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DFADefinitionBase.cs
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/ Implab / Parsing / DFADefinitionBase.cs
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Added initial JSON support...
 r55 using Implab;
using System;
using System.Collections.Generic;
using System.Diagnostics;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace Implab.Parsing {
public abstract class DFADefinitionBase : IDFADefinition {
readonly List<DFAStateDescriptior> m_states;
public const int INITIAL_STATE = 1;
public const int UNREACHEBLE_STATE = 0;
DFAStateDescriptior[] m_statesArray;
public DFADefinitionBase() {
m_states = new List<DFAStateDescriptior>();
m_states.Add(new DFAStateDescriptior());
}
public DFAStateDescriptior[] States {
get {
if (m_statesArray == null)
m_statesArray = m_states.ToArray();
return m_statesArray;
}
}
public bool InitialStateIsFinal {
get {
return m_states[INITIAL_STATE].final;
}
}
public int AddState() {
var index = m_states.Count;
m_states.Add(new DFAStateDescriptior {
final = false,
transitions = new int[AlphabetSize]
});
return index;
}
public int AddState(int[] tag) {
var index = m_states.Count;
bool final = tag == null || tag.Length == 0 ? false : true;
m_states.Add(new DFAStateDescriptior {
final = final,
transitions = new int[AlphabetSize],
tag = final ? tag : null
});
return index;
}
public void DefineTransition(int s1,int s2, int symbol) {
Safe.ArgumentInRange(s1, 0, m_states.Count-1, "s1");
Safe.ArgumentInRange(s2, 0, m_states.Count-1, "s2");
Safe.ArgumentInRange(symbol, 0, AlphabetSize-1, "symbol");
m_states[s1].transitions[symbol] = s2;
}
protected void Optimize<TA>(IDFADefinition minimalDFA,IAlphabet<TA> sourceAlphabet, IAlphabet<TA> minimalAlphabet) {
Safe.ArgumentNotNull(minimalDFA, "minimalDFA");
Safe.ArgumentNotNull(minimalAlphabet, "minimalAlphabet");
var setComparer = new CustomEqualityComparer<HashSet<int>>(
(x, y) => x.SetEquals(y),
(s) => s.Sum(x => x.GetHashCode())
);
var arrayComparer = new CustomEqualityComparer<int[]>(
(x,y) => (new HashSet<int>(x)).SetEquals(new HashSet<int>(y)),
(a) => a.Sum(x => x.GetHashCode())
);
var optimalStates = new HashSet<HashSet<int>>(setComparer);
var queue = new HashSet<HashSet<int>>(setComparer);
foreach (var g in Enumerable
.Range(INITIAL_STATE, m_states.Count-1)
.Select(i => new {
index = i,
descriptor = m_states[i]
})
.Where(x => x.descriptor.final)
.GroupBy(x => x.descriptor.tag, arrayComparer)
) {
optimalStates.Add(new HashSet<int>(g.Select(x => x.index)));
}
var state = new HashSet<int>(
Enumerable
.Range(INITIAL_STATE, m_states.Count - 1)
.Where(i => !m_states[i].final)
);
optimalStates.Add(state);
queue.Add(state);
while (queue.Count > 0) {
var stateA = queue.First();
queue.Remove(stateA);
for (int c = 0; c < AlphabetSize; c++) {
var stateX = new HashSet<int>();
for(int s = 1; s < m_states.Count; s++) {
if (stateA.Contains(m_states[s].transitions[c]))
stateX.Add(s);
}
foreach (var stateY in optimalStates.ToArray()) {
if (stateX.Overlaps(stateY) && !stateY.IsSubsetOf(stateX)) {
var stateR1 = new HashSet<int>(stateY);
var stateR2 = new HashSet<int>(stateY);
stateR1.IntersectWith(stateX);
stateR2.ExceptWith(stateX);
optimalStates.Remove(stateY);
optimalStates.Add(stateR1);
optimalStates.Add(stateR2);
