void FactorQTZRep<T>::inverse( Matrix_<T>& inverse ) const {
Matrix_<T> iden(mn,mn);
inverse.resize(mn,mn);
iden = 1.0;
doSolve( iden, inverse );
return;
}
bool SolveAlgorithm::solve(SharedContext& ctx, const SolveParams& p, const LitVec& assume) {
assumptions_ = assume;
if (!isSentinel(ctx.tagLiteral())) { assumptions_.push_back(ctx.tagLiteral()); }
bool more = limits_.conflicts == 0 || doSolve(*ctx.master(), p);
ctx.enumerator()->reportResult(!more);
if (!isSentinel(ctx.tagLiteral())) { assumptions_.pop_back(); }
ctx.detach(*ctx.master());
return more;
}
int totalNQueens(int n) {
// Start typing your C/C++ solution below
// DO NOT write int main() function
results = 0;
vector<int> cur(n);
for (int i = 0; i < n; i++) {
cur[i] = -1;
}
doSolve(cur, n, 0);
return results;
}
void FactorQTZRep<T>::solve( const Matrix_<T>& b, Matrix_<T>& x ) const {
SimTK_APIARGCHECK_ALWAYS(isFactored ,"FactorQTZ","solve",
"No matrix was passed to FactorQTZ. \n" );
SimTK_APIARGCHECK2_ALWAYS(b.nrow()==nRow,"FactorQTZ","solve",
"number of rows in right hand side=%d does not match number of rows in original matrix=%d \n",
b.nrow(), nRow );
x.resize(nCol, b.ncol() );
Matrix_<T> tb;
tb.resize(maxmn, b.ncol() );
for(int j=0;j<b.ncol();j++) for(int i=0;i<b.nrow();i++) tb(i,j) = b(i,j);
doSolve(tb, x);
}
void FactorQTZRep<T>::solve( const Vector_<T>& b, Vector_<T> &x ) const {
SimTK_APIARGCHECK_ALWAYS(isFactored ,"FactorQTZ","solve",
"No matrix was passed to FactorQTZ. \n" );
SimTK_APIARGCHECK2_ALWAYS(b.size()==nRow,"FactorQTZ","solve",
"number of rows in right hand side=%d does not match number of rows in original matrix=%d \n",
b.size(), nRow );
Matrix_<T> m(maxmn,1);
for(int i=0;i<b.size();i++) {
m(i,0) = b(i);
}
Matrix_<T> r(nCol, 1 );
doSolve( m, r );
x.copyAssign(r);
}
void doSolve(vector<int> &cur, int n, int index) {
if (index == n) {
results++;
return;
}
int i = index;
for (int j = 0; j < n; j++) {
int k;
for (k = 0; k < index; k++) {
if (j == cur[k] || abs(i - k) == abs(j - cur[k])) {
break;
}
}
if (k == index) {
cur[k] = j;
doSolve(cur, n, index + 1);
}
}
}
// Constraints up to but not including iterator it have been unified.
// The current solution is soln
// The set of all solutions is in solns
bool Constraints::doSolve(std::list<Exp*>::iterator it, ConstraintMap& soln, std::list<ConstraintMap>& solns) {
LOG << "Begin doSolve at level " << ++level << "\n";
LOG << "Soln now: " << soln.prints() << "\n";
if (it == disjunctions.end()) {
// We have gotten to the end with no unification failures
// Copy the current set of constraints as a solution
//if (soln.size() == 0)
// Awkward. There is a trivial solution, but we have no constraints
// So make a constraint of always-true
//soln.insert(new Terminal(opTrue));
// Copy the fixed constraints
soln.makeUnion(fixed);
solns.push_back(soln);
LOG << "Exiting doSolve at level " << level-- << " returning true\n";
return true;
}
Exp* dj = *it;
// Iterate through each disjunction d of dj
Exp* rem1 = dj; // Remainder
bool anyUnified = false;
Exp* d;
while ((d = nextDisjunct(rem1)) != NULL) {
LOG << " $$ d is " << d << ", rem1 is " << ((rem1==0)?"NULL":rem1->prints()) << " $$\n";
// Match disjunct d against the fixed types; it could be compatible,
// compatible and generate an additional constraint, or be
// incompatible
ConstraintMap extra; // Just for this disjunct
Exp* c;
Exp* rem2 = d;
bool unified = true;
while ((c = nextConjunct(rem2)) != NULL) {
LOG << " $$ c is " << c << ", rem2 is " << ((rem2==0)?"NULL":rem2->prints()) << " $$\n";
if (c->isFalse()) {
unified = false;
break;
}
assert(c->isEquality());
Exp* lhs = ((Binary*)c)->getSubExp1();
Exp* rhs = ((Binary*)c)->getSubExp2();
extra.insert(lhs, rhs);
ConstraintMap::iterator kk;
kk = fixed.find(lhs);
if (kk != fixed.end()) {
unified &= unify(rhs, kk->second, extra);
LOG << "Unified now " << unified << "; extra now " << extra.prints() << "\n";
if (!unified) break;
}
}
if (unified)
// True if any disjuncts had all the conjuncts satisfied
anyUnified = true;
if (!unified) continue;
// Use this disjunct
// We can't just difference out extra if this fails; it may remove
// elements from soln that should not be removed
// So need a copy of the old set in oldSoln
ConstraintMap oldSoln = soln;
soln.makeUnion(extra);
doSolve(++it, soln, solns);
// Revert to the previous soln (whether doSolve returned true or not)
// If this recursion did any good, it will have gotten to the end and
