What is the optimal time complexity of solving Valid Parentheses?

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 Valid Parentheses?

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 Valid Parentheses?

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 Valid Parentheses?

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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Valid Parentheses

Learn how to solve the 'Valid Parentheses' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Given a string s containing just the characters '(', ')', '{', '}', '[' and ']', determine if the input string is valid.

An input string is valid if:

1. Open brackets must be closed by the same type of brackets.

2. Open brackets must be closed in the correct order.

3. Every close bracket has a corresponding open bracket of the same type.

Write a function isValid(s: str) -> bool.

Constraints

•1 <= len(s) <= 10^4
•s consists of parentheses only: '()[]{}'

Examples

Example 1

Input

s = "()"

Output

True

Explanation

A single pair of matching parentheses is valid.

Example 2

Input

s = "()[]{}"

Output

True

Explanation

Three pairs of matching brackets, each closed in order.

Example 3

Input

s = "(]"

Output

False

Explanation

Opening '(' is closed by ']' which is the wrong type.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

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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