Regular Expression Matching

描述

Implement regular expression matching with support for '.' and '*'.

'.' Matches any single character.'*' Matches zero or more of the preceding element.

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

The function prototype should be:

  1. bool isMatch(const char *s, const char *p)

Some examples:

  1. isMatch("aa","a") → false
  2. isMatch("aa","aa") → true
  3. isMatch("aaa","aa") → false
  4. isMatch("aa", "a*") → true
  5. isMatch("aa", ".*") → true
  6. isMatch("ab", ".*") → true
  7. isMatch("aab", "c*a*b") → true

分析

这是一道很有挑战的题。

递归版

  1. // Regular Expression Matching
  2. // Time complexity: O(n)
  3. // Space complexity: O(1)
  4. class Solution {
  5. public:
  6.     bool isMatch(const string& s, const string& p) {
  7.         return isMatch(s.c_str(), p.c_str());
  8.     }
  9. private:
  10.     bool matchFirst(const char *s, const char *p) {
  11.         return *p == *s || (*p == '.' && *s != '\0');
  12.     }
  14.     bool isMatch(const char *s, const char *p) {
  15.         if (*p == '\0') return *s == '\0';    //empty
  17.         // next char is not '*', then must match current character
  18.         if (*(p + 1) != '*') {
  19.             if (matchFirst(s, p)) return isMatch(s + 1, p + 1);
  20.             else return false;
  21.         } else { // next char is '*'
  22.             if (isMatch(s, p + 2)) return true;    // try the length of 0
  23.             while ( matchFirst(s, p) )       // try all possible lengths 
  24.                 if (isMatch(++s, p + 2)) return true;
  25.             return false;
  26.         }
  27.     }
  28. };

相关题目

原文: https://soulmachine.gitbooks.io/algorithm-essentials/content/cpp/string/regular-expression-matching.html