strong> 的数目等于满足下述条件不同下标对 <code>(i, j)</code> 的数目:</p>\n\n<ul>\n\t<li><code>0 <= i < j < n</code></li>\n\t<li><code>nums[i] > nums[j]</code></li>\n</ul>\n\n<p><strong>局部倒置</strong> 的数目等于满足下述条件的下标 <code>i</code> 的数目:</p>\n\n<ul>\n\t<li><code>0 <= i < n - 1</code></li>\n\t<li><code>nums[i] > nums[i + 1]</code></li>\n</ul>\n\n<p>当数组 <code>nums</code> 中 <strong>全局倒置</strong> 的数量等于 <strong>局部倒置</strong> 的数量时,返回 <code>true</code> ;否则,返回 <code>false</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [1,0,2]\n<strong>输出:</strong>true\n<strong>解释:</strong>有 1 个全局倒置,和 1 个局部倒置。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>nums = [1,2,0]\n<strong>输出:</strong>false\n<strong>解释:</strong>有 2 个全局倒置,和 1 个局部倒置。\n</pre>\n \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 <= n <= 5000</code></li>\n\t<li><code>0 <= nums[i] < n</code></li>\n\t<li><code>nums</code> 中的所有整数 <strong>互不相同</strong></li>\n\t<li><code>nums</code> 是范围 <code>[0, n - 1]</code> 内所有数字组成的一个排列</li>\n</ul>\n",
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