8 #include "inc_solver.h"
9 #include "solver_interface.h"
17 void EqualOneToCNF(vector<int> literals, vector< vector<int> > & cnf){
18 int N = literals.size();
19 cnf.push_back(literals);
22 // this one is a->~b, a->~c, ...
23 for (int j=0; j<N-1; j++){
24 for (int k=j+1; k<N; k++){
25 dnf.push_back(-literals[j]);
26 dnf.push_back(-literals[k]);
33 void verticalSymmetryBreaking(vector<int> col1, vector<int> colN, vector<vector<int> > &cnf){
35 for(int i=0; i<col1.size(); i++){
36 dnf.push_back(-col1[i]);
37 for(int j=i+1; j<colN.size(); j++){
38 dnf.push_back(colN[j]);
47 void Or( vector<int> literals, vector<vector<int> > & cnf){
48 int N= literals.size();
50 for( int i=0; i<N; i++){
51 dnf.push_back(literals[i]);
56 void LessEqualOneToCNF(vector<int> literals, vector< vector<int> > & cnf){
57 int N = literals.size();
59 // this one is a->~b, a->~c, ...
60 for (int j=0; j<N-1; j++){
61 for (int k=j+1; k<N; k++){
62 dnf.push_back(-literals[j]);
63 dnf.push_back(-literals[k]);
70 bool validateSolution(int N, int *table, int size){
71 for(int k=0; k<size; k++){
75 for (int j= row*N; j<(row+1)*N; j++)
76 if(j!=k && table[j] >0){
79 for(int j=0; j<N; j++){
81 if(indx !=k && table[indx]>0){
90 if(k!=indx && table[indx]>0){
98 if(k!=indx && table[indx]>0){
105 int indx = i++*N+j--;
106 if(k!=indx && table[indx]>0){
113 int indx = i++*N+j++;
114 if(k!=indx && table[indx]>0){
124 void printValidationStatus(int N, int *table, int size){
125 if(validateSolution(N, table, size)){
126 printf("***CORRECT****\n");
128 printf("***WRONG******\n");
133 void printSolution(int N, int *table, int size){
134 for(int i=0; i<size; i++){
147 void originalNqueensEncoding(int N){
150 int ** VarName = new int * [N];
151 for (int i=0; i<N; i++){
152 VarName[i] = new int [N];
153 for (int j=0; j<N; j++){
154 VarName[i][j] = kk++;
159 vector< vector<int> > cnf;
163 // generator formula per row
164 // v1 + v2 + v3 + v4 + ... = 1r
165 for (int i=0; i<N; i++){
166 for (int j=0; j<N; j++){
167 vars.push_back(VarName[i][j]);
169 EqualOneToCNF(vars, cnf);
173 // generator formula per col
174 // v1 + v2 + v3 + v4 + ... = 1r
175 for (int i=0; i<N; i++){
176 for (int j=0; j<N; j++){
177 vars.push_back(VarName[j][i]);
179 EqualOneToCNF(vars, cnf);
184 for (int i=0; i<N-1; i++){
185 for (int j=0; j<N-i; j++){
186 vars.push_back(VarName[j][i+j]);
188 LessEqualOneToCNF(vars, cnf);
191 for (int i=1; i<N-1; i++){
192 for (int j=0; j<N-i; j++){
193 vars.push_back(VarName[j+i][j]);
195 LessEqualOneToCNF(vars, cnf);
198 for (int i=0; i<N-1; i++){
199 for (int j=0; j<N-i; j++){
200 vars.push_back(VarName[j][N-1 - (i+j)]);
202 LessEqualOneToCNF(vars, cnf);
205 for (int i=1; i<N-1; i++){
206 for (int j=0; j<N-i; j++){
207 vars.push_back(VarName[j+i][N-1-j]);
209 LessEqualOneToCNF(vars, cnf);
213 //Symmetry breaking constraint
214 int mid = 1+ ((N-1)/2);
215 for (int i=0; i<mid; i++){
216 vars.push_back(VarName[0][i]);
220 for(int i=0; i<N; i++){
221 lastCol.push_back(VarName[N-1][i]);
223 verticalSymmetryBreaking(vars, lastCol, cnf);
225 //That's it ... Let's solve the problem ...
