leetcode-problemset/leetcode-cn/originData/arithmetic-subarrays.json

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        "question": {
            "questionId": "1752",
            "questionFrontendId": "1630",
            "categoryTitle": "Algorithms",
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            "title": "Arithmetic Subarrays",
            "titleSlug": "arithmetic-subarrays",
            "content": "<p>A sequence of numbers is called <strong>arithmetic</strong> if it consists of at least two elements, and the difference between every two consecutive elements is the same. More formally, a sequence <code>s</code> is arithmetic if and only if <code>s[i+1] - s[i] == s[1] - s[0] </code>for all valid <code>i</code>.</p>\n\n<p>For example, these are <strong>arithmetic</strong> sequences:</p>\n\n<pre>\n1, 3, 5, 7, 9\n7, 7, 7, 7\n3, -1, -5, -9</pre>\n\n<p>The following sequence is not <strong>arithmetic</strong>:</p>\n\n<pre>\n1, 1, 2, 5, 7</pre>\n\n<p>You are given an array of <code>n</code> integers, <code>nums</code>, and two arrays of <code>m</code> integers each, <code>l</code> and <code>r</code>, representing the <code>m</code> range queries, where the <code>i<sup>th</sup></code> query is the range <code>[l[i], r[i]]</code>. All the arrays are <strong>0-indexed</strong>.</p>\n\n<p>Return <em>a list of </em><code>boolean</code> <em>elements</em> <code>answer</code><em>, where</em> <code>answer[i]</code> <em>is</em> <code>true</code> <em>if the subarray</em> <code>nums[l[i]], nums[l[i]+1], ... , nums[r[i]]</code><em> can be <strong>rearranged</strong> to form an <strong>arithmetic</strong> sequence, and</em> <code>false</code> <em>otherwise.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = <code>[4,6,5,9,3,7]</code>, l = <code>[0,0,2]</code>, r = <code>[2,3,5]</code>\n<strong>Output:</strong> <code>[true,false,true]</code>\n<strong>Explanation:</strong>\nIn the 0<sup>th</sup> query, the subarray is [4,6,5]. This can be rearranged as [6,5,4], which is an arithmetic sequence.\nIn the 1<sup>st</sup> query, the subarray is [4,6,5,9]. This cannot be rearranged as an arithmetic sequence.\nIn the 2<sup>nd</sup> query, the subarray is <code>[5,9,3,7]. This</code> can be rearranged as <code>[3,5,7,9]</code>, which is an arithmetic sequence.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10], l = [0,1,6,4,8,7], r = [4,4,9,7,9,10]\n<strong>Output:</strong> [false,true,false,false,true,true]\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>m == l.length</code></li>\n\t<li><code>m == r.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 500</code></li>\n\t<li><code>1 &lt;= m &lt;= 500</code></li>\n\t<li><code>0 &lt;= l[i] &lt; r[i] &lt; n</code></li>\n\t<li><code>-10<sup>5</sup> &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "等差子数组",
            "translatedContent": "<p>如果一个数列由至少两个元素组成，且每两个连续元素之间的差值都相同，那么这个序列就是 <strong>等差数列</strong> 。更正式地，数列 <code>s</code> 是等差数列，只需要满足：对于每个有效的 <code>i</code> ， <code>s[i+1] - s[i] == s[1] - s[0]</code> 都成立。</p>\n\n<p>例如，下面这些都是 <strong>等差数列</strong> ：</p>\n\n<pre>1, 3, 5, 7, 9\n7, 7, 7, 7\n3, -1, -5, -9</pre>\n\n<p>下面的数列 <strong>不是等差数列</strong> ：</p>\n\n<pre>1, 1, 2, 5, 7</pre>\n\n<p>给你一个由 <code>n</code> 个整数组成的数组 <code>nums</code>，和两个由 <code>m</code> 个整数组成的数组 <code>l</code> 和 <code>r</code>，后两个数组表示 <code>m</code> 组范围查询，其中第 <code>i</code> 个查询对应范围 <code>[l[i], r[i]]</code> 。所有数组的下标都是 <strong>从 0 开始</strong> 的。</p>\n\n<p>返回<em> </em><code>boolean</code> 元素构成的答案列表 <code>answer</code> 。如果子数组 <code>nums[l[i]], nums[l[i]+1], ... , nums[r[i]]</code> 可以 <strong>重新排列</strong> 形成 <strong>等差数列</strong> ，<code>answer[i]</code> 的值就是 <code>true</code>；否则<code>answer[i]</code> 的值就是 <code>false</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>nums = <code>[4,6,5,9,3,7]</code>, l = <code>[0,0,2]</code>, r = <code>[2,3,5]</code>\n<strong>输出：</strong><code>[true,false,true]</code>\n<strong>解释：</strong>\n第 0 个查询，对应子数组 [4,6,5] 。可以重新排列为等差数列 [6,5,4] 。\n第 1 个查询，对应子数组 [4,6,5,9] 。无法重新排列形成等差数列。\n第 2 个查询，对应子数组 <code>[5,9,3,7] 。</code>可以重新排列为等差数列 <code>[3,5,7,9] 。</code></pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>nums = [-12,-9,-3,-12,-6,15,20,-25,-20,-15,-10], l = [0,1,6,4,8,7], r = [4,4,9,7,9,10]\n<strong>输出：</strong>[false,true,false,false,true,true]\n</pre>\n\n<p> </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>m == l.length</code></li>\n\t<li><code>m == r.length</code></li>\n\t<li><code>2 &lt;= n &lt;= 500</code></li>\n\t<li><code>1 &lt;= m &lt;= 500</code></li>\n\t<li><code>0 &lt;= l[i] &lt; r[i] &lt; n</code></li>\n\t<li><code>-10<sup>5</sup> &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                    "code": "class Solution(object):\n    def checkArithmeticSubarrays(self, nums, l, r):\n        \"\"\"\n        :type nums: List[int]\n        :type l: List[int]\n        :type r: List[int]\n        :rtype: List[bool]\n        \"\"\"",
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                "To check if a given sequence is arithmetic, just check that the difference between every two consecutive elements is the same.",
                "If and only if a set of numbers can make an arithmetic sequence, then its sorted version makes an arithmetic sequence. So to check a set of numbers, sort it, and check if that sequence is arithmetic.",
                "For each query, get the corresponding set of numbers which will be the sub-array represented by the query, sort it, and check if the result sequence is arithmetic."
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