正则表达式匹配

Regular Expression Matching

专题: Algorithmic Programming / 算法编程
难度: L4
来源: Citadel

题目详情

问题：正则表达式匹配

考察：字符串、动态规划、递归

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/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 (.)".

Constraints:

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

解析

思路：二维 DP，dp[i][j] 表示 s 前 i 个字符能否匹配 p 前 j 个字符。普通字符和 . 直接匹配前一状态；遇到 * 时可表示零个前字符，或在当前字符匹配时继续消费 s。

复杂度：时间 O(mn)，空间 O(mn)。