3149 - Find the Minimum Cost Array Permutation.

Hard

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.

Example 1:

Input: nums = 1,0,2

Output: 0,1,2

Explanation:

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:

Input: nums = 0,2,1

Output: 0,2,1

Explanation:

The lexicographically smallest permutation with minimum cost is [0,2,1]. The cost of this permutation is |0 - 1| + |2 - 2| + |1 - 0| = 2.

Constraints:

• 2 <= n == nums.length <= 14

• nums is a permutation of [0, 1, 2, ..., n - 1].