使用DFA,您可以使用以下算法：

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

请注意,标记为**的步骤需要设置为true,因为重复项可以轻松地出现.

这是一个核心算法. P可以随着输出长度呈指数增长,但这只是跟踪未来输出字符串的所有可能性的代价.您可以通过在列表L中维护排序顺序并通过在达到资源限制时切断搜索来确保您提到的订单/大小/空间限制.

编辑

这里是一个玩具Java示例,其中我已经将DFA用简单的二进制浮点文字编码,并带有可选的减号.这使用与上面的伪代码稍微不同的方案来获得输出的严格排序顺序和适应字符范围.

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,{   // From 2
                new DFA.Transition(4,{   // From 3
                new DFA.Transition(3,new DFA.Transition(4,{   // From 4
                new DFA.Transition(4,}  
        };
        boolean [] accepting = { false,false,true,true };
        new DFA(transitions,accepting).emit(4);
    }

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