Given an input string (
s) and a pattern (p), 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).
Note:
scould be empty and contains only lowercase lettersa-z.pcould be empty and contains only lowercase lettersa-z, and characters like?or*.
Example:
Input:
s = "aa"
p = "a"
Output: false
Explanation: "a" does not match the entire string "aa".
Input:
s = "aa"
p = "*"
Output: true
Explanation: '*' matches any sequence.
Input:
s = "cb"
p = "?a"
Output: false
Explanation: '?' matches 'c', but the second letter is 'a', which does not match 'b'.
Input:
s = "adceb"
p = "*a*b"
Output: true
Explanation: The first '*' matches the empty sequence, while the second '*' matches the substring "dce".
Input:
s = "acdcb"
p = "a*c?b"
Output: false
Thoughts
- 类似LC10,都是字符串匹配问题，首先就会想到DP来解决问题。
- 和LC10不同的是，这里是from top to bottom，比较容易理解的dp，而LC10则是需要从后往前思考。
- 状态转换数组
dp[i][j]表示字符串s中的前i个元素是否和字符串p中的前j个元素匹配。 - 状态转换方程：
$$
dp[i][j]=
\begin{cases}
=dp[i-1][j] \ || \ dp[i][j-1] \ || \ dp[i-1][j-1]
!= \begin{cases} dp[i-1][j-1] & \text{matched}
false & \text{not match} \end{cases} \end{cases}
$$
Code(JAVA)
public boolean isMatch(String s, String p) {
boolean[][] dp = new boolean[s.length()+1][p.length(+1];
//init boundary
dp[0][0] = true;
for (int j = 1; j <= p.length(); j ++) {
if (p.charAt(j - 1) == '*') {
dp[0][j] = dp[0][j - 1];
}
}
//dp
for(int i = 1; i <= s.length(); i++) {
for(int j = 1;j <= p.length(); j++) {
boolean star = p.charAt(j-1) == '*';
boolean match = (p.charAt(j-1) == '?' || pcharAt(j-1) == s.charAt(i-1));
if(star)
dp[i][j] = dp[i-1][j] || dp[i][j-1] || dp[i-1][j-1];
else if(match)
dp[i][j] = dp[i-1][j-1];
else
dp[i][j] =false;
}
}
return dp[s.length()][p.length()];
}
