leetcode 10. Regular Expression Matching

本文介绍了一种使用递归方法实现正则表达式匹配的算法。重点讲解了如何处理‘.’和‘*’这两个特殊字符,并通过具体的代码示例展示了整个匹配过程。

1.题目

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:
bool isMatch(const char *s, const char *p)

Some examples:
isMatch("aa","a") → false
isMatch("aa","aa") → true
isMatch("aaa","aa") → false
isMatch("aa", "a*") → true
isMatch("aa", ".*") → true
isMatch("ab", ".*") → true
isMatch("aab", "c*a*b") → true

'.'  匹配单个的任意字符,

'*'  匹配0个或者多个前一个字符;

2.思路 

利用递归。

bool isMatch(const char *s, const char *p) {
         
        if (*p == 0) return *s == 0;
        if (*(p+1) != '*')
        {
            if (*s != 0 && (*p == *s || *p == '.')) return isMatch(s+1, p+1);
            else return false;
        }
        else
        {
            // *s == *p
            while (*s != 0 && (*s == *p || *p == '.'))
            {
                if (isMatch(s, p+2)) return true;
                s++;
            }
            return (isMatch(s, p+2));
        }
    }


LeetCode Problem 10, known as Regular Expression Matching, involves determining if a string matches a given pattern, considering special characters like `.` and `*`. The solution typically requires a recursive approach or dynamic programming to handle the complexities introduced by these special characters. Below is a Java implementation using recursion to solve this problem: ```java public class Solution { public boolean isMatch(String s, String p) { if (s == null || p == null) { return false; } int lenS = s.length(); int lenP = p.length(); if (lenP == 0) { return lenS == 0; } if (lenP == 1) { if (p.equals(s) || p.equals(".")) { return true; } else { return false; } } if (p.charAt(1) == '*') { while (s.length() > 0 && (p.charAt(0) == s.charAt(0) || p.charAt(0) == '.')) { if (isMatch(s, p.substring(2))) { return true; } s = s.substring(1); } return isMatch(s, p.substring(2)); } else { if (s.length() > 0 && (p.charAt(0) == s.charAt(0) || p.charAt(0) == '.')) { return isMatch(s.substring(1), p.substring(1)); } return false; } } } ``` This solution recursively checks for matches by evaluating the current characters and handling the `*` wildcard, which allows for zero or more of the preceding element. The function proceeds by either skipping the current pattern and the next (if the next character is `*`) or by matching the current character and proceeding in both strings. The implementation efficiently breaks down the problem into manageable recursive calls, ensuring all possible matches are explored, especially when dealing with the `*` operator, which introduces backtracking possibilities to find a valid match path[^2].
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