How do you solve Maximum Multiplication Score on LeetCode?

Maximum Multiplication Score (LeetCode #3290) 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: Dynamic programming allows us to build solutions incrementally, avoiding the need to check all combinations.

What is the brute force solution for Maximum Multiplication Score?

The brute force approach for Maximum Multiplication Score is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible combinations of 4 indices from array b. For each combination, we calculate the score and keep track of the maximum score found. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Multiplication Score?

Maximum Multiplication Score uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Greedy Algorithms.

What are the interview tips for Maximum Multiplication Score?

Always clarify the constraints and edge cases before diving into coding. Discuss your thought process and approach with the interviewer; it shows your problem-solving skills. If you get stuck, try to break the problem down into smaller parts or consider a simpler version of the problem.

What are common mistakes when solving Maximum Multiplication Score?

Failing to consider the order of selections can lead to incorrect results. Not initializing the DP array correctly can cause runtime errors or incorrect scores.

#3290

Maximum Multiplication Score

Medium

ArrayDynamic ProgrammingDynamic ProgrammingGreedy Algorithms

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 uses dynamic programming to build the maximum score incrementally. By maintaining an array that tracks the best scores for selecting up to 4 indices, we can efficiently calculate the maximum score without checking all combinations.

⚙️

Algorithm

4 steps

1Step 1: Initialize a DP array of size 5 (for 0 to 4 selections) with negative infinity.
2Step 2: Iterate through each element in b, updating the DP array for each selection count (from 4 down to 1).
3Step 3: For each element in b, calculate the potential new scores and update the DP array accordingly.
4Step 4: The maximum score will be found in DP[4] after processing all elements in b.

solution.py9 lines

1# Full working Python code
2
3def maxMultiplicationScore(a, b):
4    dp = [-float('inf')] * 5
5    dp[0] = 0
6    for num in b:
7        for j in range(4, 0, -1):
8            dp[j] = max(dp[j], dp[j-1] + a[j-1] * num)
9    return dp[4]

ℹ

Complexity note: The time complexity is O(n) because we iterate through the array b once and update the DP array in constant time. The space complexity is O(1) since we only use a fixed-size DP array.

1Dynamic programming allows us to build solutions incrementally, avoiding the need to check all combinations.
2Understanding how to maintain state in a DP array is crucial for optimizing problems involving selections.

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