leetcode-problemset/leetcode-cn/originData/make-lexicographically-smallest-array-by-swapping-elements.json

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        "question": {
            "questionId": "3219",
            "questionFrontendId": "2948",
            "categoryTitle": "Algorithms",
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            "title": "Make Lexicographically Smallest Array by Swapping Elements",
            "titleSlug": "make-lexicographically-smallest-array-by-swapping-elements",
            "content": "<p>You are given a <strong>0-indexed</strong> array of <strong>positive</strong> integers <code>nums</code> and a <strong>positive</strong> integer <code>limit</code>.</p>\n\n<p>In one operation, you can choose any two indices <code>i</code> and <code>j</code> and swap <code>nums[i]</code> and <code>nums[j]</code> <strong>if</strong> <code>|nums[i] - nums[j]| &lt;= limit</code>.</p>\n\n<p>Return <em>the <strong>lexicographically smallest array</strong> that can be obtained by performing the operation any number of times</em>.</p>\n\n<p>An array <code>a</code> is lexicographically smaller than an array <code>b</code> if in the first position where <code>a</code> and <code>b</code> differ, array <code>a</code> has an element that is less than the corresponding element in <code>b</code>. For example, the array <code>[2,10,3]</code> is lexicographically smaller than the array <code>[10,2,3]</code> because they differ at index <code>0</code> and <code>2 &lt; 10</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,5,3,9,8], limit = 2\n<strong>Output:</strong> [1,3,5,8,9]\n<strong>Explanation:</strong> Apply the operation 2 times:\n- Swap nums[1] with nums[2]. The array becomes [1,3,5,9,8]\n- Swap nums[3] with nums[4]. The array becomes [1,3,5,8,9]\nWe cannot obtain a lexicographically smaller array by applying any more operations.\nNote that it may be possible to get the same result by doing different operations.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,7,6,18,2,1], limit = 3\n<strong>Output:</strong> [1,6,7,18,1,2]\n<strong>Explanation:</strong> Apply the operation 3 times:\n- Swap nums[1] with nums[2]. The array becomes [1,6,7,18,2,1]\n- Swap nums[0] with nums[4]. The array becomes [2,6,7,18,1,1]\n- Swap nums[0] with nums[5]. The array becomes [1,6,7,18,1,2]\nWe cannot obtain a lexicographically smaller array by applying any more operations.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,7,28,19,10], limit = 3\n<strong>Output:</strong> [1,7,28,19,10]\n<strong>Explanation:</strong> [1,7,28,19,10] is the lexicographically smallest array we can obtain because we cannot apply the operation on any two indices.\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>1 &lt;= limit &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "交换得到字典序最小的数组",
            "translatedContent": "<p>给你一个下标从 <strong>0 </strong>开始的 <strong>正整数</strong> 数组 <code>nums</code> 和一个 <strong>正整数</strong> <code>limit</code> 。</p>\n\n<p>在一次操作中，你可以选择任意两个下标 <code>i</code> 和 <code>j</code>，<strong>如果</strong> 满足 <code>|nums[i] - nums[j]| &lt;= limit</code> ，则交换 <code>nums[i]</code> 和 <code>nums[j]</code> 。</p>\n\n<p>返回执行任意次操作后能得到的 <strong>字典序最小的数组</strong><em> </em>。</p>\n\n<p>如果在数组 <code>a</code> 和数组 <code>b</code> 第一个不同的位置上，数组 <code>a</code> 中的对应元素比数组 <code>b</code> 中的对应元素的字典序更小，则认为数组 <code>a</code> 就比数组 <code>b</code> 字典序更小。例如，数组 <code>[2,10,3]</code> 比数组 <code>[10,2,3]</code> 字典序更小，下标 <code>0</code> 处是两个数组第一个不同的位置，且 <code>2 &lt; 10</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,5,3,9,8], limit = 2\n<strong>输出：</strong>[1,3,5,8,9]\n<strong>解释：</strong>执行 2 次操作：\n- 交换 nums[1] 和 nums[2] 。数组变为 [1,3,5,9,8] 。\n- 交换 nums[3] 和 nums[4] 。数组变为 [1,3,5,8,9] 。\n即便执行更多次操作，也无法得到字典序更小的数组。\n注意，执行不同的操作也可能会得到相同的结果。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,7,6,18,2,1], limit = 3\n<strong>输出：</strong>[1,6,7,18,1,2]\n<strong>解释：</strong>执行 3 次操作：\n- 交换 nums[1] 和 nums[2] 。数组变为 [1,6,7,18,2,1] 。\n- 交换 nums[0] 和 nums[4] 。数组变为 [2,6,7,18,1,1] 。\n- 交换 nums[0] 和 nums[5] 。数组变为 [1,6,7,18,1,2] 。\n即便执行更多次操作，也无法得到字典序更小的数组。\n</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [1,7,28,19,10], limit = 3\n<strong>输出：</strong>[1,7,28,19,10]\n<strong>解释：</strong>[1,7,28,19,10] 是字典序最小的数组，因为不管怎么选择下标都无法执行操作。\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>1 &lt;= limit &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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            "hints": [
                "Construct a virtual graph where all elements in <code>nums</code> are nodes and the pairs satisfying the condition have an edge between them.",
                "Instead of constructing all edges, we only care about the connected components.",
                "Can we use DSU?",
                "Sort <code>nums</code>. Now we just need to consider if the consecutive elements have an edge to check if they belong to the same connected component. Hence, all connected components become a list of position-consecutive elements after sorting.",
                "For each index of <code>nums</code> from <code>0</code> to <code>nums.length - 1</code> we can change it to the current minimum value we have in its connected component and remove that value from the connected component."
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