Input: nums = [1,0,2]
\n\nOutput: [0,1,2]
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/04/04/example0gif.gif\")
The lexicographically smallest permutation with minimum cost is [0,1,2]. The cost of this permutation is |0 - 0| + |1 - 2| + |2 - 1| = 2.
You are given an array nums which is a permutation of [0, 1, 2, ..., n - 1]. The score of any permutation of [0, 1, 2, ..., n - 1] named perm is defined as:
score(perm) = |perm[0] - nums[perm[1]]| + |perm[1] - nums[perm[2]]| + ... + |perm[n - 1] - nums[perm[0]]|
Return the permutation perm which has the minimum possible score. If multiple permutations exist with this score, return the one that is lexicographically smallest among them.
\n
Example 1:
\n\nInput: nums = [1,0,2]
\n\nOutput: [0,1,2]
\n\nExplanation:
\n\n
The lexicographically smallest permutation with minimum cost is [0,1,2]. The cost of this permutation is |0 - 0| + |1 - 2| + |2 - 1| = 2.
Example 2:
\n\nInput: nums = [0,2,1]
\n\nOutput: [0,2,1]
\n\nExplanation:
\n\n![\"\"](\"https://assets.leetcode.com/uploads/2024/04/04/example1gif.gif\")
The lexicographically smallest permutation with minimum cost is [0,2,1]. The cost of this permutation is |0 - 1| + |2 - 2| + |1 - 0| = 2.
\n
Constraints:
\n\n2 <= n == nums.length <= 14nums is a permutation of [0, 1, 2, ..., n - 1].perm[0] = 0 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 perm."
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