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r159:5558e43c79bb v2
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1 1 using Implab;
2 2 using System;
3 3 using System.Collections.Generic;
4 4 using System.Diagnostics;
5 5 using System.Linq;
6 6
7 7 namespace Implab.Parsing {
8 8 public class DFADefinition : IDFADefinition {
9 9 readonly List<DFAStateDescriptior> m_states;
10 10
11 11 public const int INITIAL_STATE = 1;
12 12 public const int UNREACHEBLE_STATE = 0;
13 13
14 14 DFAStateDescriptior[] m_statesArray;
15 15 readonly int m_alpabetSize;
16 16
17 17 public DFADefinition(int alphabetSize) {
18 18 m_states = new List<DFAStateDescriptior>();
19 19 m_alpabetSize = alphabetSize;
20 20
21 21 m_states.Add(new DFAStateDescriptior());
22 22 }
23 23
24 24 public DFAStateDescriptior[] States {
25 25 get {
26 26 if (m_statesArray == null)
27 27 m_statesArray = m_states.ToArray();
28 28 return m_statesArray;
29 29 }
30 30 }
31 31
32 32 public bool InitialStateIsFinal {
33 33 get {
34 34 return m_states[INITIAL_STATE].final;
35 35 }
36 36 }
37 37
38 38 public int AddState() {
39 39 var index = m_states.Count;
40 40 m_states.Add(new DFAStateDescriptior {
41 41 final = false,
42 42 transitions = new int[AlphabetSize]
43 43 });
44 44 m_statesArray = null;
45 45
46 46 return index;
47 47 }
48 48
49 49 public int AddState(int[] tag) {
50 50 var index = m_states.Count;
51 51 bool final = tag != null && tag.Length != 0;
52 52 m_states.Add(new DFAStateDescriptior {
53 53 final = final,
54 54 transitions = new int[AlphabetSize],
55 55 tag = final ? tag : null
56 56 });
57 57 m_statesArray = null;
58 58 return index;
59 59 }
60 60
61 61 public void DefineTransition(int s1,int s2, int symbol) {
62 62 Safe.ArgumentInRange(s1, 0, m_states.Count-1, "s1");
63 63 Safe.ArgumentInRange(s2, 0, m_states.Count-1, "s2");
64 64 Safe.ArgumentInRange(symbol, 0, AlphabetSize-1, "symbol");
65 65
66 66 m_states[s1].transitions[symbol] = s2;
67 67 }
68 68
69 69 public void Optimize<TA>(IDFADefinition minimalDFA,IAlphabet<TA> sourceAlphabet, IAlphabet<TA> minimalAlphabet) {
70 70 Safe.ArgumentNotNull(minimalDFA, "minimalDFA");
71 71 Safe.ArgumentNotNull(minimalAlphabet, "minimalAlphabet");
72 72
73 73 var setComparer = new CustomEqualityComparer<HashSet<int>>(
74 74 (x, y) => x.SetEquals(y),
75 75 (s) => s.Sum(x => x.GetHashCode())
76 76 );
77 77
78 78 var arrayComparer = new CustomEqualityComparer<int[]>(
79 79 (x,y) => (new HashSet<int>(x)).SetEquals(new HashSet<int>(y)),
80 80 (a) => a.Sum(x => x.GetHashCode())
81 81 );
82 82
83 83 var optimalStates = new HashSet<HashSet<int>>(setComparer);
84 84 var queue = new HashSet<HashSet<int>>(setComparer);
85 85
86 86 foreach (var g in Enumerable
87 87 .Range(INITIAL_STATE, m_states.Count-1)
88 88 .Select(i => new {
89 89 index = i,
90 90 descriptor = m_states[i]
91 91 })
92 92 .Where(x => x.descriptor.final)
93 93 .GroupBy(x => x.descriptor.tag, arrayComparer)
94 94 ) {
95 95 optimalStates.Add(new HashSet<int>(g.Select(x => x.index)));
96 96 }
97 97
98 98 var state = new HashSet<int>(
99 99 Enumerable
100 100 .Range(INITIAL_STATE, m_states.Count - 1)
101 101 .Where(i => !m_states[i].final)
102 102 );
103 103 optimalStates.Add(state);
104 104 queue.Add(state);
105 105
106 106 while (queue.Count > 0) {
107 107 var stateA = queue.First();
108 108 queue.Remove(stateA);
109 109
110 110 for (int c = 0; c < AlphabetSize; c++) {
111 111 var stateX = new HashSet<int>();
112 112
113 113 for(int s = 1; s < m_states.Count; s++) {
114 114 if (stateA.Contains(m_states[s].transitions[c]))
115 115 stateX.Add(s);
116 116 }
117 117
118 118 foreach (var stateY in optimalStates.ToArray()) {
119 119 if (stateX.Overlaps(stateY) && !stateY.IsSubsetOf(stateX)) {
120 120 var stateR1 = new HashSet<int>(stateY);
121 121 var stateR2 = new HashSet<int>(stateY);
122 122
123 123 stateR1.IntersectWith(stateX);
124 124 stateR2.ExceptWith(stateX);
125 125
126 126 optimalStates.Remove(stateY);
127 127 optimalStates.Add(stateR1);
128 128 optimalStates.Add(stateR2);
129 129
130 130 if (queue.Contains(stateY)) {
131 131 queue.Remove(stateY);
132 132 queue.Add(stateR1);
133 133 queue.Add(stateR2);
134 134 } else {
135 135 queue.Add(stateR1.Count <= stateR2.Count ? stateR1 : stateR2);
136 136 }
137 137 }
138 138 }
139 139 }
140 140 }
141 141
142 142 // строим ΠΊΠ°Ρ€Ρ‚Ρ‹ соотвСствия ΠΎΠΏΡ‚ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹Ρ… состояний с ΠΎΡ€ΠΈΠ³ΠΈΠ½Π°Π»ΡŒΠ½Ρ‹ΠΌΠΈ
143 143
144 144 var initialState = optimalStates.Single(x => x.Contains(INITIAL_STATE));
145 145
146 146 // ΠΊΠ°Ρ€Ρ‚Π° получСния ΠΎΠΏΡ‚ΠΈΠΌΠ°Π»ΡŒΠ½ΠΎΠ³ΠΎ состояния ΠΏΠΎ ΡΠΎΠΎΡ‚Π²Π΅ΡΡ‚Π²ΡƒΡŽΡ‰Π΅ΠΌΡƒ Π΅ΠΌΡƒ простому ΡΠΎΡΡ‚ΠΎΡΠ½ΠΈΡŽ
147 147 int[] reveseOptimalMap = new int[m_states.Count];
148 148 // ΠΊΠ°Ρ€Ρ‚Π° с индСксами ΠΎΠΏΡ‚ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹Ρ… состояний
149 149 HashSet<int>[] optimalMap = new HashSet<int>[optimalStates.Count + 1];
150 150 {
151 151 optimalMap[0] = new HashSet<int>(); // unreachable state
152 152 optimalMap[1] = initialState; // initial state
153 153 foreach (var ss in initialState)
154 154 reveseOptimalMap[ss] = 1;
155 155
156 156 int i = 2;
157 157 foreach (var s in optimalStates) {
158 158 if (s.SetEquals(initialState))
159 159 continue;
160 160 optimalMap[i] = s;
161 161 foreach (var ss in s)
162 162 reveseOptimalMap[ss] = i;
163 163 i++;
164 164 }
165 165 }
166 166
167 167 // ΠΏΠΎΠ»ΡƒΡ‡Π°Π΅ΠΌ ΠΌΠΈΠ½ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹ΠΉ Π°Π»Ρ„Π°Π²ΠΈΡ‚
168 168
169 169 var minClasses = new HashSet<HashSet<int>>(setComparer);
170 170 var alphaQueue = new Queue<HashSet<int>>();
171 171 alphaQueue.Enqueue(new HashSet<int>(Enumerable.Range(0,AlphabetSize)));
172 172
173 173 for (int s = 1 ; s < optimalMap.Length; s++) {
174 174 var newQueue = new Queue<HashSet<int>>();
