What is the optimal time complexity of solving Balanced Parenthesis Problem?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Balanced Parenthesis Problem?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Balanced Parenthesis Problem?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Balanced Parenthesis Problem?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Balanced Parenthesis Problem

Learn how to solve the 'Balanced Parenthesis Problem' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function is_balanced(s) that takes a string s containing only the characters '(', ')', '{', '}', '[' and ']', and returns True if the parentheses are balanced and properly nested, False otherwise. An empty string is considered balanced.

Constraints

•0 <= len(s) <= 10^4
•s consists only of '(', ')', '{', '}', '[', ']'

Examples

Example 1

Input

s = '({[]})'

Output

True

Explanation

Each opening bracket has a matching closing bracket in the correct order: ( matches ), { matches }, [ matches ].

Example 2

Input

s = '({[})'

Output

False

Explanation

The [ is closed by } which is a mismatch.

Example 3

Input

s = ''

Output

True

Explanation

An empty string is considered balanced.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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