How do I write a simple regular expression pattern matching function in C or C++?

Question

This is a question in my paper test today, the function signature is

int is_match(char* pattern,char* string)

The pattern is limited to only A

Answer 1

The full power of regular expressions and finite state machines are not needed to solve this problem. As an alternative there is a relatively simple dynamic programming solution.

Let match(i, j) be 1 if it is possible to match the the sub-string string[i..n-1] with the sub-pattern pattern[j, m - 1], where n and m are the lengths of string and pattern respectively. Otherwise let match(i, j) be 0.

The base cases are:

• match(n, m) = 1, you can match an empty string with an empty pattern;

• match(i, m) = 0, you can't match a non-empty string with an empty pattern;

The transition is divided into 3 cases depending on whether the current sub-pattern starts with a character followed by a '*', or a character followed by a '?' or just starts with a character with no special symbol after it.

#include 
#include 
#include 

int is_match(char* pattern, char* string)
{
  int n = strlen(string);
  int m = strlen(pattern);

  int i, j;
  int **match;

  match = (int **) malloc((n + 1) * sizeof(int *));
  for(i = 0; i <= n; i++) {
    match[i] = (int *) malloc((m + 1) * sizeof(int));
  }

  for(i = n; i >= 0; i--) {
    for(j = m; j >= 0; j--) {
      if(i == n && j == m) {
        match[i][j] = 1;
      }
      else if(i < n && j == m) {
        match[i][j] = 0;
      }
      else {
        match[i][j] = 0;
        if(pattern[j + 1] == '*') {
          if(match[i][j + 2]) match[i][j] = 1;
          if(i < n && pattern[j] == string[i] && match[i + 1][j]) match[i][j] = 1;
        }
        else if(pattern[j + 1] == '?') {
          if(match[i][j + 2]) match[i][j] = 1;
          if(i < n && pattern[j] == string[i] && match[i + 1][j + 2]) match[i][j] = 1;
        }
        else if(i < n && pattern[j] == string[i] && match[i + 1][j + 1]) {
          match[i][j] = 1;
        }
      }
    }
  }

  int result = match[0][0];

  for(i = 0; i <= n; i++) {
    free(match[i]);
  }

  free(match);

  return result;
}

int main(void)
{
  printf("is_match(dummy, dummy)  = %d\n", is_match("dummy","dummy"));
  printf("is_match(dumm?y, dummy) = %d\n", is_match("dumm?y","dummy"));
  printf("is_match(dum?y, dummy)  = %d\n", is_match("dum?y","dummy"));
  printf("is_match(dum*y, dummy)  = %d\n", is_match("dum*y","dummy")); 

  system("pause");

  return 0;
}

The time complexity of this approach is O(n * m). The memory complexity is also O(n * m) but with a simple modification can be reduced to O(m).