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"question": {
"questionId": "3000",
"questionFrontendId": "2817",
"categoryTitle": "Algorithms",
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"title": "Minimum Absolute Difference Between Elements With Constraint",
"titleSlug": "minimum-absolute-difference-between-elements-with-constraint",
"content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code> and an integer <code>x</code>.</p>\n\n<p>Find the <strong>minimum absolute difference</strong> between two elements in the array that are at least <code>x</code> indices apart.</p>\n\n<p>In other words, find two indices <code>i</code> and <code>j</code> such that <code>abs(i - j) &gt;= x</code> and <code>abs(nums[i] - nums[j])</code> is minimized.</p>\n\n<p>Return<em> an integer denoting the <strong>minimum</strong> absolute difference between two elements that are at least</em> <code>x</code> <em>indices apart</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [4,3,2,4], x = 2\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> We can select nums[0] = 4 and nums[3] = 4. \nThey are at least 2 indices apart, and their absolute difference is the minimum, 0. \nIt can be shown that 0 is the optimal answer.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,3,2,10,15], x = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can select nums[1] = 3 and nums[2] = 2.\nThey are at least 1 index apart, and their absolute difference is the minimum, 1.\nIt can be shown that 1 is the optimal answer.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4], x = 3\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We can select nums[0] = 1 and nums[3] = 4.\nThey are at least 3 indices apart, and their absolute difference is the minimum, 3.\nIt can be shown that 3 is the optimal answer.\n</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\t<li><code>0 &lt;= x &lt; nums.length</code></li>\n</ul>\n",
"translatedTitle": "限制条件下元素之间的最小绝对差",
"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;和一个整数&nbsp;<code>x</code>&nbsp;。</p>\n\n<p>请你找到数组中下标距离至少为 <code>x</code>&nbsp;的两个元素的 <strong>差值绝对值</strong>&nbsp;的 <strong>最小值</strong>&nbsp;。</p>\n\n<p>换言之,请你找到两个下标&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;,满足&nbsp;<code>abs(i - j) &gt;= x</code> 且&nbsp;<code>abs(nums[i] - nums[j])</code>&nbsp;的值最小。</p>\n\n<p>请你返回一个整数,表示下标距离至少为 <code>x</code>&nbsp;的两个元素之间的差值绝对值的 <strong>最小值</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><b>示例 1</b></p>\n\n<pre>\n<b>输入:</b>nums = [4,3,2,4], x = 2\n<b>输出:</b>0\n<b>解释:</b>我们选择 nums[0] = 4 和 nums[3] = 4 。\n它们下标距离满足至少为 2 ,差值绝对值为最小值 0 。\n0 是最优解。\n</pre>\n\n<p><strong class=\"example\">示例 2</strong></p>\n\n<pre>\n<b>输入:</b>nums = [5,3,2,10,15], x = 1\n<b>输出:</b>1\n<b>解释:</b>我们选择 nums[1] = 3 和 nums[2] = 2 。\n它们下标距离满足至少为 1 ,差值绝对值为最小值 1 。\n1 是最优解。\n</pre>\n\n<p><strong class=\"example\">示例 3</strong></p>\n\n<pre>\n<b>输入:</b>nums = [1,2,3,4], x = 3\n<b>输出:</b>3\n<strong>解释:</strong>我们选择 nums[0] = 1 和 nums[3] = 4 。\n它们下标距离满足至少为 3 ,差值绝对值为最小值 3 。\n3 是最优解。\n</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\t<li><code>0 &lt;= x &lt; nums.length</code></li>\n</ul>\n",
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"<div class=\"_1l1MA\">Let's only consider the cases where <code>i < j</code>, as the problem is symmetric.</div>",
"<div class=\"_1l1MA\">For an index <code>j</code>, we are interested in an index <code>i</code> in the range <code>[0, j - x]</code> that minimizes <code>abs(nums[i] - nums[j])</code>.</div>",
"<div class=\"_1l1MA\">For every index <code>j</code>, while going from left to right, add <code>nums[j - x]</code> to a set (C++ set, Java TreeSet, and Python sorted set).</div>",
"<div class=\"_1l1MA\">After inserting <code>nums[j - x]</code>, we can calculate the closest value to <code>nums[j]</code> in the set using binary search and store the absolute difference. In C++, we can achieve this by using lower_bound and/or upper_bound.</div>",
"<div class=\"_1l1MA\">Calculate the minimum absolute difference among all indices.</div>"
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