Problem Statement

At Amazon, a user owns a unique tool called the "Parentheses Perfection Kit." This kit contains different types of parentheses, each with a specific efficiency rating. The goal is to create a balanced sequence of parentheses by adding zero or more parentheses from the kit to maximize the sequence's total EfficiencyScore. The EfficiencyScore of a sequence is the sum of the efficiency ratings of the parentheses used from the kit.

Definition of a Balanced Sequence:

A sequence is considered balanced if:

1. It has an equal number of opening ( and closing ) parentheses.
2. Each opening parenthesis is properly matched with a closing one in the correct order (i.e., circular balance).

Examples of balanced sequences:

• ()
• (())
• (()())

Examples of unbalanced sequences:

• )
• (()
• (()(()))

Input Details:

1. An initial parentheses sequence represented by the string s.
2. A Parentheses Perfection Kit containing:
   • kitParentheses: Different types of parentheses.
   • efficiencyRatings: Their respective efficiency ratings in an array.

Both kitParentheses and efficiencyRatings have a size of m. Initially, the EfficiencyScore of the sequence s is 0. The user can use any number of unused parentheses from the kit to create the final sequence, as long as the final sequence remains balanced.

Objective:

Determine the maximum possible EfficiencyScore for the resulting balanced sequence.

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Sample Case 0

Input:

• s = "()"
• kitParentheses = "(())"
• efficiencyRatings = [4, 2, -3, -3]

Explanation:

1. The initial sequence is already balanced.
2. The user can add parentheses from the kit to maximize the total EfficiencyScore:
   • Use the 0th indexed parentheses (4) and add it to the start of the sequence.
   • Use the 2nd indexed parentheses (-3) and add it to the end of the sequence.
3. The resulting sequence becomes:
   • "(0)" (still balanced).
   EfficiencyScore: 4 + (-3) = 1

There are no other combinations of parentheses that yield a higher EfficiencyScore. Therefore, the answer is 1.

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Output:

1

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