iframe-proxy | Sunbelt Computer Software

Repository navigation

History

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

// Deterministic Finite Automata Minimization

// Description:

// Hopcroft minimization algorithm. See Wikipedia.

// Complexity:

// O(|A| n log n).

#include <bits/stdc++.h>

using namespace std;

#define fst first

#define snd second

#define all(c) ((c).begin()), ((c).end())

#define TEST(s) if (!(s)) { cout << __LINE__ << " " << #s << endl; exit(-1); }

struct Automaton {

vector<vector<int>> trans;

vector<bool> is_accept;

int init = 0;

int next(int state, int a) { return trans[state][a]; }

bool accept(int state) { return is_accept[state]; }

int size() { return trans.size(); }

};

template <class AM>

Automaton minimizeAutomaton(AM A) {

// remove unreachables

vector<int> seen(A.size());

seen[A.init] = 1;

vector<int> partition = {A.init}, pos, label;

for (int i = 0; i < partition.size(); ++i) {

pos.push_back(i);

label.push_back(0);

int state = partition[i];

for (int a = 0; a <= 9; ++a) {

int state_ = A.next(state, a);

if (!seen[state_]) {

seen[state_] = 1;

partition.push_back(state_);

}

// make inverse mapping

vector<int> inverse[partition.size()][10];

for (int i = 0; i < partition.size(); ++i) {

int state = partition[i];

for (int a = 0; a <= 9; ++a) {

inverse[A.next(state, a)][a].push_back(state);

}

// Hopcroft minimization

vector<int> begin = {0}, mid = {0}, end = {partition.size()};

auto mark = [&](int state) {

int x = label[state];

if (pos[state] < mid[x]) return;

int state_ = partition[mid[x]++];

swap(pos[state], pos[state_]);

swap(partition[pos[state]], partition[pos[state_]]);

};

auto refine = [&](int x) {

if (mid[x] == begin[x]) return -1;

if (mid[x] == end[x]) { mid[x] = begin[x]; return -1; }

int y = begin.size();

if (mid[x] - begin[x] < end[x] - mid[x]) {

begin.push_back(begin[x]);

end.push_back(mid[x]);

mid.push_back(begin[x]);

begin[x] = mid[x];

} else {

begin.push_back(mid[x]);

end.push_back(end[x]);

mid.push_back(mid[x]);

end[x] = mid[x];

mid[x] = begin[x];

}

for (int i = begin.back(); i < end.back(); ++i)

label[partition[i]] = y;

return y;

};

for (int state: partition)

if (A.accept(state)) mark(state);

if (refine(0) >= 0) { // do Hopcroft minimization

fill(all(seen), 0);

seen[0] = seen[1] = 1;

vector<int> process = {0, 1};

vector<int> is_suspect(partition.size());

while (!process.empty()) {

int x = process.back(); process.pop_back();

seen[x] = 0;

for (int a = 0; a <= 9; ++a) {

vector<int> suspect;

for (int i = begin[x]; i < end[x]; ++i) {

int u = partition[i];

for (int state: inverse[u][a]) {

int y = label[state];

mark(state);

if (!is_suspect[y]) {

is_suspect[y] = 1;

suspect.push_back(y);

}

for (int y: suspect) {

is_suspect[y] = 0;

int z = refine(y);

if (z < 0) continue;

if (seen[y]) {

process.push_back(z);

seen[z] = 1;

} else {

if (end[y] - begin[y] < end[z] - begin[z]) {

process.push_back(y);

seen[y] = 1;

} else {

process.push_back(z);

seen[z] = 1;

}

Automaton M; // completion

M.trans.assign(begin.size(), vector<int>(10));

M.is_accept.resize(begin.size());

for (int x = 0; x < begin.size(); ++x) {

int state = partition[begin[x]];

M.is_accept[x] = A.accept(state);

for (int a = 0; a <= 9; ++a) {

int y = label[A.next(state, a)];

M.trans[x][a] = label[A.next(state, a)];

}

M.init = label[A.init];

return M;

}

// state = x : x == n % mod

struct ModuloAutomaton {

int mod;

ModuloAutomaton(int mod) : mod(mod) { }

int init = 0;

int size() { return mod; }

int next(int state, int a) { return (10 * state + a) % mod; }

bool accept(int state) { return state == 0; }

};

// state = 0 : empty

// 1 : fail

// 2 ... 10 : singleton and last number is state-1

// 11 ... 19 : increased and last number is state-10

// 20 ... 28 : decreased and last number is state-20

struct ZigZagAutomaton {

int init = 0;

int size() { return 29; }

int next(int state, int a) {

if (state == 0) return a == 0 ? 0 : a + 1;

if (state == 1) return 1;

if (state <= 10) {

int last = state - 1;

if (a > last) return a + 10;

else if (a < last) return a + 20;