// added the resultant soln to solns
soln = oldSoln;
LOG << "After doSolve returned: soln back to: " << soln.prints() << "\n";
// Back to the current disjunction
it--;
// Continue for more disjuncts this disjunction
}
// We have run out of disjuncts. Return true if any disjuncts had no
// unification failures
LOG << "Exiting doSolve at level " << level-- << " returning " << anyUnified << "\n";
return anyUnified;
}
bool Constraints::solve(std::list<ConstraintMap>& solns) {
LOG << conSet.size() << " constraints:";
std::ostringstream os; conSet.print(os); LOG << os.str().c_str();
// Replace Ta[loc] = ptr(alpha) with
// Tloc = alpha
LocationSet::iterator cc;
for (cc = conSet.begin(); cc != conSet.end(); cc++) {
Exp* c = *cc;
if (!c->isEquality()) continue;
Exp* left = ((Binary*)c)->getSubExp1();
if (!left->isTypeOf()) continue;
Exp* leftSub = ((Unary*)left)->getSubExp1();
if (!leftSub->isAddrOf()) continue;
Exp* right = ((Binary*)c)->getSubExp2();
if (!right->isTypeVal()) continue;
Type* t = ((TypeVal*)right)->getType();
if (!t->isPointer()) continue;
// Don't modify a key in a map
Exp* clone = c->clone();
// left is typeof(addressof(something)) -> typeof(something)
left = ((Binary*)clone)->getSubExp1();
leftSub = ((Unary*)left)->getSubExp1();
Exp* something = ((Unary*)leftSub)->getSubExp1();
((Unary*)left)->setSubExp1ND(something);
((Unary*)leftSub)->setSubExp1ND(NULL);
delete leftSub;
// right is <alpha*> -> <alpha>
right = ((Binary*)clone)->getSubExp2();
t = ((TypeVal*)right)->getType();
((TypeVal*)right)->setType(((PointerType*)t)->getPointsTo()->clone());
delete t;
conSet.remove(c);
conSet.insert(clone);
delete c;
}
// Sort constraints into a few categories. Disjunctions go to a special
// list, always true is just ignored, and constraints of the form
// typeof(x) = y (where y is a type value) go to a map called fixed.
// Constraint terms of the form Tx = Ty go into a map of LocationSets
// called equates for fast lookup
for (cc = conSet.begin(); cc != conSet.end(); cc++) {
Exp* c = *cc;
if (c->isTrue()) continue;
if (c->isFalse()) {
if (VERBOSE || DEBUG_TA)
LOG << "Constraint failure: always false constraint\n";
return false;
}
if (c->isDisjunction()) {
disjunctions.push_back(c);
continue;
}
// Break up conjunctions into terms
Exp* rem = c, *term;
while ((term = nextConjunct(rem)) != NULL) {
assert(term->isEquality());
Exp* lhs = ((Binary*)term)->getSubExp1();
Exp* rhs = ((Binary*)term)->getSubExp2();
if (rhs->isTypeOf()) {
// Of the form typeof(x) = typeof(z)
// Insert into equates
equates.addEquate(lhs, rhs);
} else {
// Of the form typeof(x) = <typeval>
// Insert into fixed
assert(rhs->isTypeVal());
fixed[lhs] = rhs;
}
}
}
{LOG << "\n" << (unsigned)disjunctions.size() << " disjunctions: "; std::list<Exp*>::iterator dd;
for (dd = disjunctions.begin(); dd != disjunctions.end(); dd++) LOG << *dd << ",\n"; LOG << "\n";}
LOG << fixed.size() << " fixed: " << fixed.prints();
LOG << equates.size() << " equates: " << equates.prints();
// Substitute the fixed types into the disjunctions
substIntoDisjuncts(fixed);
// Substitute the fixed types into the equates. This may generate more
// fixed types
substIntoEquates(fixed);
LOG << "\nAfter substitute fixed into equates:\n";
{LOG << "\n" << (unsigned)disjunctions.size() << " disjunctions: "; std::list<Exp*>::iterator dd;
for (dd = disjunctions.begin(); dd != disjunctions.end(); dd++) LOG << *dd << ",\n"; LOG << "\n";}
LOG << fixed.size() << " fixed: " << fixed.prints();
LOG << equates.size() << " equates: " << equates.prints();
// Substitute again the fixed types into the disjunctions
// (since there may be more fixed types from the above)
substIntoDisjuncts(fixed);
LOG << "\nAfter second substitute fixed into disjunctions:\n";
{LOG << "\n" << (unsigned)disjunctions.size() << " disjunctions: "; std::list<Exp*>::iterator dd;
for (dd = disjunctions.begin(); dd != disjunctions.end(); dd++) LOG << *dd << ",\n"; LOG << "\n";}
LOG << fixed.size() << " fixed: " << fixed.prints();
LOG << equates.size() << " equates: " << equates.prints();
ConstraintMap soln;
bool ret = doSolve(disjunctions.begin(), soln, solns);
if (ret) {
// For each solution, we need to find disjunctions of the form
// <alphaN> = <type> or
// <type> = <alphaN>
// and substitute these into each part of the solution
std::list<ConstraintMap>::iterator it;
for (it = solns.begin(); it != solns.end(); it++)
it->substAlpha();
}
return ret;
}
