Maximum Score from Performing Multiplication Operations

arraydynamic programming

Problem Statement

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 ( 0-indexed ) you will:

Choose one integer x from either the start or the end of the array nums .

Add multipliers[i] * x to your score.

Note that multipliers[0] corresponds to the first operation, multipliers[1] to the second operation, and so on.

Remove x from nums .

Return the maximum score after performing m operations.

Examples

Example 1

Input: nums = [1,2,3], multipliers = [3,2,1]
Output: 14
An optimal solution is as follows:
- Choose from the end, [1,2, 3 ], adding 3 * 3 = 9 to the score.
- Choose from the end, [1, 2 ], adding 2 * 2 = 4 to the score.
- Choose from the end, [ 1 ], adding 1 * 1 = 1 to the score.
The total score is 9 + 4 + 1 = 14.

Example 2

Input: nums = [-5,-3,-3,-2,7,1], multipliers = [-10,-5,3,4,6]
Output: 102
An optimal solution is as follows:
- Choose from the start, [ -5 ,-3,-3,-2,7,1], adding -5 * -10 = 50 to the score.
- Choose from the start, [ -3 ,-3,-2,7,1], adding -3 * -5 = 15 to the score.
- Choose from the start, [ -3 ,-2,7,1], adding -3 * 3 = -9 to the score.
- Choose from the end, [-2,7, 1 ], adding 1 * 4 = 4 to the score.
- Choose from the end, [-2, 7 ], adding 7 * 6 = 42 to the score. 
The total score is 50 + 15 - 9 + 4 + 42 = 102.

Constraints

n == nums.length

m == multipliers.length

1 <= m <= 300

m <= n <= 10 ^5

-1000 <= nums[i], multipliers[i] <= 1000

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Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming