3149_Find_the_Minimum_Cost_Array_Permutation.md

3149. Find the Minimum Cost Array Permutation

Difficulty: hard

Link: https://leetcode.com/problems/find-the-minimum-cost-array-permutation/

Contains PNG: No

Problem Statement

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].

Hints

• 1. The score function is cyclic, so we can always set perm[0] = 0 for the smallest lexical order.
• 2. It’s similar to the Traveling Salesman Problem. Use Dynamic Programming.
• 3. Use a bitmask to track which elements have been assigned to perm.

Code Templates

Cpp

class Solution {
public:
    vector<int> findPermutation(vector<int>& nums) {
        
    }
};

Java

class Solution {
    public int[] findPermutation(int[] nums) {
        
    }
}

Python

class Solution:
    def findPermutation(self, nums: List[int]) -> List[int]: