├── LICENSE ├── README.md ├── cppsat.cpp ├── cppsat.hpp └── examples ├── adder.cpp ├── natural.cpp ├── nqueens.cpp └── sudoku.cpp /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. By contrast, 15 | the GNU General Public License is intended to guarantee your freedom to 16 | share and change all versions of a program--to make sure it remains free 17 | software for all its users. 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Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | See cppsat's project website: https://abau.org/cppsat.html 2 | -------------------------------------------------------------------------------- /cppsat.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | #include 5 | #include "cppsat.hpp" 6 | 7 | namespace { 8 | static Minisat::Solver solver; 9 | 10 | Minisat::Lit toMinisatLit (const cppsat::Bit& bit) { 11 | assert (bit.isConstant () == false); 12 | return Minisat::toLit (bit.literal ()); 13 | } 14 | 15 | Minisat::Var toMinisatVar (const cppsat::Bit& bit) { 16 | assert (bit.isConstant () == false); 17 | return Minisat::var (toMinisatLit (bit)); 18 | } 19 | 20 | template 21 | std::pair halfAdder (const T& a, const T& b) { 22 | return std::make_pair (a != b, a && b); 23 | } 24 | 25 | template 26 | std::pair fullAdder (const T& a, const T& b, const T& c) { 27 | 28 | auto ha1 = halfAdder (a, b); 29 | auto ha2 = halfAdder (ha1.first, c); 30 | 31 | return std::make_pair (ha2.first, ha1.second || ha2.second); 32 | } 33 | 34 | std::vector toBinary (size_t s, unsigned int i) { 35 | std::vector bits; 36 | 37 | std::function go = [s, &bits, &go] (unsigned int j) { 38 | assert (bits.size () < s); 39 | if (j < 2) { 40 | bits.push_back (bool (j)); 41 | } 42 | else { 43 | const std::div_t d = std::div (j, 2); 44 | 45 | bits.push_back (bool (d.rem)); 46 | go (d.quot); 47 | } 48 | }; 49 | go ((unsigned int) std::abs (i)); 50 | 51 | while (bits.size () < s) { 52 | bits.push_back (false); 53 | } 54 | return bits; 55 | } 56 | 57 | unsigned int fromBinary (const std::vector & bits) { 58 | int result = 0; 59 | 60 | for (size_t i = 0; i < bits.size (); i++) { 61 | result += bits[i] ? (1 << i) : 0; 62 | } 63 | return result; 64 | } 65 | 66 | void equalizeLength (cppsat::Bits& a, cppsat::Bits& b) { 67 | const size_t max = std::max (a.size (), b.size ()); 68 | 69 | while (a.size () < max) { 70 | a.add (cppsat::Bit (false)); 71 | } 72 | while (b.size () < max) { 73 | b.add (cppsat::Bit (false)); 74 | } 75 | } 76 | 77 | typedef std::pair BitPair; 78 | 79 | BitPair compare (const cppsat::Bits& x, const cppsat::Bits& y) { 80 | cppsat::Bits a (x); 81 | cppsat::Bits b (y); 82 | 83 | equalizeLength (a, b); 84 | 85 | std::function go = [&go,&a,&b] (size_t i) { 86 | if (i < a.size ()) { 87 | auto rest = go (i+1); 88 | cppsat::Bit& leRest = rest.first; 89 | cppsat::Bit& eqRest = rest.second; 90 | 91 | return BitPair ( leRest || (eqRest && !a[i] && b[i]) 92 | , eqRest && (a[i] == b[i]) ); 93 | } 94 | else { 95 | return BitPair (cppsat::Bit (false), cppsat::Bit (true)); 96 | } 97 | }; 98 | return go (0); 99 | } 100 | } 101 | 102 | namespace cppsat { 103 | 104 | Bit :: Bit () 105 | : _isConstant (false) 106 | , _value (Minisat::toInt (Minisat::mkLit (solver.newVar ()))) 107 | {} 