Check for Balanced Parentheses Using Stack and Queue: A Complete Guide

In programming, validating expressions with parentheses is crucial in various applications, including compilers, calculators, and text editors. The most efficient way to check for balanced parentheses is by using Stack and Queue, two fundamental data structures.

This guide will cover:
✅ What are balanced parentheses?
✅ How Stack and Queue help in checking them
✅ Algorithm and implementation in Python
✅ Real-world applications

By the end of this blog, you’ll have a solid understanding of how to use Stack and Queue to validate expressions efficiently.

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What Are Balanced Parentheses?

An expression has balanced parentheses if:

1. Every opening bracket has a corresponding closing bracket.
2. Parentheses close in the correct order.

Examples of Balanced and Unbalanced Parentheses

Expression	Balanced?
((()))	✅ Yes
{[()()]}	✅ Yes
{[(])}	❌ No
({[}	❌ No

If an expression is unbalanced, it means there’s a missing or misplaced closing bracket.

How Stack Helps in Checking Balanced Parentheses

A stack follows the LIFO (Last In, First Out) principle, making it an excellent choice for validating parentheses.

Stack Approach to Check for Balanced Parentheses

1. Traverse the expression from left to right.
2. Push every opening bracket ((, {, [) onto the stack.
3. For every closing bracket (), }, ]):
   • Check if the stack is empty (if yes, return False).
   • Pop the top element and check if it matches the current closing bracket.
4. If the stack is empty after traversing the expression, the parentheses are balanced. Otherwise, they are unbalanced.

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Python Implementation Using Stack

def is_balanced(expression):
    stack = []
    bracket_pairs = {')': '(', '}': '{', ']': '['}
    
    for char in expression:
        if char in "({[":
            stack.append(char)
        elif char in ")}]":
            if not stack or stack[-1] != bracket_pairs[char]:
                return False
            stack.pop()
    
    return len(stack) == 0

# Test Cases
print(is_balanced("((()))"))  # Output: True
print(is_balanced("{[()()]}"))  # Output: True
print(is_balanced("{[(])}"))  # Output: False
print(is_balanced("({[}"))  # Output: False

How Queue Helps in Checking Balanced Parentheses

A queue follows the FIFO (First In, First Out) principle. While it is less commonly used than a stack for this problem, it can still validate an expression by storing pairs of parentheses and verifying their correct sequence.

Queue Approach to Check for Balanced Parentheses

1. Enqueue all characters of the expression.
2. Process each element and check if closing brackets match their corresponding opening brackets.
3. If mismatches exist, return False.

Python Implementation Using Queue

from collections import deque

def is_balanced_queue(expression):
    queue = deque(expression)
    stack = []
    bracket_pairs = {')': '(', '}': '{', ']': '['}

    while queue:
        char = queue.popleft()
        if char in "({[":
            stack.append(char)
        elif char in ")}]":
            if not stack or stack[-1] != bracket_pairs[char]:
                return False
            stack.pop()

    return len(stack) == 0

# Test Cases
print(is_balanced_queue("((()))"))  # Output: True
print(is_balanced_queue("{[()()]}"))  # Output: True
print(is_balanced_queue("{[(])}"))  # Output: False
print(is_balanced_queue("({[}"))  # Output: False

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Stack vs Queue for Balanced Parentheses

Feature	Stack	Queue
Principle	LIFO (Last In, First Out)	FIFO (First In, First Out)
Common Use	Checking balanced parentheses	Processing bracket sequences
Efficiency	Faster for validation	Slower due to extra traversal

Stack is generally preferred over Queue for this problem due to its direct LIFO property.

Also Read: SQL Tutorial for Data Analysts: A Step-by-Step Guide to Mastering Data Queries

Time Complexity Analysis

Operation	Time Complexity
Push (Stack)	O(1)
Pop (Stack)	O(1)
Enqueue (Queue)	O(1)
Dequeue (Queue)	O(1)
Check Balanced Parentheses (Full Expression)	O(n)

Since we traverse the expression once, the overall time complexity is O(n), where n is the length of the expression.

Real-World Applications of Checking Balanced Parentheses

🔹 Compilers & Syntax Checkers – Validate code syntax in programming languages.
🔹 Expression Evaluation – Convert infix to postfix notation in mathematics.
🔹 Code Formatters – Ensure proper indentation and formatting in editors like VS Code.
🔹 HTML/XML Validation – Verify proper nesting of tags in web development.
🔹 Chatbots & NLP – Detect and process expressions with parentheses in AI chat systems.

Common Mistakes and How to Avoid Them

🔸 Forgetting to check if the stack is empty before popping – Can cause runtime errors.
🔸 Not considering edge cases – Example: "((", "()())" should be tested.
🔸 Using Queue when Stack is more efficient – Queue is less optimal for this problem.
🔸 Not handling mismatched parentheses properly – Always check if the popped element matches the closing bracket.

FAQs

Conclusion

The Stack and Queue approach to check for balanced parentheses is essential for validating expressions, ensuring correct nesting in programming, and preventing syntax errors.

🚀 Key Takeaways:
✅ Use Stack for efficient LIFO checking.
✅ Queue can be used, but it’s less optimal.
✅ O(n) complexity ensures fast validation.
✅ Real-world applications include compilers, text editors, and HTML parsing.

Mastering this concept is crucial for solving data structure problems, competitive programming, and software development! Start practicing today!