What is the optimal time complexity of solving Regular Expression Matching?

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 Regular Expression Matching?

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 Regular Expression Matching?

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 Regular Expression Matching?

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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Top 150 InterviewMedium

Regular Expression Matching

Learn how to solve the 'Regular Expression Matching' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Medium

Given an input string s and a pattern p, implement regular expression matching with support for '.' and '*' where:

- '.' Matches any single character.

- '*' Matches zero or more of the preceding element.

The matching should cover the entire input string (not partial).

Write a function isMatch(s: str, p: str) -> bool.

Constraints

•1 <= len(s) <= 20
•1 <= len(p) <= 20
•s contains only lowercase English letters.
•p contains only lowercase English letters, '.', and '*'.
•It is guaranteed for each appearance of the character '*', there will be a previous valid character to match.

Examples

Example 1

Input

s = "aa", p = "a"

Output

False

Explanation

"a" does not match the entire string "aa".

Example 2

Input

s = "aa", p = "a*"

Output

True

Explanation

'*' repeats the preceding 'a' once to match "aa".

Example 3

Input

s = "ab", p = ".*"

Output

True

Explanation

".*" matches zero or more of any character.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

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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