Maximum Score from Performing Multiplication Operations — LeetCode 1770 Python Solution

The problem

You are given two 0-indexed integer arrays nums and multipliers of size n and m respectively, where n >= m. You begin with a score of 0.

Example

Input

nums = [1,2,3], multipliers = [3,2,1]

Output

14

Explanation

An optimal solution is as follows:

Python solution

class Solution:
    def maximumScore(self, nums: List[int], multipliers: List[int]) -> int:
        @cache
        def f(i, j, k):
            if k >= m or i >= n or j < 0:
                return 0
            a = f(i + 1, j, k + 1) + nums[i] * multipliers[k]
            b = f(i, j - 1, k + 1) + nums[j] * multipliers[k]
            return max(a, b)

        n = len(nums)
        m = len(multipliers)
        return f(0, n - 1, 0)

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1770. Maximum Score from Performing Multiplication Operations is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

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