} else if (state <= 19) {

int last = state - 10;

if (a < last) return a + 20;

} else if (state <= 28) {

int last = state - 20;

if (a > last) return a + 10;

}

return 1;

}

bool accept(int state) { return state != 1; }

};

template <class Automaton1, class Automaton2>

Automaton intersectionAutomaton(Automaton1 A, Automaton2 B) {

Automaton M;

vector<vector<int>> table(A.size(), vector<int>(B.size(), -1));

vector<int> x = {A.init}, y = {B.init};

table[x[0]][y[0]] = 0;

for (int i = 0; i < x.size(); ++i) {

M.trans.push_back(vector<int>(10, -1));

M.is_accept.push_back(A.accept(x[i]) && B.accept(y[i]));

for (int a = 0; a <= 9; ++a) {

int u = A.next(x[i], a), v = B.next(y[i], a);

if (table[u][v] == -1) {

table[u][v] = x.size();

x.push_back(u);

y.push_back(v);

}

M.trans[i][a] = table[u][v];

}

return M;

}

template <class Automaton>

int digitDP(string num, Automaton A, int eq = 1) {

int n = num.size();

vector<vector<vector<int>>> dp(n+1);

dp[0] = vector<vector<int>>(2, vector<int>(A.size()));

dp[0][1][A.init] = 1;

auto addTo = [&](int &x, int y) {

if ((x += y) >= 10000) x -= 10000;

};

for (int i = 0; i < n; ++i) {

dp[i+1] = vector<vector<int>>(2, vector<int>(A.size()));

for (int tight = 0; tight <= 1; ++tight) {

for (int state = 0; state < A.size(); ++state) {

if (dp[i][tight][state] == 0) continue;

int lim = (tight ? num[i] - '0' : 9);

for (int d = 0; d <= lim; ++d) {

int tight_ = tight && d == lim;

int state_ = A.next(state, d);

addTo(dp[i+1][tight_][state_], dp[i][tight][state]);

}

dp[i].clear();

}

int ans = 0;

for (int tight = 0; tight <= eq; ++tight)

for (int state = 0; state < A.size(); ++state)

if (A.accept(state)) addTo(ans, dp[n][tight][state]);

return ans;

}

template <class Automaton>

int debug(string num, Automaton A) {

function<void(int,int,int,string)> rec

= [&](int i, int tight, int state, string s) {

if (i == num.size()) {

if (A.accept(state)) cout << s << endl;

return;

}

int lim = (tight ? num[i] - '0' : 9);

for (int d = 0; d <= lim; ++d) {

int tight_ = tight && d == lim;

int state_ = A.next(state, d);

s.push_back('0' + d);

rec(i+1, tight_, state_, s);

s.pop_back();

}

};

rec(0, 1, A.init, "");

}

void AOJ_ZIGZAG() {

char A[1000], B[1000];

int M;

scanf("%s %s %d", A, B, &M);

ZigZagAutomaton zigzag;

ModuloAutomaton modulo(M);

auto IM = minimizeAutomaton(intersectionAutomaton(zigzag, modulo));

int a = digitDP(A, IM, 0);

int b = digitDP(B, IM, 1);

cout << (b + (10000 - a)) % 10000 << endl;

}

int main() {

AOJ_ZIGZAG();

Automaton A;

A.trans.assign(7, vector<int>(10, 6));

A.trans[0][0] = 1;

A.trans[0][1] = 2;

A.trans[1][0] = 0;

A.trans[1][1] = 3;

A.trans[2][0] = 4;

A.trans[2][1] = 5;

A.trans[3][0] = 4;

A.trans[3][1] = 5;

A.trans[4][0] = 4;

A.trans[4][1] = 5;

A.trans[5][0] = 5;

A.trans[5][1] = 5;

A.is_accept.assign(7, 0);

A.is_accept[2] = 1;

A.is_accept[3] = 1;

A.is_accept[4] = 1;

auto B = minimizeAutomaton(A);

cout << B.size() << endl;

//minimizeAutomaton(ZigZagAutomaton());

}

Sunbelt Computer Software

PL/B Language Development and Support

Navigation Menu

Repository navigation

dfa_minimization.cc

dfa_minimization.cc

Sunbelt Computer Software

PL/B Language Development and Support

FilesExpand file tree

dfa_minimization.cc

Latest commit

History

dfa_minimization.cc

File metadata and controls