通配符模式匹配

给定文本和通配符模式，实现通配符模式匹配算法，以查找通配符模式是否与文本匹配。匹配应涵盖整个文本(而不是部分文本)。
通配符模式可以包含字符“?”和 ‘*’
‘? – 匹配任何单个字符
‘*’ – 匹配任何字符序列(包括空序列)

例如，

Text = "baaabab",
Pattern = “*****ba*****ab", output : true
Pattern = "baaa?ab", output : true
Pattern = "ba*a?", output : true
Pattern = "a*ab", output : false 

每次出现“?”通配符模式中的字符可以替换为任何其他字符，并且每次出现的 ‘*’ 都带有一个字符序列，这样通配符模式在替换后变得与输入字符串相同。

让我们考虑模式中的任何字符。

情况一：字符为’*’
这里出现两种情况

1. 我们可以忽略“*”字符并移动到模式中的下一个字符。
2. ‘*’字符与 Text 中的一个或多个字符匹配。在这里，我们将移至字符串的下一个字符。

情况 2：字符是 ‘?’
我们可以忽略 Text 中的当前字符并移动到 Pattern 和 Text 中的下一个字符。
案例3：字符不是字符
如果在文本当前字符与图形当前字符相匹配，我们移动到图形和文本下一个字符。如果它们不匹配，则通配符模式和文本不匹配。
我们可以使用动态规划来解决这个问题——
如果在给定的字符串的第一字符我图案的第j个字符匹配令T [i] [j]是真实的。

DP初始化：

// both text and pattern are null
T[0][0] = true; 

// pattern is null
T[i][0] = false; 

// text is null
T[0][j] = T[0][j - 1] if pattern[j – 1] is '*'  

DP关系：

// If current characters match, result is same as 
// result for lengths minus one. Characters match
// in two cases:
// a) If pattern character is '?' then it matches  
//    with any character of text. 
// b) If current characters in both match
if ( pattern[j – 1] == ‘?’) || 
     (pattern[j – 1] == text[i - 1])
    T[i][j] = T[i-1][j-1]   
 
// If we encounter ‘*’, two choices are possible-
// a) We ignore ‘*’ character and move to next 
//    character in the pattern, i.e., ‘*’ 
//    indicates an empty sequence.
// b) '*' character matches with ith character in
//     input 
else if (pattern[j – 1] == ‘*’)
    T[i][j] = T[i][j-1] || T[i-1][j]  

else // if (pattern[j – 1] != text[i - 1])
    T[i][j]  = false 

下面是上述动态规划方法的实现。

C++

// C++ program to implement wildcard
// pattern matching algorithm
#include 
using namespace std;
 
// Function that matches input str with
// given wildcard pattern
bool strmatch(char str[], char pattern[], int n, int m)
{
    // empty pattern can only match with
    // empty string
    if (m == 0)
        return (n == 0);
 
    // lookup table for storing results of
    // subproblems
    bool lookup[n + 1][m + 1];
 
    // initialize lookup table to false
    memset(lookup, false, sizeof(lookup));
 
    // empty pattern can match with empty string
    lookup[0][0] = true;
 
    // Only '*' can match with empty string
    for (int j = 1; j <= m; j++)
        if (pattern[j - 1] == '*')
            lookup[0][j] = lookup[0][j - 1];
 
    // fill the table in bottom-up fashion
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            // Two cases if we see a '*'
            // a) We ignore ‘*’ character and move
            //    to next  character in the pattern,
            //     i.e., ‘*’ indicates an empty sequence.
            // b) '*' character matches with ith
            //     character in input
            if (pattern[j - 1] == '*')
                lookup[i][j]
                    = lookup[i][j - 1] || lookup[i - 1][j];
 
            // Current characters are considered as
            // matching in two cases
            // (a) current character of pattern is '?'
            // (b) characters actually match
            else if (pattern[j - 1] == '?'
                     || str[i - 1] == pattern[j - 1])
                lookup[i][j] = lookup[i - 1][j - 1];
 
            // If characters don't match
            else
                lookup[i][j] = false;
        }
    }
 
    return lookup[n][m];
}
 
int main()
{
    char str[] = "baaabab";
    char pattern[] = "*****ba*****ab";
    // char pattern[] = "ba*****ab";
    // char pattern[] = "ba*ab";
    // char pattern[] = "a*ab";
    // char pattern[] = "a*****ab";
    // char pattern[] = "*a*****ab";
    // char pattern[] = "ba*ab****";
    // char pattern[] = "****";
    // char pattern[] = "*";
    // char pattern[] = "aa?ab";
    // char pattern[] = "b*b";
    // char pattern[] = "a*a";
    // char pattern[] = "baaabab";
    // char pattern[] = "?baaabab";
    // char pattern[] = "*baaaba*";
 
    if (strmatch(str, pattern, strlen(str),
                 strlen(pattern)))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
 
    return 0;
}

Java

// Java program to implement wildcard
// pattern matching algorithm
import java.util.Arrays;
public class GFG {
 