226 IncrementalSolver *solver =allocIncrementalSolver();
228 for (int i=0; i<cnf.size(); i++){
229 addArrayClauseLiteral(solver, cnf[i].size(), cnf[i].data());
231 finishedClauses(solver);
233 int result = solve(solver);
235 cout << "SAT Solving time: " << (stop_s-start_s)/double(CLOCKS_PER_SEC)*1000 << " ms" << endl;
238 printf("Problem is unsat\n");
241 printSolution(N, &solver->solution[1], solver->solutionsize);
242 printValidationStatus(N, &solver->solution[1], solver->solutionsize);
246 printf("Unknown results from SAT Solver...\n");
249 deleteIncrementalSolver(solver);
253 void csolverNQueensSub(int N, bool serialize=false){
254 CSolver *solver = new CSolver();
256 for(int i=0; i<N; i++){
259 uint64_t range[2*N-1];
260 for(int i=0; i<2*N-1; i++){
263 Set *domainSet = solver->createSet(1, domain, N);
264 Set *rangeSet = solver->createSet(1, range, 2*N-1);
265 vector<Element *> Xs;
266 vector<Element *> Ys;
267 for(int i=0; i<N; i++){
268 Xs.push_back(solver->getElementVar(domainSet));
269 Ys.push_back(solver->getElementVar(domainSet));
271 Set *d1[] = {domainSet, domainSet};
272 Function *sub = solver->createFunctionOperator(SATC_SUB, rangeSet, SATC_NOOVERFLOW);
273 //X shouldn't be equal
274 for(int i=0; i<N-1; i++){
275 for(int j=i+1; j<N; j++ ){
276 Element *e1x = Xs[i];
277 Element *e2x = Xs[j];
278 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
279 Element *inputs2 [] = {e1x, e2x};
280 BooleanEdge equals = solver->applyPredicate(eq, inputs2, 2);
281 solver->addConstraint(solver->applyLogicalOperation(SATC_NOT, equals));
284 //Y shouldn't be equal
285 for(int i=0; i<N-1; i++){
286 for(int j=i+1; j<N; j++ ){
287 Element *e1y = Ys[i];
288 Element *e2y = Ys[j];
289 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
290 Element *inputs2 [] = {e1y, e2y};
291 BooleanEdge equals = solver->applyPredicate(eq, inputs2, 2);
292 solver->addConstraint(solver->applyLogicalOperation(SATC_NOT, equals));
295 //vertical difference and horizontal difference shouldn't be equal shouldn't be equal
296 BooleanEdge overflow = solver->getBooleanVar(2);
297 Set *d2[] = {rangeSet, rangeSet};
298 for(int i=0; i<N-1; i++){
299 for(int j=i+1; j<N; j++ ){
300 Element *e1y = Ys[i];
301 Element *e2y = Ys[j];
302 Element *e1x = Xs[i];
303 Element *e2x = Xs[j];
304 Function *f1 = solver->createFunctionOperator(SATC_SUB, rangeSet, SATC_IGNORE);
305 Element *in1[] = {e1x, e2x};
306 Element *subx = solver->applyFunction(f1, in1, 2, overflow);
307 Element *in2[] = {e1y, e2y};
308 Element *suby = solver->applyFunction(f1, in2, 2, overflow);
309 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
310 Element *inputs2 [] = {subx, suby};
311 BooleanEdge equals = solver->applyPredicate(eq, inputs2, 2);
312 solver->addConstraint(solver->applyLogicalOperation(SATC_NOT, equals));
318 if (solver->solve() != 1){
319 printf("Problem is Unsolvable ...\n");
322 memset( table, 0, N*N*sizeof(int) );
323 for(int i=0; i<N; i++){
324 uint x = solver->getElementValue(Xs[i]);
325 uint y = solver->getElementValue(Ys[i]);
326 // printf("X=%d, Y=%d\n", x, y);
330 printSolution(N, table, N*N);
331 printValidationStatus(N, table, N*N);
336 void atmostOneConstraint(CSolver *solver, vector<BooleanEdge> &constraints){
337 int size = constraints.size();
341 solver->addConstraint(constraints[0]);
343 // solver->addConstraint(solver->applyLogicalOperation(SATC_OR, &constraints[0], size))
344 for(int i=0; i<size-1; i++){
345 for(int j=i+1; j<size; j++){
346 BooleanEdge const1 = solver->applyLogicalOperation(SATC_NOT, constraints[i]);
347 BooleanEdge const2 = solver->applyLogicalOperation(SATC_NOT, constraints[j]);
348 BooleanEdge array[] = {const1, const2};
349 solver->addConstraint( solver->applyLogicalOperation(SATC_OR, (BooleanEdge *)array, 2));
356 void mustHaveValueConstraint(CSolver* solver, vector<Element*> &elems){
357 for(int i=0; i<elems.size(); i++){
358 solver->mustHaveValue(elems[i]);
362 void differentInEachRow(CSolver* solver, int N, vector<Element*> &elems){
363 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
364 for(int i=0; i<N-1; i++){
365 for(int j=i+1; j<N; j++ ){
