static
//Formula buildBDD(const Linear& c, int size, int lower_limit, int upper_limit, int material_left, Map<Pair<int,Int>,Formula>& memo, int max_cost)
Formula buildBDD(const Linear& c, int size, Int sum, Int material_left, Map<Pair<int,Int>,Formula>& memo, int max_cost)
{
Int lower_limit = (c.lo == Int_MIN) ? Int_MIN : c.lo - sum;
Int upper_limit = (c.hi == Int_MAX) ? Int_MAX : c.hi - sum;
if (lower_limit <= 0 && upper_limit >= material_left)
return _1_;
else if (lower_limit > material_left || upper_limit < 0)
return _0_;
else if (FEnv::topSize() > max_cost)
return _undef_; // (mycket elegant!)
Pair<int,Int> key = Pair_new(size, lower_limit);
Formula ret;
if (!memo.peek(key, ret)){
assert(size != 0);
size--;
material_left -= c(size);
Int hi_sum = sign(c[size]) ? sum : sum + c(size);
Int lo_sum = sign(c[size]) ? sum + c(size) : sum;
Formula hi = buildBDD(c, size, hi_sum, material_left, memo, max_cost);
if (hi == _undef_) return _undef_;
Formula lo = buildBDD(c, size, lo_sum, material_left, memo, max_cost);
if (lo == _undef_) return _undef_;
ret = ITE(var(var(c[size])), hi, lo);
memo.set(key, ret);
}
return ret;
}
void Map_set(Map* map, void* key, void* value)
{
Pair* pair = Pair_new();
pair->left = key;
pair->right = value;
BinarySearchTree_insert((BinarySearchTree*) map, pair);
}
// Normalize a PB constraint to only positive constants. Depends on:
//
// bool ok -- Will be set to FALSE if constraint is unsatisfiable.
// lbool value(Lit) -- Returns the value of a literal (however, it is sound to always return 'l_Undef', but produces less efficient results)
// bool addUnit(Lit) -- Enqueue unit fact for propagation (returns FALSE if conflict detected).
//
// The two vectors 'ps' and 'Cs' (which are modififed by this method) should be interpreted as:
//
// 'p[0]*C[0] + p[1]*C[1] + ... + p[N-1]*C[N-1] >= C[N]'
//
// The method returns TRUE if constraint was normalized, FALSE if the constraint was already
// satisfied or determined contradictory. The vectors 'ps' and 'Cs' should ONLY be used if
// TRUE is returned.
//
bool PbSolver::normalizePb(vec<Lit>& ps, vec<Int>& Cs, Int& C)
{
assert(ps.size() == Cs.size());
if (!ok) return false;
// Remove assigned literals and literals with zero coefficients:
int new_sz = 0;
for (int i = 0; i < ps.size(); i++){
if (value(ps[i]) != l_Undef){
if (value(ps[i]) == l_True)
C -= Cs[i];
}else if (Cs[i] != 0){
ps[new_sz] = ps[i];
Cs[new_sz] = Cs[i];
new_sz++;
}
}
ps.shrink(ps.size() - new_sz);
Cs.shrink(Cs.size() - new_sz);
//**/reportf("No zero, no assigned :"); for (int i = 0; i < ps.size(); i++) reportf(" %d*%sx%d", Cs[i], sign(ps[i])?"~":"", var(ps[i])); reportf(" >= %d\n", C);
// Group all x/~x pairs
//
Map<Var, Pair<Int,Int> > var2consts(Pair_new(0,0)); // Variable -> negative/positive polarity constant
for (int i = 0; i < ps.size(); i++){
Var x = var(ps[i]);
Pair<Int,Int> consts = var2consts.at(x);
if (sign(ps[i]))
consts.fst += Cs[i];
else
consts.snd += Cs[i];
var2consts.set(x, consts);
}
// Normalize constants to positive values only:
//
vec<Pair<Var, Pair<Int,Int> > > all;
var2consts.pairs(all);
vec<Pair<Int,Lit> > Csps(all.size());
for (int i = 0; i < all.size(); i++){
if (all[i].snd.fst < all[i].snd.snd){
// Negative polarity will vanish
C -= all[i].snd.fst;
Csps[i] = Pair_new(all[i].snd.snd - all[i].snd.fst, Lit(all[i].fst));
}else{
// Positive polarity will vanish
C -= all[i].snd.snd;
Csps[i] = Pair_new(all[i].snd.fst - all[i].snd.snd, ~Lit(all[i].fst));
}
}
// Sort literals on growing constant values:
//
sort(Csps); // (use lexicographical order of 'Pair's here)
Int sum = 0;
for (int i = 0; i < Csps.size(); i++){
Cs[i] = Csps[i].fst, ps[i] = Csps[i].snd, sum += Cs[i];
if (sum < 0) fprintf(stderr, "ERROR! Too large constants encountered in constraint.\n"), exit(1);
}
ps.shrink(ps.size() - Csps.size());
Cs.shrink(Cs.size() - Csps.size());
// Propagate already present consequences:
//
bool changed;
do{
changed = false;
while (ps.size() > 0 && sum-Cs.last() < C){
changed = true;
if (!addUnit(ps.last())){
ok = false;
return false; }
sum -= Cs.last();
C -= Cs.last();
ps.pop(); Cs.pop();
}
// Trivially true or false?
if (C <= 0)
return false;
if (sum < C){
ok = false;
return false; }
assert(sum - Cs[ps.size()-1] >= C);
// GCD:
assert(Cs.size() > 0);
Int div = Cs[0];
for (int i = 1; i < Cs.size(); i++)
div = gcd(div, Cs[i]);
for (int i = 0; i < Cs.size(); i++)
Cs[i] /= div;
C = (C + div-1) / div;
if (div != 1)
changed = true;
// Trim constants:
for (int i = 0; i < Cs.size(); i++)
if (Cs[i] > C)
changed = true,
Cs[i] = C;
}while (changed);
//**/reportf("Normalized constraint:"); for (int i = 0; i < ps.size(); i++) reportf(" %d*%sx%d", Cs[i], sign(ps[i])?"~":"", var(ps[i])); reportf(" >= %d\n", C);
return true;
}
