Wildcard Matching

Description

Implement wildcard pattern matching with support for '?' and '*'.

'?' Matches any single character.
'*' Matches any sequence of characters (including the empty sequence).

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", "*") → true
isMatch("aa", "a*") → true
isMatch("ab", "?*") → true
isMatch("aab", "c*a*b") → false

Tags: String, Dynamic Programming, Backtracking, Greedy

思路0

题意是让让你从判断s字符串是否通配符匹配于p，这道题和Regular Expression Matching很是相似，区别在于*，正则匹配的*不能单独存在，前面必须具有一个字符，其意义是表明前面的这个字符个数可以是任意个数，包括0个；而通配符的*是可以随意出现的，跟前面字符没有任何关系，其作用是可以表示任意字符串。在此我们可以利用贪心算法来解决这个问题，需要两个额外指针p和match来分别记录最后一个*的位置和*匹配到s字符串的位置，其贪心体现在如果遇到*，那就尽可能取匹配后方的内容，如果匹配失败，那就回到上一个遇到*的位置来继续贪心。

class Solution {
    public boolean isMatch(String s, String p) {
        if (p.length() == 0) return s.length() == 0;
        int si = 0, pi = 0, match = 0, star = -1;
        int sl = s.length(), pl = p.length();
        char[] sc = s.toCharArray(), pc = p.toCharArray();
        while (si < sl) {
            if (pi < pl && (pc[pi] == sc[si] || pc[pi] == '?')) {
                si++;
                pi++;
            } else if (pi < pl && pc[pi] == '*') {
                star = pi++;
                match = si;
            } else if (star != -1) {
                si = ++match;
                pi = star + 1;
            } else return false;
        }
        while (pi < pl && pc[pi] == '*') pi++;
        return pi == pl;
    }
}

思路1

另一种思路就是动态规划了，我们定义dp[i][j]的真假来表示s[0..i)是否匹配p[0..j)，其状态转移方程如下所示：

• 如果p[j - 1] != '*'，P[i][j] = P[i - 1][j - 1] && (s[i - 1] == p[j - 1] || p[j - 1] == '?');
• 如果p[j - 1] == '*'，P[i][j] = P[i][j - 1] || P[i - 1][j]

class Solution {
    public boolean isMatch(String s, String p) {
        if (p.length() == 0) return s.length() == 0;
        int sl = s.length(), pl = p.length();
        boolean[][] dp = new boolean[sl + 1][pl + 1];
        char[] sc = s.toCharArray(), pc = p.toCharArray();
        dp[0][0] = true;
        for (int i = 1; i <= pl; ++i) {
            if (pc[i - 1] == '*') dp[0][i] = dp[0][i - 1];
        }
        for (int i = 1; i <= sl; ++i) {
            for (int j = 1; j <= pl; ++j) {
                if (pc[j - 1] != '*') {
                    dp[i][j] = dp[i - 1][j - 1] && (sc[i - 1] == pc[j - 1] || pc[j - 1] == '?');
                } else {
                    dp[i][j] = dp[i][j - 1] || dp[i - 1][j];
                }
            }
        }
        return dp[sl][pl];
    }
}

结语

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