## Sunday, June 12, 2016

### Wildcard Pattern Matching - GeeksforGeeks

Related: Wildcard Matching, Leetcode

Wildcard Pattern Matching - GeeksforGeeks
Given a text and a wildcard pattern, implement wildcard pattern matching algorithm that finds if wildcard pattern is matched with text. The matching should cover the entire text (not partial text).
The wildcard pattern can include the characters '?' and '*'
'?' – matches any single character
'*' – Matches any sequence of characters (including the empty sequence)
Case 1: The character is ‘*’
Here two cases arise
1. We can ignore ‘*’ character and move to next character in the Pattern.
2. ‘*’ character matches with one or more characters in Text. Here we will move to next character in the string.
Case 2: The character is ‘?’
We can ignore current character in Text and move to next character in the Pattern and Text.
Case 3: The character is not a wildcard character
If current character in Text matches with current character in Pattern, we move to next character in the Pattern and Text. If they do not match, wildcard pattern and Text do not match.
We can use Dynamic Programming to solve this problem –
Let T[i][j] is true if first i characters in given string matches the first j characters of pattern.
DP Initialization:
```// 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 relation :
```// 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
```
`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];`

`    ``// initailze 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];`
`}`