    // Function that matches input str with
    // given wildcard pattern
    static boolean strmatch(String str, String pattern,
                            int n, int m)
    {
        // empty pattern can only match with
        // empty string
        if (m == 0)
            return (n == 0);
 
        // lookup table for storing results of
        // subproblems
        boolean[][] lookup = new boolean[n + 1][m + 1];
 
        // initialize lookup table to false
        for (int i = 0; i < n + 1; i++)
            Arrays.fill(lookup[i], false);
 
        // empty pattern can match with empty string
        lookup[0][0] = true;
 
        // Only '*' can match with empty string
        for (int j = 1; j <= m; j++)
            if (pattern.charAt(j - 1) == '*')
                lookup[0][j] = lookup[0][j - 1];
 
        // fill the table in bottom-up fashion
        for (int i = 1; i <= n; i++)
        {
            for (int j = 1; j <= m; j++)
            {
                // Two cases if we see a '*'
                // a) We ignore '*'' character and move
                //    to next  character in the pattern,
                //     i.e., '*' indicates an empty
                //     sequence.
                // b) '*' character matches with ith
                //     character in input
                if (pattern.charAt(j - 1) == '*')
                    lookup[i][j] = lookup[i][j - 1]
                                   || lookup[i - 1][j];
 
                // Current characters are considered as
                // matching in two cases
                // (a) current character of pattern is '?'
                // (b) characters actually match
                else if (pattern.charAt(j - 1) == '?'
                         || str.charAt(i - 1)
                                == pattern.charAt(j - 1))
                    lookup[i][j] = lookup[i - 1][j - 1];
 
                // If characters don't match
                else
                    lookup[i][j] = false;
            }
        }
 
        return lookup[n][m];
    }
 
   
    // Driver code
    public static void main(String args[])
    {
        String str = "baaabab";
        String pattern = "*****ba*****ab";
        // String pattern = "ba*****ab";
        // String pattern = "ba*ab";
        // String pattern = "a*ab";
        // String pattern = "a*****ab";
        // String pattern = "*a*****ab";
        // String pattern = "ba*ab****";
        // String pattern = "****";
        // String pattern = "*";
        // String pattern = "aa?ab";
        // String pattern = "b*b";
        // String pattern = "a*a";
        // String pattern = "baaabab";
        // String pattern = "?baaabab";
        // String pattern = "*baaaba*";
 
        if (strmatch(str, pattern, str.length(),
                     pattern.length()))
            System.out.println("Yes");
        else
            System.out.println("No");
    }
}
// This code is contributed by Sumit Ghosh

Python3

# Python program to implement wildcard
# pattern matching algorithm
 
# Function that matches input strr with
# given wildcard pattern
 
 
def strrmatch(strr, pattern, n, m):
 
    # empty pattern can only match with
    # empty string
    if (m == 0):
        return (n == 0)
 
    # lookup table for storing results of
    # subproblems
    lookup = [[False for i in range(m + 1)] for j in range(n + 1)]
 
    # empty pattern can match with empty string
    lookup[0][0] = True
 
    # Only '*' can match with empty string
    for j in range(1, m + 1):
        if (pattern[j - 1] == '*'):
            lookup[0][j] = lookup[0][j - 1]
 
    # fill the table in bottom-up fashion
    for i in range(1, n + 1):
        for j in range(1, m + 1):
 
            # Two cases if we see a '*'
            # a) We ignore ‘*’ character and move
            # to next character in the pattern,
            # i.e., ‘*’ indicates an empty sequence.
            # b) '*' character matches with ith
            # character in input
            if (pattern[j - 1] == '*'):
                lookup[i][j] = lookup[i][j - 1] or lookup[i - 1][j]
 
            # Current characters are considered as
            # matching in two cases
            # (a) current character of pattern is '?'
            # (b) characters actually match
            elif (pattern[j - 1] == '?' or strr[i - 1] == pattern[j - 1]):
                lookup[i][j] = lookup[i - 1][j - 1]
 
            # If characters don't match
            else:
                lookup[i][j] = False
 
    return lookup[n][m]
 
# Driver code
 
 
strr = "baaabab"
pattern = "*****ba*****ab"
# char pattern[] = "ba*****ab"
# char pattern[] = "ba*ab"
# char pattern[] = "a*ab"
# char pattern[] = "a*****ab"
# char pattern[] = "*a*****ab"
# char pattern[] = "ba*ab****"
# char pattern[] = "****"
# char pattern[] = "*"
# char pattern[] = "aa?ab"
# char pattern[] = "b*b"
# char pattern[] = "a*a"
# char pattern[] = "baaabab"
# char pattern[] = "?baaabab"
# char pattern[] = "*baaaba*"
 
if (strrmatch(strr, pattern, len(strr), len(pattern))):
    print("Yes")
else:
    print("No")
 
