LeetCode 3149: Find the Minimum Cost Array Permutation Solution

Master LeetCode problem 3149 (Find the Minimum Cost Array Permutation), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

3149. Find the Minimum Cost Array Permutation

Problem Explanation

Explanation:

To find the permutation with the minimum cost, we need to consider all possible permutations and calculate the cost for each permutation. We can use backtracking to generate all permutations and then calculate the cost for each permutation. Finally, we select the permutation with the minimum cost and is lexicographically smallest.

  1. Generate all permutations using backtracking.
  2. Calculate the cost for each permutation using the given formula.
  3. Keep track of the permutation with the minimum cost and is lexicographically smallest.
  4. Return the permutation with the minimum cost.

Time Complexity: The time complexity of this solution is O(n!) where n is the length of the input array.

Space Complexity: The space complexity is O(n) for storing the current permutation during backtracking.

:

Solution Code

class Solution {
    int minCost = Integer.MAX_VALUE;
    int[] result;

    public int[] minCostArrayPermutation(int[] nums) {
        int n = nums.length;
        boolean[] visited = new boolean[n];
        int[] currentPerm = new int[n];

        generatePermutations(nums, visited, currentPerm, 0);

        return result;
    }

    private void generatePermutations(int[] nums, boolean[] visited, int[] currentPerm, int index) {
        if (index == nums.length) {
            int cost = calculateCost(currentPerm, nums);
            if (cost < minCost) {
                minCost = cost;
                result = currentPerm.clone();
            }
            return;
        }

        for (int i = 0; i < nums.length; i++) {
            if (!visited[i]) {
                visited[i] = true;
                currentPerm[index] = i;
                generatePermutations(nums, visited, currentPerm, index + 1);
                visited[i] = false;
            }
        }
    }

    private int calculateCost(int[] perm, int[] nums) {
        int cost = 0;
        for (int i = 0; i < perm.length; i++) {
            cost += Math.abs(i - nums[perm[i]]);
        }
        return cost;
    }
}

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