# LeetCode 10. Regular Expression Matching

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: false
Explanation: "a" does not match the entire string "aa".
```

**Example 2:**

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

**Example 3:**

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

**Example 4:**

```
Input: s = "aab", p = "c*a*b"
Output: true
Explanation: c can be repeated 0 times, a can be repeated 1 time. Therefore, it matches "aab".
```

**Example 5:**

```
Input: s = "mississippi", p = "mis*is*p*."
Output: false
```

**Constraints:**

* `0 <= s.length <= 20`
* `0 <= 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.

## Solution:

[English Version in Youtube](https://youtu.be/_U3vZCgLhXE)

[中文版解答Youtube Link](https://youtu.be/cHwEdvY8rRg)

[中文版解答Bilibili Link](https://www.bilibili.com/video/BV1Tb4y1R7Fs/)

```
class Solution {
    
    bool isMatch(const string& s, int sidx, const string& p, int pidx) {
        if (pidx >= p.length()) {
            return sidx == s.length();
        }
        if ((pidx + 1) < p.length() && p[pidx + 1] == '*') {
            if (isMatch(s, sidx, p, pidx + 2)) {
                return true;
            }
            if (sidx < s.length() && (p[pidx] == '.' || s[sidx] == p[pidx])) {
                return isMatch(s, sidx + 1, p, pidx);
            }
        } else if (sidx < s.length() && (p[pidx] == '.' || s[sidx] == p[pidx])) {
            return isMatch(s, sidx + 1, p, pidx + 1);
        }
        return false;
    }
    
public:
    bool isMatch(string s, string p) {
        return isMatch(s, 0, p, 0);
    }
};
```