108 | 109 | Bit :: Bit (bool b) 110 | : _isConstant (true) 111 | , _value (b) 112 | {} 113 | 114 | Bit :: Bit (int i) 115 | : _isConstant (false) 116 | , _value (i) 117 | {} 118 | 119 | Bit Bit :: operator! () const { return this->negate (); } 120 | Bit Bit :: operator&& (const Bit& o) const { return cppsat::all ({ *this, o }); } 121 | Bit Bit :: operator|| (const Bit& o) const { return cppsat::any ({ *this, o }); } 122 | Bit Bit :: operator== (const Bit& o) const { return this->equals (o); } 123 | Bit Bit :: operator!= (const Bit& o) const { return this->equalsNot (o); } 124 | 125 | bool Bit :: isConstant () const { 126 | return this->_isConstant; 127 | } 128 | 129 | int Bit :: literal () const { 130 | assert (this->isConstant () == false); 131 | return this->_value; 132 | } 133 | 134 | bool Bit :: hasValue () const { 135 | if (this->isConstant ()) { 136 | return true; 137 | } 138 | else { 139 | return solver.model.size () > toMinisatVar (*this); 140 | } 141 | } 142 | 143 | bool Bit :: hasValue (bool b) const { 144 | return this->hasValue () && this->value () == b; 145 | } 146 | 147 | bool Bit :: value () const { 148 | if (this->isConstant ()) { 149 | return bool (this->_value); 150 | } 151 | else { 152 | assert (this->hasValue ()); 153 | 154 | Minisat::lbool v = solver.modelValue (toMinisatLit (*this)); 155 | if (v == Minisat::l_True) { 156 | return true; 157 | } 158 | else if (v == Minisat::l_False) { 159 | return false; 160 | } 161 | else { 162 | std::abort (); 163 | } 164 | } 165 | } 166 | 167 | Bit Bit :: negate () const { 168 | return this->isConstant () ? Bit (! this->value ()) 169 | : Bit (Minisat::toInt (~toMinisatLit (*this))); 170 | } 171 | 172 | Bit Bit :: implies (const Bit& other) const { 173 | return this->negate () || other; 174 | } 175 | 176 | Bit Bit :: equals (const Bit& other) const { 177 | return this->equalsNot (other).negate (); 178 | } 179 | 180 | Bit Bit :: equalsNot (const Bit& other) const { 181 | if (this->hasValue ()) { 182 | return this->value () ? other.negate () 183 | : other; 184 | } 185 | else if (other.hasValue ()) { 186 | return other.value () ? this->negate () 187 | : *this; 188 | } 189 | else { 190 | Bit result; 191 | cppsat::assertAny ({ this->negate (), other , result }); 192 | cppsat::assertAny ({*this , other.negate (), result }); 193 | cppsat::assertAny ({*this , other , result.negate () }); 194 | cppsat::assertAny ({ this->negate (), other.negate (), result.negate () }); 195 | return result; 196 | } 197 | } 198 | 199 | Bit Bit :: ifThenElse (const Bit& t, const Bit& f) const { 200 | if (this->hasValue ()) { 201 | return this->value () ? t : f; 202 | } 203 | else { 204 | Bit result; 205 | cppsat::assertAny ({ this->negate (), t.negate (), result }); 206 | cppsat::assertAny ({ this->negate (), t , result.negate () }); 207 | cppsat::assertAny ({*this , f.negate (), result }); 208 | cppsat::assertAny ({*this , f , result.negate () }); 209 | return result; 210 | } 211 | } 212 | 213 | Bits :: Bits () {} 214 | 215 | Bits :: Bits (size_t s) 216 | : _bits (s) 217 | {} 218 | 219 | Bits :: Bits (size_t s, unsigned int i) 220 | : Bits (toBinary (s, i)) 221 | {} 222 | 223 | Bits :: Bits (const std::vector & bits) 224 | : _bits (bits) 225 | {} 226 | 227 | Bits :: Bits (const std::vector & bits) { 228 | for (bool b : bits) { 229 | this->add (Bit (b)); 230 | } 231 | } 232 | 233 | Bits Bits :: operator! () const { return this->negate (); } 234 | 235 | Bits Bits :: operator+ (const Bits& other) const { 236 | Bits a (*this); 237 | Bits b (other); 238 | Bits result; 239 | 240 | equalizeLength (a, b); 241 | 242 | std::function go = [&go, &a, &b, &result] 243 | (size_t i, const Bit& carry) 244 | { 245 | if (i < a.size ()) { 246 | BitPair r = fullAdder (a[i], b[i], carry); 247 | 248 | result.add (r.first); 249 | return go (i + 1, r.second); 250 | } 251 | else { 252 | return carry; 253 | } 254 | }; 255 | cppsat::assertAny ({ ! go (0, Bit (false)) }); 256 | return result; 257 | } 258 | 259 | Bits Bits :: operator* (const Bits& other) const { 260 | Bits a (*this); 261 | Bits b (other); 262 | 263 | equalizeLength (a, b); 264 | 265 | std::vector > weights; 266 | weights.resize ((a.size () * 2) - 1); 267 | 268 | auto isReducable = [&weights] () { 269 | for (const std::vector & ws : weights) { 270 | if (ws.size () > 2) { 271 | return true; 272 | } 273 | } 274 | return false; 275 | }; 276 | auto reduce = [&weights] () { 277 | for (int i = weights.size () - 1; i >= 0; i--) { 278 | const size_t numW = weights[i].size (); 279 | 280 | if (numW == 1) { 281 | continue; 282 | } 283 | else if (numW == 2) { 284 | BitPair r = halfAdder (weights[i][0], weights[i][1]); 285 | weights[i].clear (); 286 | weights[i].push_back (r.first); 287 | 288 | if (weights.size () == (unsigned int)(i + 1)) { 289 | weights.resize (weights.size () + 1); 290 | } 291 | weights[i+1].push_back (r.second); 292 | } 293 | else if (numW >= 3) { 294 | BitPair r = fullAdder ( weights[i][numW - 1] 295 | , weights[i][numW - 2] 296 | , weights[i][numW - 3] ); 297 | weights[i].pop_back (); 298 | weights[i].pop_back (); 299 | weights[i].pop_back (); 300 | weights[i].push_back (r.first); 301 | 302 | if (weights.size () == (unsigned int) (i + 1)) { 303 | weights.resize (weights.size () + 1); 304 | } 305 | weights[i+1].push_back (r.second); 306 | } 307 | } 308 | }; 309 | auto add = [&weights] () { 310 | Bits result; 311 | std::function go = [&go, &result, &weights] 312 | (size_t i, const Bit& carry) 313 | { 314 | if (i >= weights.size ()) { 315 | return carry; 316 | } 317 | else { 318 | assert (weights[i].size () == 1 || weights[i].size () == 2); 319 | 320 | BitPair r = fullAdder ( weights[i][0] 321 | , weights[i].size () == 1 ? Bit (false) 322 | : weights[i][1] 323 | , carry ); 324 | result.add (r.first); 325 | return go (i + 1, r.second); 326 | } 327 | }; 328 | cppsat::assertAny ({ ! go (0, Bit (false)) }); 329 | return result; 330 | }; 331 | 332 | for (size_t i = 0; i < a.size (); i++) { 333 | for (size_t j = 0; j < b.size (); j++) { 334 | weights[i+j].push_back (a[i] && b[j]); 335 | } 336 | } 337 | while (isReducable ()) { 338 | reduce (); 339 | } 340 | 341 | Bits fullResult = add (); 342 | Bits result; 343 | 344 | for (size_t i = 0; i < fullResult.size (); i++) { 345 | if (i < a.size ()) { 346 | result.add (fullResult[i]); 347 | } 348 | else { 349 | cppsat::assertAny ({ ! fullResult[i] }); 350 | } 351 | } 352 | return result; 353 | } 354 | 355 | Bit Bits :: operator== (const Bits& other) const { 356 | BitPair r = compare (*this, other); 357 | 358 | return !r.first && r.second; 359 | } 360 | 361 | Bit Bits :: operator!