10. Regular Expression Matching （dp）

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") → falseisMatch("aa","aa") → trueisMatch("aaa","aa") → falseisMatch("aa", "a*") → trueisMatch("aa", ".*") → trueisMatch("ab", ".*") → trueisMatch("aab", "c*a*b") → true

这个跟之前多校有道题很像，除了"."的匹配不一样。

#include <iostream>#include <algorithm>#include <string.h>#include <vector>#include <sstream>#include <stdio.h>using namespace std;bool isMatch(const string& s, const string& p) {    int slen = s.size();    int plen = p.size();    //dp[i + 1][j + 1]表示 s[i]跟p[j]当前的匹配情况    /**     * bp[i + 1][j + 1]: if s[0..i] matches p[0..j]     * if p[j] != '*'     * bp[i + 1][j + 1] = bp[i][j] && s[i] == p[j]     * if p[j] == '*', denote p[j - 1] with x,     * then bp[i + 1][j + 1] is true iff any of the following is true     * 1) "x*" repeats 0 time and matches empty: bp[i + 1][j -1]     * 2) "x*" repeats 1 time and matches x: bp[i + 1][j]     * 3) "x*" repeats >= 2 times and matches "x*x": s[i] == x && bp[i][j + 1]     * '.' matches any single character     可以画一个方格图，就像最长公共子序列一样，就比较好理解了     */        bool dp[slen + 1][plen + 1];    dp[0][0] = 1;    for (int i = 0; i < slen; ++i) {        dp[i + 1][0] = 0;    }    for (int i = 0; i < plen; ++i) {        dp[0][i + 1] = i > 0 && p[i] == '*' && dp[0][i - 1];    }        for (int i = 0; i < slen; ++i) {        for (int j = 0; j < plen; ++j) {            if (p[j] == '*') {           //x*匹配0个x的时候         x*匹配1个x的时候   x*匹配>=2个x的时候 x*x                dp[i + 1][j + 1] = (j > 0 && dp[i + 1][j - 1]) || dp[i + 1][j] || (dp[i][j + 1] && j > 0 && (p[j - 1] == '.' || s[i] == p[j - 1]));            } else {                dp[i + 1][j + 1] = dp[i][j] && (s[i] == p[j] || p[j] == '.');            }        }    }        return dp[slen][plen];}int main() {    cout << isMatch("aab", "c*a*b") << endl;;}