Finite Automaton Matching: String Matching

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#finite #automation #matching #algorithm #java

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本文介绍了一种基于有限状态机的字符串匹配算法，并提供了详细的Java实现代码。该算法通过构建状态转移矩阵，能够高效地在目标文本中查找指定模式串出现的位置。

Finite automation machine:

这里写图片描述

Pseudo code:

这里写图片描述

Java code:

/**
 * Created with IntelliJ IDEA.
 * User: 1O1O
 * Date: 2015-03-31
 * Time: 21:29 PM
 * :)~
 * FINITE-AUTOMATON-MATCH:STRING-MATCH
 */
public class Main {
    public static int[][] COMPUTE_TRANSITION_FUNCTION(String Pattern, char[] sigma){
        int m = Pattern.length();
        int n = sigma.length;
        int[][] delta = new int[m+1][n];
        for(int q=0; q<=m; q++){
            for(int i=0; i<n; i++){
                int k = ((m+1)<=(q+2))?(m+1):(q+2);
                do{
                    k = k-1;
                    if(k == 0){
                        delta[q][i] = 0;
                        break;
                    }
                    String Pk = Pattern.substring(0, k);
                    String Pq = Pattern.substring(0, q) + sigma[i];
                    int Pq_len = Pq.length();
                    int j;
                    for(j=k-1; j>-1; j--){
                        if(Pk.charAt(j) == Pq.charAt(--Pq_len))
                            continue;
                        else
                            break;
                    }
                    if(j == -1){
                        delta[q][i] = k;
                        break;
                    }
                }while(true);

            }
        }

        //Format Output:
        System.out.println("Stat  a     b     c     P");
        for(int i=0; i<=m; i++){
            System.out.print(String.format("%-6s", i));
            for(int j=0; j<n; j++){
                System.out.print(String.format("%-6s", delta[i][j]));
            }
            if(i != m)
                System.out.print(Pattern.charAt(i));
            System.out.println();
        }
        return delta;
    }

    public static void FINITE_AUTOMATON_MATCHER(String Text, int[][] delta, int m){
        int n = Text.length();
        int q = 0;
        int index;
        for(int i=0; i<n; i++){
            switch(Text.charAt(i)){
                case 'a': index = 0; break;
                case 'b': index = 1; break;
                case 'c': index = 2; break;
                default: index = 0;
            }
            q = delta[q][index];
            if(q == m){
                System.out.println("Pattern occurs with shift: "+(i-m+2));
            }
        }
    }

    public static void main(String[] args) {
        String Text = "bacbababaabcbabababacababbababacabbc";
        String Pattern = "ababaca";
        int m = Pattern.length();
        char[] sigma = {'a','b','c'};
        int[][] delta = COMPUTE_TRANSITION_FUNCTION(Pattern, sigma);
        FINITE_AUTOMATON_MATCHER(Text, delta, m);
    }
}

Output：

Stat  a     b     c     P
0     1     0     0     a
1     1     2     0     b
2     3     0     0     a
3     1     4     0     b
4     5     0     0     a
5     1     4     6     c
6     7     0     0     a
7     1     2     0     
Pattern occurs with shift: 16
Pattern occurs with shift: 27

Reference:

From: 《INTRODUCTION TO ALGORITHMS》THIRD EDITION.