= (const Bits& other) const { 362 | return this->operator== (other).negate (); 363 | } 364 | 365 | Bit Bits :: operator< (const Bits& other) const { 366 | BitPair r = compare (*this, other); 367 | 368 | return r.first && !r.second; 369 | } 370 | 371 | Bit Bits :: operator<= (const Bits& other) const { 372 | BitPair r = compare (*this, other); 373 | 374 | return r.first || r.second; 375 | } 376 | 377 | Bit Bits :: operator>= (const Bits& other) const { 378 | return other.operator<= (*this); 379 | } 380 | 381 | Bit Bits :: operator> (const Bits& other) const { 382 | return other.operator< (*this); 383 | } 384 | 385 | Bit Bits :: operator&& (const Bits& other) const { 386 | Bits both (this->_bits); 387 | both.add (other); 388 | return both.all (); 389 | } 390 | 391 | Bit Bits :: operator|| (const Bits& other) const { 392 | Bits both (this->_bits); 393 | both.add (other); 394 | return both.any (); 395 | } 396 | 397 | const Bit& Bits :: operator[] (size_t i) const { 398 | return this->_bits [i]; 399 | } 400 | 401 | size_t Bits :: size () const { 402 | return this->_bits.size (); 403 | } 404 | 405 | void Bits :: add (const Bit& bit) { 406 | this->_bits.push_back (bit); 407 | } 408 | 409 | void Bits :: add (const Bits& bits) { 410 | for (const Bit& b : bits) { 411 | this->add (b); 412 | } 413 | } 414 | 415 | bool Bits :: hasValue () const { 416 | return std::all_of (this->begin (), this->end (), [] (const Bit& b) { 417 | return b.hasValue (); 418 | }); 419 | } 420 | 421 | std::vector Bits :: value () const { 422 | assert (this->hasValue ()); 423 | 424 | std::vector result; 425 | for (const Bit& b : *this) { 426 | result.push_back (b.value ()); 427 | } 428 | return result; 429 | } 430 | 431 | unsigned int Bits :: valueNat () const { 432 | assert (this->hasValue ()); 433 | return fromBinary (this->value ()); 434 | } 435 | 436 | Bits Bits :: negate () const { 437 | std::vector negBits; 438 | for (const Bit& b : this->_bits) { 439 | negBits.push_back (!b); 440 | } 441 | return Bits (negBits); 442 | } 443 | 444 | void Bits :: assertAny () const { cppsat::assertAny (this->_bits); } 445 | void Bits :: assertAll () const { cppsat::assertAll (this->_bits); } 446 | Bit Bits :: all () const { return cppsat::all (this->_bits); } 447 | Bit Bits :: any () const { return cppsat::any (this->_bits); } 448 | Bit Bits :: none () const { return cppsat::none (this->_bits); } 449 | Bit Bits :: atmost (unsigned int k) const { return cppsat::atmost (k, this->_bits); } 450 | Bit Bits :: exactly (unsigned int k) const { return cppsat::exactly (k, this->_bits); } 451 | 452 | const std::vector & Bits :: vector () const { return this->_bits; } 453 | std::vector ::iterator Bits :: begin () { return this->_bits.begin (); } 454 | std::vector ::const_iterator Bits :: begin () const { return this->_bits.begin (); } 455 | std::vector ::const_iterator Bits :: cbegin () const { return this->_bits.cbegin (); } 456 | std::vector ::iterator Bits :: end () { return this->_bits.end (); } 457 | std::vector ::const_iterator Bits :: end () const { return this->_bits.end (); } 458 | std::vector ::const_iterator Bits :: cend () const { return this->_bits.cend (); } 459 | 460 | void assertAll (const std::vector & bits) { 461 | for (const Bit& bit : bits) { 462 | cppsat::assertAny ({ bit }); 463 | } 464 | } 465 | 466 | void assertAny (const std::vector & bits) { 467 | if (std::none_of ( bits.begin (), bits.end () 468 | , [] (const Bit& b) { return b.hasValue (true); } )) 469 | { 470 | Minisat::vec vec; 471 | vec.capacity (bits.size ()); 472 | 473 | for (const Bit& bit : bits) { 474 | if (bit.hasValue () == false) { 475 | vec.push (toMinisatLit (bit)); 476 | } 477 | } 478 | solver.addClause (vec); 479 | } 480 | } 481 | 482 | Bit all (const std::vector & bits) { 483 | if (bits.size () == 0) { 484 | return Bit (true); 485 | } 486 | else if (bits.size () == 1) { 487 | return *bits.begin (); 488 | } 489 | else if (std::any_of ( bits.begin (), bits.end () 490 | , [] (const Bit& b) { return b.hasValue (false); } )) 491 | { 492 | return Bit (false); 493 | } 494 | else if (std::all_of ( bits.begin (), bits.end () 495 | , [] (const Bit& b) { return b.hasValue (true); } )) 496 | { 497 | return Bit (true); 498 | } 499 | else { 500 | Bit result; 501 | for (const Bit& bit : bits) { 502 | cppsat::assertAny ({ result.negate (), bit }); 503 | } 504 | std::vector negBits (Bits (bits).negate ().vector ()); 505 | negBits.push_back (result); 506 | cppsat::assertAny (negBits); 507 | 508 | return result; 509 | } 510 | } 511 | 512 | Bit any (const std::vector & bits) { 513 | return Bits (bits).negate ().all ().negate (); 514 | } 515 | 516 | Bit none (const std::vector & bits) { 517 | return cppsat::any (bits).negate (); 518 | } 519 | 520 | Bit atmost (unsigned int k, const std::vector & bits) { 521 | if (k == 0) { 522 | return cppsat::none (bits); 523 | } 524 | else if (bits.empty ()) { 525 | return Bit (true); 526 | } 527 | else { 528 | const Bit& firstBit (bits.front ()); 529 | const std::vector lessBits (++bits.begin (), bits.end ()); 530 | 531 | return (firstBit.negate () && cppsat::atmost (k , lessBits)) 532 | || (firstBit && cppsat::atmost (k-1, lessBits)); 533 | } 534 | } 535 | 536 | Bit exactly (unsigned int k, const std::vector & bits) { 537 | if (k == 0) { 538 | return cppsat::none (bits); 539 | } 540 | else if (bits.empty ()) { 541 | return Bit (false); 542 | } 543 | else { 544 | const Bit& firstBit (bits.front ()); 545 | const std::vector lessBits (++bits.begin (), bits.end ()); 546 | 547 | return (firstBit.negate () && cppsat::exactly (k , lessBits)) 548 | || (firstBit && cppsat::exactly (k-1, lessBits)); 549 | } 550 | } 551 | 552 | Bit allEqual (const std::vector & bits) { 553 | assert (bits.size () > 0); 554 | 555 | return cppsat::forall ( bits.begin (), bits.end () 556 | , [&bits] (const Bits& b) 557 | { 558 | return b == bits[0]; 559 | }); 560 | } 561 | 562 | Bit allDifferent (const std::vector & bits) { 563 | Bits diffs; 564 | for (size_t i = 0; i < bits.size () - 1; i++) { 565 | for (size_t j = i + 1; j < bits.size (); j++) { 566 | diffs.add (bits[i] != bits[j]); 567 | } 568 | } 569 | return diffs.all (); 570 | } 571 | 572 | bool solve () { 573 | return solver.solve (); 574 | } 575 | 576 | bool solve (Bit bit) { 577 | cppsat::assertAny ({ bit }); 578 | return cppsat::solve (); 579 | } 580 | 581 | void reset () { 582 | solver.model.clear (); 583 | } 584 | 585 | void printStatistics () { 586 | std::cerr << "#variables: " << solver.nVars () 587 | << ", #clauses: " << solver.nClauses () 588 | << ", #literals: " << solver.clauses_literals 589 | << std::endl; 590 | } 591 | } 592 | 593 | std::ostream& operator<< (std::ostream& os, const cppsat::Bit& bit) { 594 | if (bit.hasValue ()) { 595 | os << bit.value (); 596 | } 597 | else { 598 | os << bit.literal (); 599 | } 600 | return os; 601 | } 602 | 603 | std::ostream& operator<< (std::ostream& os, const cppsat::Bits& bits) { 604 | auto it = bits.begin (); 605 | os << "["; 606 | if (it != bits.end ()) { 607 | os << *it; 608 | } 609 | ++it; 610 | for ( ; it != bits.end (); ++it) { 611 | os << ", " << *it; 612 | } 613 | os << "]"; 614 | return os; 615 | } 616 | -------------------------------------------------------------------------------- /cppsat.hpp: -------------------------------------------------------------------------------- 1 | #ifndef CPPSAT 2 | #define CPPSAT 3 | 4 | #include 5 | #include 6 | 7 | namespace cppsat { 8 | 9 | class Bit { 10 | public: 11 | Bit (); 12 | explicit Bit (bool); 13 | 14 | Bit operator! () const; 15 | Bit operator&& (const Bit&) const; 16 | Bit operator|| (const Bit&) const; 17 | Bit operator== (const Bit&) const; 18 | Bit operator!= (const Bit&) const; 19 | 20 | bool isConstant () const; 21 | int literal () const; 22 | bool hasValue () const; 23 | bool hasValue (bool) const; 24 | bool value () const; 25 | Bit negate () const; 26 | Bit implies (const Bit&) const; 27 | Bit equals (const Bit&) const; 28 | Bit equalsNot (const Bit&) const; 29 | Bit ifThenElse (const Bit&, const Bit&) const; 30 | 31 | private: 32 | explicit Bit (int); 33 | 34 | const bool _isConstant; 35 | const int _value; 36 | }; 37 | 38 | class Bits { 39 | public: 40 | Bits (); 41 | Bits (size_t); 42 | Bits (size_t, unsigned int); 43 | Bits (const std::vector &); 44 | Bits (const std::vector &); 45 | 46 | Bits operator! () const; 47 | Bits operator+ (const Bits&) const; 48 | Bits operator* (const Bits&) const; 49 | Bit operator== (const Bits&) const; 50 | Bit operator!= (const Bits&) const; 51 | Bit operator< (const Bits&) const; 52 | Bit operator<= (const Bits&) const; 53 | Bit operator>= (const Bits&) const; 54 | Bit operator> (const Bits&) const; 55 | Bit operator&& (const Bits&) const; 56 | Bit operator|| (const Bits&) const; 57 | const Bit& operator[] (size_t) const; 58 | 59 | size_t size () const; 60 | void add (const Bit&); 61 | void add (const Bits&); 62 | bool hasValue () const; 63 | std::vector value () const; 64 | unsigned int valueNat () const; 65 | 66 | Bits negate () const; 67 | void assertAll () const; 68 | void assertAny () const; 69 | Bit all () const; 70 | Bit any () const; 71 | Bit none () const; 72 | Bit atmost (unsigned int) const; 73 | Bit exactly (unsigned int) const; 74 | 75 | const std::vector & vector () const; 76 | std::vector ::iterator begin (); 77 | std::vector ::const_iterator begin () const; 78 | std::vector ::const_iterator cbegin () const; 79 | std::vector ::iterator end (); 80 | std::vector ::const_iterator end () const; 81 | std::vector ::const_iterator cend () const; 82 | 83 | private: 84 | std::vector _bits; 85 | }; 86 | 87 | void assertAll (const std::vector &); 88 | void assertAny (const std::vector &); 89 | Bit all (const std::vector &); 90 | Bit any (const std::vector &); 91 | Bit none (const std::vector &); 92 | Bit atmost (unsigned int, const std::vector &); 93 | Bit exactly (unsigned int, const std::vector &); 94 | Bit allEqual (const std::vector &); 95 | Bit allDifferent (const std::vector &); 96 | 97 | bool solve (); 98 | bool solve (Bit); 99 | void reset (); 100 | void printStatistics (); 101 | 102 | template 103 | Bit forall (It first, It last, F f) { 104 | std::vector bits; 105 | for (; first != last; ++first) { 106 | bits.push_back (f (*first)); 107 | } 108 | return cppsat::all (bits); 109 | } 110 | 111 | template 112 | Bit exists (It first, It last, F f) { 113 | std::vector bits; 114 | for (; first != last; ++first) { 115 | bits.push_back (f (*first)); 116 | } 117 | return cppsat::any (bits); 118 | } 119 | } 120 | 121 | std::ostream& operator<<(std::ostream&, const cppsat::Bit&); 122 | std::ostream& operator<<(std::ostream&, const cppsat::Bits&); 123 | 124 | #endif 125 | -------------------------------------------------------------------------------- /examples/adder.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include "../cppsat.hpp" 4 | 5 | using cppsat::Bit; 6 | 7 | std::pair halfAdder (const Bit& a, const Bit& b) { 8 | return std::make_pair (a != b, a && b); 9 | } 10 | 11 | std::pair fullAdder (const Bit& a, const Bit& b, const Bit& c) { 12 | auto ha1 = halfAdder (a, b); 13 | auto ha2 = halfAdder (ha1.first, c); 14 | 15 | return std::make_pair (ha2.first, ha1.second || ha2.second); 16 | } 17 | 18 | int main () { 19 | Bit a, b, c; 20 | 21 | if (cppsat::solve (fullAdder (a, b, c).second == Bit (true))) { 22 | std::cout << "a: " << a << std::endl; 23 | std::cout << "b: " << b << std::endl; 24 | std::cout << "c: " << c << std::endl; 25 | } 26 | else { 27 | std::cout << "unsatisfiable\n"; 28 | } 29 | return 0; 30 | } 31 | -------------------------------------------------------------------------------- /examples/natural.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include "../cppsat.hpp" 3 | 4 | using cppsat::Bit; 5 | using cppsat::Bits; 6 | 7 | int main () { 8 | const unsigned int width = 8; 9 | const unsigned int result = 234; 10 | 11 | Bits b1 (width); 12 | Bits b2 (width); 13 | 14 | cppsat::assertAll ( { b1 * b2 == Bits (width, result) 15 | , b1 > Bits (width, 1) 16 | , b2 > Bits (width, 1) 17 | } ); 18 | 19 | if (cppsat::solve ()) { 20 | std::cout << b1.valueNat () << " * " 21 | << b2.valueNat () << " = " 22 | << (b1 * b2).valueNat () 23 | << std::endl; 24 | } 25 | else { 26 | std::cout << "unsatisfiable\n"; 27 | } 28 | return 0; 29 | } 30 | -------------------------------------------------------------------------------- /examples/nqueens.