How do you solve Minimum Cost to Equalize Array on LeetCode?

Minimum Cost to Equalize Array (LeetCode #3139) 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: If cost2 > cost1 * 2, always use cost1 for individual increments.

What is the time complexity of Minimum Cost to Equalize Array?

The optimal solution for Minimum Cost to Equalize Array runs in O(n) time and uses O(1) space. The time complexity is O(n) because we only iterate through the array once to calculate the total cost based on the maximum value.

What is the brute force solution for Minimum Cost to Equalize Array?

The brute force approach for Minimum Cost to Equalize Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves calculating the cost to equalize the array by considering each possible target value (from the minimum to the maximum of the array) and summing the costs of operations needed to reach that target. This is simple but inefficient for larger arrays. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Minimum Cost to Equalize Array?

Minimum Cost to Equalize Array uses the following concepts: Array, Greedy, Enumeration. The recommended patterns to study are: Greedy algorithms for cost minimization., Array manipulation techniques..

What are the interview tips for Minimum Cost to Equalize Array?

Always analyze the costs associated with each operation before jumping to a solution. Consider edge cases, such as when all elements are already equal. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Minimum Cost to Equalize Array?

Not considering the relationship between cost1 and cost2 when deciding the approach. Failing to optimize the solution and relying solely on brute force for larger inputs.

#3139

Minimum Cost to Equalize Array

Hard

ArrayGreedyEnumerationGreedy algorithms for cost minimization.Array manipulation techniques.

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 approach leverages the observation that if cost2 is greater than cost1 multiplied by 2, we should only use cost1 to equalize the array. Otherwise, we can use a combination of cost1 and cost2 efficiently to minimize the total cost.

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Algorithm

3 steps

1Step 1: Determine the maximum value in the array.
2Step 2: Calculate the cost to equalize all elements to this maximum value using cost1 and cost2 based on the differences.
3Step 3: Return the minimum cost found.

solution.py12 lines

1# Full working Python code
2
3def minCost(nums, cost1, cost2):
4    max_val = max(nums)
5    total_cost = 0
6    for num in nums:
7        diff = max_val - num
8        if diff % 2 == 0:
9            total_cost += (diff // 2) * cost2
10        else:
11            total_cost += (diff // 2) * cost2 + cost1
12    return total_cost % (10**9 + 7)

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Complexity note: The time complexity is O(n) because we only iterate through the array once to calculate the total cost based on the maximum value.

1If cost2 > cost1 * 2, always use cost1 for individual increments.
2Using cost2 effectively can reduce the total cost when it is cheaper to increase two elements at once.

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