Regular Expression Matching

Problem statement

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).

Example 1:

Input: s = "aa", p = "a"Output: falseExplanation: "a" does not match the entire string "aa".

Example 2:

Input: s = "aa", p = "a*"Output: trueExplanation: '*' means zero or more of the preceding element, 'a'. Therefore, by repeating 'a' once, it becomes "aa".

Example 3:

Input: s = "ab", p = ".*"Output: trueExplanation: ".*" means "zero or more (*) of any character (.)".

Constraints:

• 1 <= s.length <= 20
• 1 <= p.length <= 30
• 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.

My solution

/**
 * @param {string} s
 * @param {string} p
 * @return {boolean}
 */
var isMatch = function(s, p) {
    let result = false
    let memo = new Set();
    
    function traverse(iIdx, jIdx) {
        const key = `${iIdx}:${jIdx}`;
        
        if (iIdx > s.length || jIdx > p.length || memo.has(key) || result) {
            return;
        }
        
        memo.add(key);
        
        if (iIdx === s.length && jIdx === p.length) {
            result = true;
            return;
        }
        
        const pChar = p.charAt(jIdx);
        const pNextChar = p.charAt(jIdx + 1);
        const sChar = s.charAt(iIdx)
        
        if (pChar === ".") {
            traverse(iIdx + 1, jIdx + 1);
        }
        if (pNextChar === "*") {
            if (sChar === pChar || pChar === ".") {
                traverse(iIdx + 1, jIdx)
            }
            traverse(iIdx, jIdx + 2)
        }
        if (pChar === sChar) {
            traverse(iIdx + 1, jIdx + 1);
        }
        return
    }
    
    traverse(0, 0);
    
    return result;
};