//NFA
import edu.princeton.cs.algs4.*;
public class NFA {
    private  Digraph G;
    private  char[] ch;
    private int N;

    public NFA(String regexp) {
        Stack<Integer> ops = new Stack<>();
        ch = regexp.toCharArray();
        this.N = regexp.length();
        G = new Digraph(N + 1);
        for (int i = 0 ; i < N ; i++) {
            int bracket = i;
            if (ch[i] == '(' || ch[i] == '|') ops.push(i);
            else if (ch[i] == ')') {
                int or = ops.pop();
                if (or == '|') {
                    bracket = ops.pop();
                    G.addEdge(bracket, or + 1);
                    G.addEdge(or, i);
                }else bracket = or;
            }
            if (i < N-1 && ch[i+1] == '*') {
                G.addEdge(bracket, i + 1);
                G.addEdge(i + 1,bracket);
            }
            if (ch[i] == '*' || ch[i] == '(' || ch[i] == ')') G.addEdge(i, i + 1);
        }
    }

    public boolean recognizes(String txt) {
        Bag<Integer> pc = new Bag<>();
        DirectedDFS dfs = new DirectedDFS(G, 0);
        for (int v = 0 ; v < G.V();v++) {
            if (dfs.marked(v)) pc.add(v);
        }

        for (int i = 0; i < txt.length();i++) {
            Bag<Integer> match = new Bag<>();
            for (int v : pc) {
                if (v < N) {
                    if (ch[v] == txt.charAt(i) || ch[v] == '.') {
                        match.add(v);
                    }
                }
            }
            pc = new Bag<>();
            dfs = new DirectedDFS(G, match);
            for (int v = 0 ; v < G.V();v++) {
                if (dfs.marked(v)) pc.add(v);
            }
        }

        for (int v : pc) if (v == N) return true;
        return false;

        }

    }