# This code is contributed by shubhamsingh10

C#

// C# program to implement wildcard
// pattern matching algorithm
using System;
 
class GFG {
 
    // Function that matches input str with
    // given wildcard pattern
    static Boolean strmatch(String str,
                            String pattern,
                            int n, int m)
    {
        // empty pattern can only match with
        // empty string
        if (m == 0)
            return (n == 0);
 
        // lookup table for storing results of
        // subproblems
        Boolean[, ] lookup = new Boolean[n + 1, m + 1];
 
        // initialize lookup table to false
        for (int i = 0; i < n + 1; i++)
            for (int j = 0; j < m + 1; j++)
                lookup[i, j] = false;
 
        // empty pattern can match with
        // empty string
        lookup[0, 0] = true;
 
        // Only '*' can match with empty string
        for (int j = 1; j <= m; j++)
            if (pattern[j - 1] == '*')
                lookup[0, j] = lookup[0, j - 1];
 
        // fill the table in bottom-up fashion
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= m; j++) {
                // Two cases if we see a '*'
                // a) We ignore '*'' character and move
                // to next character in the pattern,
                //     i.e., '*' indicates an empty
                //     sequence.
                // b) '*' character matches with ith
                //     character in input
                if (pattern[j - 1] == '*')
                    lookup[i, j] = lookup[i, j - 1]
                                   || lookup[i - 1, j];
 
                // Current characters are considered as
                // matching in two cases
                // (a) current character of pattern is '?'
                // (b) characters actually match
                else if (pattern[j - 1] == '?'
                         || str[i - 1] == pattern[j - 1])
                    lookup[i, j] = lookup[i - 1, j - 1];
 
                // If characters don't match
                else
                    lookup[i, j] = false;
            }
        }
        return lookup[n, m];
    }
 
    // Driver Code
    public static void Main(String[] args)
    {
        String str = "baaabab";
        String pattern = "*****ba*****ab";
        // String pattern = "ba*****ab";
        // String pattern = "ba*ab";
        // String pattern = "a*ab";
        // String pattern = "a*****ab";
        // String pattern = "*a*****ab";
        // String pattern = "ba*ab****";
        // String pattern = "****";
        // String pattern = "*";
        // String pattern = "aa?ab";
        // String pattern = "b*b";
        // String pattern = "a*a";
        // String pattern = "baaabab";
        // String pattern = "?baaabab";
        // String pattern = "*baaaba*";
 
        if (strmatch(str, pattern, str.Length,
                     pattern.Length))
            Console.WriteLine("Yes");
        else
            Console.WriteLine("No");
    }
}
 
// This code is contributed by Rajput-Ji

输出

Yes

时间复杂度： O(mxn)
辅助空间： O(mxn)

DP 记忆解决方案：-

C++

// C++ program to implement wildcard
// pattern matching algorithm
#include 
using namespace std;
 
// Function that matches input str with
// given wildcard pattern
vector > dp;
int finding(string& s, string& p, int n, int m)
{
    // return 1 if n and m are negative
    if (n < 0 && m < 0)
        return 1;
   
    // return 0 if m is negative
    if (m < 0)
        return 0;
   
    // return n if n is negative
    if (n < 0)
    {
        // while m is positve
        while (m >= 0)
        {
            if (p[m] != '*')
                return 0;
            m--;
        }
        return 1;
    }
    
    // if dp state is not visited
    if (dp[n][m] == -1)
    {
        if (p[m] == '*')
        {
            return dp[n][m] = finding(s, p, n - 1, m)
                              || finding(s, p, n, m - 1);
        }
        else
        {
            if (p[m] != s[n] && p[m] != '?')
                return dp[n][m] = 0;
            else
                return dp[n][m]
                       = finding(s, p, n - 1, m - 1);
        }
    }
   
    // return dp[n][m] if dp state is previsited
    return dp[n][m];
}
 
 
bool isMatch(string s, string p)
{
    dp.clear();
     
    // resize the dp array
    dp.resize(s.size() + 1, vector(p.size() + 1, -1));
    return dp[s.size()][p.size()]
           = finding(s, p, s.size() - 1, p.size() - 1);
}
 
// Driver code
int main()
{
    string str = "baaabab";
    string pattern = "*****ba*****ab";
    // char pattern[] = "ba*****ab";
    // char pattern[] = "ba*ab";
    // char pattern[] = "a*ab";
    // char pattern[] = "a*****ab";
    // char pattern[] = "*a*****ab";
    // char pattern[] = "ba*ab****";
    // char pattern[] = "****";
    // char pattern[] = "*";
    // char pattern[] = "aa?ab";
    // char pattern[] = "b*b";
    // char pattern[] = "a*a";
    // char pattern[] = "baaabab";
    // char pattern[] = "?baaabab";
    // char pattern[] = "*baaaba*";
 
    if (isMatch(str, pattern))
        cout << "Yes" << endl;
    else
        cout << "No" << endl;
 
    return 0;
}

输出

Yes

时间复杂度：O(mxn)。
辅助空间： O(mxn)。

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