366 Element *e1x = elems[i];
367 Element *e2x = elems[j];
368 Element *inputs2 [] = {e1x, e2x};
369 BooleanEdge equals = solver->applyPredicate(eq, inputs2, 2);
370 solver->addConstraint(solver->applyLogicalOperation(SATC_NOT, equals));
377 void oneQueenInEachRow(CSolver* solver, vector<Element*> &elems){
378 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
379 int N = elems.size();
380 for(int i=0; i<N; i++){
381 vector<BooleanEdge> rowConstr;
382 for(int j=0; j<N; j++){
383 Element* e1 = elems[j];
384 Element* e2 = solver->getElementConst(3, (uint64_t) i);
385 Element* in[] = {e1, e2};
386 BooleanEdge equals = solver->applyPredicate(eq, in, 2);
387 rowConstr.push_back(equals);
389 if(rowConstr.size()>0){
390 solver->addConstraint(solver->applyLogicalOperation(SATC_OR, &rowConstr[0], rowConstr.size()) );
395 void generateRowConstraints(CSolver* solver, int N, vector<Element*> &elems){
396 oneQueenInEachRow(solver, elems);
397 differentInEachRow(solver, N, elems);
400 void diagonallyDifferentConstraint(CSolver *solver, int N, vector<Element*> &elems){
401 Predicate *eq = solver->createPredicateOperator(SATC_EQUALS);
402 for(int i=N-1; i>0; i--){
403 // cout << "i:" << i << "\t";
404 vector<BooleanEdge> diagonals;
405 for(int j=i; j>=0; j--){
407 Element* e1 = elems[index];
408 // cout << "e" << e1 <<"=" << j << ", ";
409 Element* e2 = solver->getElementConst(2, (uint64_t) j);
410 Element* in[] = {e1, e2};
411 BooleanEdge equals = solver->applyPredicate(eq, in, 2);
412 diagonals.push_back(equals);
416 atmostOneConstraint(solver, diagonals);
418 for(int i=1; i< N-1; i++){
419 // cout << "i:" << i << "\t";
420 vector<BooleanEdge> diagonals;
421 for(int j=i; j<N; j++){
422 int index =N-1- (j-i);
423 Element* e1 = elems[index];
424 // cout << "e" << e1 <<"=" << j << ", ";
425 Element* e2 = solver->getElementConst(2, (uint64_t) j);
426 Element* in[] = {e1, e2};
427 BooleanEdge equals = solver->applyPredicate(eq, in, 2);
428 diagonals.push_back(equals);
432 atmostOneConstraint(solver, diagonals);
438 void diagonallyDifferentConstraintBothDir(CSolver *solver, int N, vector<Element*> &elems){
439 diagonallyDifferentConstraint(solver, N, elems);
440 reverse(elems.begin(), elems.end());
441 // cout << "Other Diagonal:" << endl;
442 diagonallyDifferentConstraint(solver, N, elems);
445 void symmetryBreakingConstraint(CSolver *solver, int N, vector<Element*>& elems){
446 Predicate *lt = solver->createPredicateOperator(SATC_LT);
448 Element *e1x = elems[0];
449 Element *e2x = solver->getElementConst(2, mid);
450 Element *inputs [] = {e1x, e2x};
451 solver->addConstraint(solver->applyPredicate(lt, inputs, 2));
454 Element *inputs2 [] = {e1x, e2x};
455 BooleanEdge equals = solver->applyPredicate(lt, inputs2, 2);
456 solver->addConstraint(equals);
460 void csolverNQueens(int N, bool serialize=false){
465 CSolver *solver = new CSolver();
467 for(int i=0; i<N; i++){
470 Set *domainSet = solver->createSet(1, domain, N);
471 vector<Element *> elems;
472 for(int i=0; i<N; i++){
473 elems.push_back(solver->getElementVar(domainSet));
475 mustHaveValueConstraint(solver, elems);
476 generateRowConstraints(solver, N, elems);
477 diagonallyDifferentConstraintBothDir(solver, N, elems);
478 symmetryBreakingConstraint(solver, N, elems);
479 // solver->printConstraints();
483 if (solver->solve() != 1){
484 printf("Problem is Unsolvable ...\n");
487 memset( table, 0, N*N*sizeof(int) );
488 for(int i=0; i<N; i++){
489 uint x = solver->getElementValue(elems[i]);
490 // printf("X=%d, Y=%d\n", x, i);
494 printSolution(N, table, N*N);
495 printValidationStatus(N, table, N*N);
502 int main(int argc, char * argv[]){
504 printf("Two arguments are needed\n./nqueen <size> [--csolver]\n");
507 int N = atoi(argv[1]);
509 printf("Running the original encoding ...\n");
510 originalNqueensEncoding(N);
511 }else if( strcmp( argv[2], "--csolver") == 0){
512 printf("Running the CSolver encoding ...\n");
514 }else if (strcmp( argv[2], "--dump") == 0){
515 printf("Running the CSolver encoding ...\n");
516 csolverNQueens(N, true);
518 printf("Unknown argument %s", argv[2]);