Score of Parentheses - Practice Coding Problems

Score of Parentheses - Problem

String Stack Medium

Given a balanced parentheses string s, calculate its score based on a simple scoring system that rewards proper nesting.

The Scoring Rules:

() has a score of 1
Concatenated strings AB have score A + B, where A and B are balanced parentheses strings
Nested strings (A) have score 2 * A, where A is a balanced parentheses string

For example, "()()" scores 2 (1 + 1), while "(())" scores 2 (2 * 1). The deeper the nesting, the higher the exponential growth!

Your task: Return the total score of the given balanced parentheses string.

Input & Output

example_1.py — Basic nesting

$ Input: "(())"

› Output: 2

💡 Note: The inner () scores 1 point. The outer parentheses double this score: 2 × 1 = 2.

example_2.py — Adjacent pairs

$ Input: "()()"

› Output: 2

💡 Note: Two adjacent () pairs, each scoring 1 point. Total: 1 + 1 = 2.

example_3.py — Complex nesting

$ Input: "(()())"

› Output: 4

💡 Note: Inside the outer parentheses: () scores 1, () scores 1, so inner total is 1 + 1 = 2. The outer parentheses double this: 2 × 2 = 4.

Constraints

1 ≤ s.length ≤ 50
s consists of only '(' and ')' characters
s is a balanced parentheses string

Visualization

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Understanding the Visualization

Identify the dolls

Each () pair represents a complete doll. Nested pairs represent dolls inside other dolls

Score innermost dolls

The smallest dolls () are worth 1 point each

Apply nesting multiplier

Each layer that wraps around doubles the inner value

Add adjacent values

Dolls sitting side by side contribute their values independently

Key Takeaway

🎯 Key Insight: Use a stack to track nesting levels and apply scoring rules in real-time, avoiding the need for complex recursive parsing!

Asked in

G Google 45 f Meta 32 a Amazon 28 ⊞ Microsoft 22

The optimal solution uses a stack-based approach to simulate the scoring process. Each stack level represents a nesting depth, and we apply the scoring rules in real-time. This achieves O(n) time complexity with a single pass through the string, making it significantly more efficient than recursive parsing approaches.

Common Approaches

Approach	Time	Space	Notes
✓ Stack-Based Simulation (Optimal)	O(n)	O(n)	Use a stack to track scores at each nesting level

Stack-Based Simulation (Optimal) — Algorithm Steps

Initialize a stack with 0 (root level score)
For each '(': push 0 onto stack (new nesting level)
For each ')': pop current level, apply scoring rules, add to parent level
Return the final score at root level

Visualization

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Step-by-Step Walkthrough

Initialize stack

Start with [0] representing the root level score

Process opening parentheses

Push 0 for each '(' to start a new nesting level

Process closing parentheses

Pop current level, apply rules, add to parent

Return result

The final stack[0] contains the total score

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

int scoreOfParentheses(char* s) {
    int stack[1000];
    int top = 0;
    stack[top] = 0; // Root level
    
    for (int i = 0; s[i] != '\0'; i++) {
        if (s[i] == '(') {
            // Start new nesting level
            stack[++top] = 0;
        } else { // s[i] == ')'
            // End current nesting level
            int currentScore = stack[top--];
            // Apply scoring rules: () = 1, (A) = 2*A
            int scoreToAdd = currentScore > 0 ? 2 * currentScore : 1;
            stack[top] += scoreToAdd;
        }
    }
    
    return stack[0];
}

int main() {
    char s[1000];
    scanf("%s", s);
    // Remove quotes if present
    int len = strlen(s);
    if (s[0] == '"') {
        for (int i = 1; i < len - 1; i++) {
            s[i-1] = s[i];
        }
        s[len-2] = '\0';
    }
    printf("%d\n", scoreOfParentheses(s));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Single pass through the string, each character processed once

✓ Linear Growth

Space Complexity

O(n)

Stack depth equals maximum nesting level, which can be at most n/2

⚡ Linearithmic Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Stack-Based Simulation (Optimal) — Algorithm Steps

Visualization

Code -

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