Find the Minimum Cost Array Permutation - Problem
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.
Input & Output
Example 1 — Basic Case
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Input:
nums = [1, 0, 2]
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Output:
[0, 1, 2]
💡 Note:
For permutation [0,1,2]: score = |0-nums[1]| + |1-nums[2]| + |2-nums[0]| = |0-0| + |1-2| + |2-1| = 0 + 1 + 1 = 2. This is the minimum possible score.
Example 2 — Minimum Size
$
Input:
nums = [0]
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Output:
[0]
💡 Note:
Only one element, so the only permutation is [0]. Score = |0-nums[0]| = |0-0| = 0.
Example 3 — Larger Array
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Input:
nums = [1, 3, 0, 2]
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Output:
[0, 2, 3, 1]
💡 Note:
Optimal permutation gives score = |0-nums[2]| + |2-nums[3]| + |3-nums[1]| + |1-nums[0]| = |0-0| + |2-2| + |3-3| + |1-1| = 0. This is lexicographically smallest among optimal solutions.
Constraints
- 1 ≤ nums.length ≤ 14
- nums is a permutation of [0, 1, 2, ..., n - 1]
Visualization
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Explanation
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