Maximum Score from Performing Multiplication Operations

Problem Description

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. You want to perform exactly m operations. On the i-th operation, you will:

• Choose one integer x from either the start or the end of the array nums.
• Add multipliers[i] * x to your score.
• Remove x from nums.

Return the maximum score after performing m operations.

Key Insights

• You can only select elements from the start or end of the nums array.
• The order of multipliers affects the total score since they multiply the selected numbers.
• Dynamic programming can efficiently compute the maximum score by keeping track of the best possible scores at each step.

Space and Time Complexity

Time Complexity: O(m^2)
Space Complexity: O(m)

Solution

The problem can be solved using a dynamic programming approach. We define a 2D DP array dp[i][j] where i represents the number of operations performed and j represents the number of elements taken from the start of the nums array. The remaining elements for the current operation will be taken from the end of the array.

1. Initialize dp[0][0] to 0 (no operations, no score).
2. Iterate through the number of operations from 1 to m.
3. For each operation, calculate the maximum score for all possible selections of elements from the start and end of the nums array.
4. Use the multipliers to update the score based on the selected element.
5. The final result will be the maximum score after all operations.

Code Solutions