175 175
176 176 foreach (var A in alphaQueue) {
177 177 if (A.Count == 1) {
178 178 minClasses.Add(A);
179 179 continue;
180 180 }
181 181
182 182 // Ρ€Π°Π·Π»ΠΈΡ‡Π°Π΅ΠΌ классы символов, ΠΊΠΎΡ‚ΠΎΡ€Ρ‹Π΅ пСрСводят Π² Ρ€Π°Π·Π»ΠΈΡ‡Π½Ρ‹Π΅ ΠΎΠΏΡ‚ΠΈΠΌΠ°Π»ΡŒΠ½Ρ‹Π΅ состояния
183 183 // optimalState -> alphaClass
184 184 var classes = new Dictionary<int, HashSet<int>>();
185 185
186 186 foreach (var term in A) {
187 187 // ΠΈΡ‰Π΅ΠΌ всС ΠΏΠ΅Ρ€Π΅Ρ…ΠΎΠ΄Ρ‹ класса ΠΏΠΎ символу term
188 188 var s2 = reveseOptimalMap[
189 189 optimalMap[s].Select(x => m_states[x].transitions[term]).FirstOrDefault(x => x != 0) // ΠΏΠ΅Ρ€Π²ΠΎΠ΅ допустимоС элСмСнтарноС состояниС, Ссли Π΅ΡΡ‚ΡŒ
190 190 ];
191 191
192 192 HashSet<int> A2;
193 193 if (!classes.TryGetValue(s2, out A2)) {
194 194 A2 = new HashSet<int>();
195 195 newQueue.Enqueue(A2);
196 196 classes[s2] = A2;
197 197 }
198 198 A2.Add(term);
199 199 }
200 200 }
201 201
202 202 if (newQueue.Count == 0)
203 203 break;
204 204 alphaQueue = newQueue;
205 205 }
206 206
207 207 foreach (var A in alphaQueue)
208 208 minClasses.Add(A);
209 209
210 210 var alphabetMap = sourceAlphabet.Reclassify(minimalAlphabet, minClasses);
211 211
212 212 // построСниС Π°Π²Ρ‚ΠΎΠΌΠ°Ρ‚Π°
213 213
214 214 var states = new int[ optimalMap.Length ];
215 215 states[0] = UNREACHEBLE_STATE;
216 216
217 217 for(var s = INITIAL_STATE; s < states.Length; s++) {
218 218 var tags = optimalMap[s].SelectMany(x => m_states[x].tag ?? Enumerable.Empty<int>()).Distinct().ToArray();
219 219 if (tags.Length > 0)
220 220 states[s] = minimalDFA.AddState(tags);
221 221 else
222 222 states[s] = minimalDFA.AddState();
223 223 }
224 224
225 225 Debug.Assert(states[INITIAL_STATE] == INITIAL_STATE);
226 226
227 227 for (int s1 = 1; s1 < m_states.Count; s1++) {
228 228 for (int c = 0; c < AlphabetSize; c++) {
229 229 var s2 = m_states[s1].transitions[c];
230 230 if (s2 != UNREACHEBLE_STATE) {
231 231 minimalDFA.DefineTransition(
232 232 reveseOptimalMap[s1],
233 233 reveseOptimalMap[s2],
234 234 alphabetMap[c]
235 235 );
236 236 }
237 237 }
238 238 }
239 239
240 240 }
241 241
242 242 public void PrintDFA<TA>(IAlphabet<TA> alphabet) {
243 243
244 244 var reverseMap = alphabet.CreateReverseMap();
245 245
246 246 for (int i = 1; i < reverseMap.Length; i++) {
247 247 Console.WriteLine("C{0}: {1}", i, String.Join(",", reverseMap[i]));
248 248 }
249 249
250 250 for (int i = 1; i < m_states.Count; i++) {
251 251 var s = m_states[i];
252 252 for (int c = 0; c < AlphabetSize; c++)
253 253 if (s.transitions[c] != UNREACHEBLE_STATE)
254 254 Console.WriteLine("S{0} -{1}-> S{2}{3}", i, String.Join(",", reverseMap[c]), s.transitions[c], m_states[s.transitions[c]].final ? "$" : "");
255 255 }
256 256 }
257 257
258 258 public int AlphabetSize {
259 get;
259 get {
260 return m_alpabetSize;
260 261 }
261 262 }
262 263 }
264 }
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