leetcode-problemset/leetcode-cn/originData/find-the-minimum-cost-array-permutation.json

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            "title": "Find the Minimum Cost Array Permutation",
            "titleSlug": "find-the-minimum-cost-array-permutation",
            "content": "<p>You are given an array <code>nums</code> which is a <span data-keyword=\"permutation\">permutation</span> of <code>[0, 1, 2, ..., n - 1]</code>. The <strong>score</strong> of any permutation of <code>[0, 1, 2, ..., n - 1]</code> named <code>perm</code> is defined as:</p>\n\n<p><code>score(perm) = |perm[0] - nums[perm[1]]| + |perm[1] - nums[perm[2]]| + ... + |perm[n - 1] - nums[perm[0]]|</code></p>\n\n<p>Return the permutation <code>perm</code> which has the <strong>minimum</strong> possible score. If <em>multiple</em> permutations exist with this score, return the one that is <span data-keyword=\"lexicographically-smaller-array\">lexicographically smallest</span> among them.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [1,0,2]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[0,1,2]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/04/example0gif.gif\" style=\"width: 235px; height: 235px;\" /></strong></p>\n\n<p>The lexicographically smallest permutation with minimum cost is <code>[0,1,2]</code>. The cost of this permutation is <code>|0 - 0| + |1 - 2| + |2 - 1| = 2</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [0,2,1]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[0,2,1]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/04/example1gif.gif\" style=\"width: 235px; height: 235px;\" /></strong></p>\n\n<p>The lexicographically smallest permutation with minimum cost is <code>[0,2,1]</code>. The cost of this permutation is <code>|0 - 1| + |2 - 2| + |1 - 0| = 2</code>.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == nums.length &lt;= 14</code></li>\n\t<li><code>nums</code> is a permutation of <code>[0, 1, 2, ..., n - 1]</code>.</li>\n</ul>\n",
            "translatedTitle": "找出分数最低的排列",
            "translatedContent": "<p>给你一个数组 <code>nums</code> ，它是 <code>[0, 1, 2, ..., n - 1]</code> 的一个<span data-keyword=\"permutation\">排列</span> 。对于任意一个 <code>[0, 1, 2, ..., n - 1]</code> 的排列 <code>perm</code> ，其 <strong>分数 </strong>定义为：</p>\n\n<p><code>score(perm) = |perm[0] - nums[perm[1]]| + |perm[1] - nums[perm[2]]| + ... + |perm[n - 1] - nums[perm[0]]|</code></p>\n\n<p>返回具有<strong> 最低</strong> 分数的排列 <code>perm</code> 。如果存在多个满足题意且分数相等的排列，则返回其中<span data-keyword=\"lexicographically-smaller-array\">字典序最小</span>的一个。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [1,0,2]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">[0,1,2]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/04/example0gif.gif\" style=\"width: 235px; height: 235px;\" /></strong></p>\n\n<p>字典序最小且分数最低的排列是 <code>[0,1,2]</code>。这个排列的分数是 <code>|0 - 0| + |1 - 2| + |2 - 1| = 2</code> 。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [0,2,1]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">[0,2,1]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/04/04/example1gif.gif\" style=\"width: 235px; height: 235px;\" /></strong></p>\n\n<p>字典序最小且分数最低的排列是 <code>[0,2,1]</code>。这个排列的分数是 <code>|0 - 1| + |2 - 2| + |1 - 0| = 2</code> 。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n == nums.length &lt;= 14</code></li>\n\t<li><code>nums</code> 是 <code>[0, 1, 2, ..., n - 1]</code> 的一个排列。</li>\n</ul>\n",
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            "hints": [
                "The score function is cyclic, so we can always set <code>perm[0] = 0</code> for the smallest lexical order.",
                "It’s similar to the Traveling Salesman Problem. Use Dynamic Programming.",
                "Use a bitmask to track which elements have been assigned to <code>perm</code>."
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