if (queue.Contains(stateY)) {
queue.Remove(stateY);
queue.Add(stateR1);
queue.Add(stateR2);
} else {
queue.Add(stateR1.Count <= stateR2.Count ? stateR1 : stateR2);
}
}
}
}
}
// строим карты соотвествия оптимальных состояний с оригинальными
var initialState = optimalStates.Where(x => x.Contains(INITIAL_STATE)).Single();
// карта получения оптимального состояния по соотвествующему ему простому состоянию
int[] reveseOptimalMap = new int[m_states.Count];
// карта с индексами оптимальных состояний
HashSet<int>[] optimalMap = new HashSet<int>[optimalStates.Count + 1];
{
optimalMap[0] = new HashSet<int>(); // unreachable state
optimalMap[1] = initialState; // initial state
foreach (var ss in initialState)
reveseOptimalMap[ss] = 1;
int i = 2;
foreach (var s in optimalStates) {
if (s.SetEquals(initialState))
continue;
optimalMap[i] = s;
foreach (var ss in s)
reveseOptimalMap[ss] = i;
i++;
}
}
// получаем минимальный алфавит
var minClasses = new HashSet<HashSet<int>>(setComparer);
var alphaQueue = new Queue<HashSet<int>>();
alphaQueue.Enqueue(new HashSet<int>(Enumerable.Range(0,AlphabetSize)));
for (int s = 1 ; s < optimalMap.Length; s++) {
var newQueue = new Queue<HashSet<int>>();
foreach (var A in alphaQueue) {
if (A.Count == 1) {
minClasses.Add(A);
continue;
}
// различаем классы символов, которые переводят в различные оптимальные состояния
// optimalState -> alphaClass
var classes = new Dictionary<int, HashSet<int>>();
foreach (var term in A) {
// ищем все переходы класса по символу term
var s2 = reveseOptimalMap[
optimalMap[s].Select(x => m_states[x].transitions[term]) // все элементарные состояния, куда переходит класс s
.Where(x => x != 0) // только допустимые
.FirstOrDefault() // первое допустимое элементарное состояние, если есть
];
HashSet<int> A2;
if (!classes.TryGetValue(s2, out A2)) {
A2 = new HashSet<int>();
newQueue.Enqueue(A2);
classes[s2] = A2;
}
A2.Add(term);
}
}
if (newQueue.Count == 0)
break;
alphaQueue = newQueue;
}
foreach (var A in alphaQueue)
minClasses.Add(A);
var alphabetMap = sourceAlphabet.Reclassify(minimalAlphabet, minClasses);
// построение автомата
var states = new int[ optimalMap.Length ];
states[0] = UNREACHEBLE_STATE;
for(var s = INITIAL_STATE; s < states.Length; s++) {
var tags = optimalMap[s].SelectMany(x => m_states[x].tag ?? Enumerable.Empty<int>()).Distinct().ToArray();
if (tags.Length > 0)
states[s] = minimalDFA.AddState(tags);
else
states[s] = minimalDFA.AddState();
}
Debug.Assert(states[INITIAL_STATE] == INITIAL_STATE);
for (int s1 = 1; s1 < m_states.Count; s1++) {
for (int c = 0; c < AlphabetSize; c++) {
var s2 = m_states[s1].transitions[c];
if (s2 != UNREACHEBLE_STATE) {
minimalDFA.DefineTransition(
reveseOptimalMap[s1],
reveseOptimalMap[s2],
alphabetMap[c]
);
}
}
}
}
protected void PrintDFA<TA>(IAlphabet<TA> alphabet) {
var reverseMap = alphabet.CreateReverseMap();
for (int i = 1; i < reverseMap.Length; i++) {
Console.WriteLine("C{0}: {1}", i, String.Join(",", reverseMap[i]));
}
for (int i = 1; i < m_states.Count; i++) {
var s = m_states[i];
for (int c = 0; c < AlphabetSize; c++)
if (s.transitions[c] != UNREACHEBLE_STATE)
Console.WriteLine("S{0} -{1}-> S{2}{3}", i, String.Join(",", reverseMap[c]), s.transitions[c], m_states[s.transitions[c]].final ? "$" : "");
}
}
public abstract int AlphabetSize {
get;
}
}
}