Question

I wonder wether it is feasible to implement an optimal string generator Class meeting the following second thought requirements:

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• Generation criteria using regex
• Lexicographical order enumeration.
• Count propetry
• Indexed access

I don’t feel comfortable with regular expression: I cannot come up with a starting piece of code but I just think of a naive implementation using a TList as a base class and use a filter (Regex) against “brute force” generated string.

What are the other optimal alternatives ?

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• Ordering: First by length (shortest first), then lexicographically.
• Specification of the range of characters to be used in the generation: All printable or any possible combination of [A-Z], [a-z], numbers, special symbols, and eventually space (regex ?).
• String Length bounded with a given Min/Max.
• Space of search constrained with bounds: Start string an End string with possibility of filtering (regex ?)

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Last Edit

To begin with, I rephrased the header using regex like instead of regex.

I am considering to revise the first requirement as it is an open door which may lead to untractable issue.

I need suggestions and help for the correct wording.

Second thought requirements edit done. Still open to suggestion for refinement.

Answer 1

I’d do this by constructing the minimum Deterministic Finite Automaton for the language. If you are starting with a regex, this can be done automatically by Thompson’s Construction followed by the Subset Construction and minimization. See this description for example.

With a DFA in hand, you can use something like this algorithm:

Let P = { < START, [""] > } be a set of pairs <State, list of strings>
for n = 0, 1, ... Max
  Let P' = {} be a new set 
  while P is not empty 
    Remove the pair <s, L> from P 
    For each transition s -- c --> t in alpha order of c
      if t is an accepting state,
          output l + c for each string l in L
      put <t, L + c> in P' (** i.e. append c to each string in L)
  end
  Set P = P'
end

Note that the step marked ** needs to be true set insertion, as duplicates can easily crop up.

This is a core algorithm. P can grow exponentially with output length, but this is just the price of tracking all possibilities for a future output string. The order/size/space constraints you mentioned can be ensured by maintaining sorted order in the lists L and by cutting off the search when resource limits are reached.

Edit

Here is a toy Java example where I’ve hard coded the DFA for simple binary floating point literals with optional minus sign. This uses a slightly different scheme than the pseudocode above to get strict sorted order of output and to accomodate character ranges.

import java.util.Comparator;
import java.util.TreeSet;

public class Test{

    public static class DFA {

        public static class Transition  {

            final int to;
            final char lo, hi; // Character range.

            public Transition(int to, char lo, char hi) {
                this.to = to;
                this.lo = lo;
                this.hi = hi;
            }

            public Transition(int to, char ch) {
                this(to, ch, ch);
            }
        }

        // transitions[i] is a vector of transitions from state i.
        final Transition [] [] transitions;

        // accepting[i] is true iff state i is accepting
        final boolean [] accepting;

        // Make a fresh immutable DFA.
        public DFA(Transition [] [] transitions, boolean [] accepting) {
            this.transitions = transitions;
            this.accepting = accepting;
        }

        // A pair is a DFA state number and the input string read to get there.
        private static class Pair {
            final int at;
            final String s;

            Pair(int at, String s) {
                this.at = at;
                this.s = s;
            }
        }

        // Compare pairs ignoring `at` states, since 
        // they are equal iff the strings are equal.
        private Comparator<Pair> emitOrder = new Comparator<Pair>() {
            @Override
            public int compare(Pair a, Pair b) {
                return a.s.compareTo(b.s);
            }
        };

        // Emit all strings accepted by the DFA of given max length.
        // Output is in sorted order.
        void emit(int maxLength) {
            TreeSet<Pair> pairs = new TreeSet<Pair>(emitOrder);
            pairs.add(new Pair(0, ""));
            for (int len = 0; len <= maxLength; ++len) {
                TreeSet<Pair> newPairs = new TreeSet<Pair>(emitOrder);
                while (!pairs.isEmpty()) {
                    Pair pair = pairs.pollFirst();
                    for (Transition x : transitions[pair.at]) {
                        for (char ch = x.lo; ch <= x.hi; ch++) {
                            String s = pair.s + ch;
                            if (newPairs.add(new Pair(x.to, s)) && accepting[x.to]) {
                                System.out.println(s);
                            }
                        }
                    }
                }
                pairs = newPairs;
            }
        }
    }

    // Emit with a little DFA for floating point numbers.
    public void run() {
        DFA.Transition [] [] transitions = {
            {   // From 0
                new DFA.Transition(1, '-'),
                new DFA.Transition(2, '.'),
                new DFA.Transition(3, '0', '1'),
            },
            {   // From 1
                new DFA.Transition(2, '.'),
                new DFA.Transition(3, '0', '1'),
            },
            {   // From 2
                new DFA.Transition(4, '0', '1'),
            },
            {   // From 3
                new DFA.Transition(3, '0', '1'),
                new DFA.Transition(4, '.'),
            },
            {   // From 4
                new DFA.Transition(4, '0', '1'),
            }  
        };
        boolean [] accepting = { false, false, false, true, true };
        new DFA(transitions, accepting).emit(4);
    }

    public static void main (String [] args) {
        new Test().run();
    }
}