Problem Statement

Given a balanced parenthesis string s, return the score of the given string.

Follow the below rules to determine the score of the string s.

• "()" has score 1.
• XY has score X + Y, where X and Y both are balanced parentheses strings.
• (X) has score 2 * X, where X is a balanced parentheses string.

Examples

Example 1:

• Input: "((()))"
• Expected Output: 4
• Justification: The string represents a pair of parentheses inside another pair, which is again inside another pair. This structure results in a score of ((())) = ((1*2)*2) = 4.

Example 2:

• Input: "(()())"
• Expected Output: 4
• Justification: Here, we have a pair of parentheses inside another pair (()()) and another pair next to it. The total score is (1*2) + (1*2) = 4.

Example 3:

• Input: "(()(()))"
• Expected Output: 6
• Justification: The innermost () scores 1, its surrounding () doubles it to 2, the previous () adjacent to the inner pair scores 1 and is then doubled by its surrounding pair, resulting in 2 + (1*2)*2 = 6.

Try it yourself

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