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include "../cppsat.hpp" 3 | 4 | using cppsat::Bit; 5 | using cppsat::Bits; 6 | 7 | int main () { 8 | const int n = 8; 9 | 10 | // build board 11 | std::vector board; 12 | for (int i = 0; i < n; i++) { 13 | board.push_back (Bits (n)); 14 | } 15 | 16 | // horizontal 17 | for (Bits& row : board) { 18 | cppsat::assertAny ({ row.exactly (1) }); 19 | } 20 | 21 | // vertical 22 | for (int c = 0; c < n; c++) { 23 | Bits column; 24 | for (int r = 0; r < n; r++) { 25 | column.add (board [r][c]); 26 | } 27 | cppsat::assertAny ({ column.exactly (1) }); 28 | } 29 | 30 | // (anti-)diagonal 31 | for (int c = -n + 1; c < n; c++) { 32 | Bits diagonal, antiDiagonal; 33 | for (int r = 0; r < n; r++) { 34 | if (c + r >= 0 && c + r < n) { 35 | diagonal.add (board [r][c + r]); 36 | antiDiagonal.add (board [n - r - 1][c + r]); 37 | } 38 | } 39 | cppsat::assertAny ({ diagonal.atmost (1) }); 40 | cppsat::assertAny ({ antiDiagonal.atmost (1) }); 41 | } 42 | 43 | // solve 44 | cppsat::printStatistics (); 45 | 46 | if (cppsat::solve ()) { 47 | for (Bits& row : board) { 48 | std::cout << row << std::endl; 49 | } 50 | } 51 | else { 52 | std::cout << "unsatisfiable\n"; 53 | } 54 | return 0; 55 | } 56 | -------------------------------------------------------------------------------- /examples/sudoku.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include "../cppsat.hpp" 4 | 5 | using cppsat::Bit; 6 | using cppsat::Bits; 7 | 8 | typedef std::vector > BoardSpecification; 9 | typedef std::vector > Board; 10 | 11 | Board sudoku (const BoardSpecification&); 12 | 13 | int main () { 14 | Board board = sudoku ( { { 5, 3, -1, -1, 7, -1, -1, -1, -1 } 15 | , { 6, -1, -1, 1, 9, 5, -1, -1, -1 } 16 | , { -1, 9, 8, -1, -1, -1, -1, 6, -1 } 17 | , { 8, -1, -1, -1, 6, -1, -1, -1, 3 } 18 | , { 4, -1, -1, 8, -1, 3, -1, -1, 1 } 19 | , { 7, -1, -1, -1, 2, -1, -1, -1, 6 } 20 | , { -1, 6, -1, -1, -1, -1, 2, 8, -1 } 21 | , { -1, -1, -1, 4, 1, 9, -1, -1, 5 } 22 | , { -1, -1, -1, -1, 8, -1, -1, 7, 9 } }); 23 | 24 | if (cppsat::solve ()) { 25 | for (std::vector & row : board) { 26 | for (Bits& b : row) { 27 | std::cout << b.valueNat () << " "; 28 | } 29 | std::cout << std::endl; 30 | } 31 | } 32 | else { 33 | std::cout << "unsatisfiable\n"; 34 | } 35 | return 0; 36 | } 37 | 38 | Board sudoku (const BoardSpecification& spec) { 39 | assert (spec.size () == 9); 40 | 41 | Board board; 42 | board.resize (9); 43 | 44 | // build board 45 | for (size_t i = 0; i < 9; i++) { 46 | assert (spec[i].size () == 9); 47 | 48 | for (size_t j = 0; j < 9; j++) { 49 | assert (spec[i][j] <= 9); 50 | 51 | Bits number = spec[i][j] < 1 ? Bits (4) : Bits (4, spec[i][j]); 52 | 53 | cppsat::assertAll ({ number >= Bits (4, 1), number <= Bits (4, 9) }); 54 | 55 | board [i].push_back (number); 56 | } 57 | } 58 | 59 | // horizontal 60 | for (std::vector & row : board) { 61 | cppsat::assertAny ({ cppsat::allDifferent (row) }); 62 | } 63 | 64 | // vertical 65 | for (size_t i = 0; i < 9; i++) { 66 | std::vector column; 67 | for (size_t j = 0; j < 9; j++) { 68 | column.push_back (board [j][i]); 69 | } 70 | cppsat::assertAny ({ cppsat::allDifferent (column) }); 71 | } 72 | 73 | // blocks 74 | for (size_t i = 0; i < 3; i++) { 75 | for (size_t j = 0; j < 3; j++) { 76 | std::vector block; 77 | for (size_t u = 0; u < 3; u++) { 78 | for (size_t v = 0; v < 3; v++) { 79 | block.push_back (board [(3*i)+u] [(3*j)+v]); 80 | } 81 | } 82 | cppsat::assertAny ({ cppsat::allDifferent (block) }); 83 | } 84 | } 85 | return board; 86 | } 87 | --------------------------------------------------------------------------------