LeetCode Java First 400 题解-010

Regular Expression Matching    Hard

Given an input string (s) and a pattern (p), 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).

Note:

• s could be empty and contains only lowercase letters a-z.
• p could be empty and contains only lowercase letters a-z, and characters like . or *.

Example 1:

Input:

s = "aa"

p = "a"

Output: false

Explanation: "a" does not match the entire string "aa".

Example 2:

Input:

s = "aa"

p = "a*"

Output: true

Explanation: '*' means zero or more of the precedeng element, 'a'. Therefore, by repeating 'a' once, it becomes "aa".

Example 3:

Input:

s = "ab"

p = ".*"

Output: true

Explanation: ".*" means "zero or more (*) of any character (.)".

Example 4:

Input:

s = "aab"

p = "c*a*b"

Output: true

Explanation: c can be repeated 0 times, a can be repeated 1 time. Therefore it matches "aab".

Example 5:

Input:

s = "mississippi"

p = "mis*is*p*."

Output: false

public boolean isMatch(String str, String regex) {

    int m = str.length(), n = regex.length();

    boolean[][] dp = new boolean[m + 1][n + 1];

    dp[0][0] = true;

    for (int i = 1; i <= n; ++i) {

        if (regex.charAt(i - 1) == '*')

            dp[0][i] = dp[0][i - 2];

    }



    for (int i = 1; i <= m; i++) {

        for (int j = 1; j <= n; j++) {

            if (match(str.charAt(i - 1), regex.charAt(j - 1)))

                dp[i][j] = dp[i - 1][j - 1];

            else if (regex.charAt(j - 1) == '*') {

                dp[i][j] = dp[i][j - 2];// *前字符出现0次

                if (match(str.charAt(i - 1), regex.charAt(j - 2)))

                    dp[i][j] |= dp[i - 1][j];//*前字符出现过

            }

        }

    }

    return dp[m][n];

}



private boolean match(char s, char p) {

    return p == '.' || s == p;

}

思路：动态规划。如果P(regex,i)和S(str,j)当前字符相当（或P是.），则结果与上一位置(i-1,j-1)相同。如果当前位置不等，则为False。如果当前位置P值为*，如果P上一位置与S当前相等或为”.”，则结果与上一S位置相同(i-1,j)。

动态规划的基本特点：先看到当前点最优情况，记录下来，到下一点看最优情况，记录，所有点完成后，取最后叠加最优。