How do you solve Minimum Cost to Make Arrays Identical on LeetCode?

Minimum Cost to Make Arrays Identical (LeetCode #3424) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Rearranging subarrays can help minimize the total adjustment cost.

What is the brute force solution for Minimum Cost to Make Arrays Identical?

The brute force approach for Minimum Cost to Make Arrays Identical is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves calculating the cost of transforming `arr` into `brr` without rearranging subarrays. This means we simply compute the total cost of changing each element in `arr` to match the corresponding element in `brr` and add the fixed cost for rearranging. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Cost to Make Arrays Identical?

Minimum Cost to Make Arrays Identical uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Minimum Cost to Make Arrays Identical?

Always clarify the operations allowed before diving into the solution. Think about edge cases, such as when `arr` and `brr` are already equal. Discuss your thought process with the interviewer to demonstrate your understanding.

What are common mistakes when solving Minimum Cost to Make Arrays Identical?

Not considering the fixed cost `k` when calculating the total cost. Overcomplicating the problem by trying to implement unnecessary operations.

#3424

Minimum Cost to Make Arrays Identical

Medium

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

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Intuition

Time O(n)Space O(1)

The optimal solution leverages the fact that rearranging subarrays allows us to minimize the cost of adjustments. By calculating the total cost of adjustments and comparing it with the fixed cost of rearranging, we can determine the minimum cost efficiently.

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Algorithm

3 steps

1Step 1: Calculate the total adjustment cost by summing the absolute differences between `arr[i]` and `brr[i]`.
2Step 2: Compare the total adjustment cost with the fixed cost `k`.
3Step 3: Return the minimum of the total adjustment cost and the total adjustment cost plus `k`.

solution.py3 lines

1def minCost(arr, brr, k):
2    totalAdjustmentCost = sum(abs(arr[i] - brr[i]) for i in range(len(arr)))
3    return min(totalAdjustmentCost, totalAdjustmentCost + k)

ℹ

Complexity note: This complexity is linear because we only traverse the arrays once to compute the total adjustment cost. The space complexity is constant since we are not using any additional data structures.

1Rearranging subarrays can help minimize the total adjustment cost.
2The fixed cost of rearranging can be compared against the total adjustment cost to find the minimum.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.