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class FrobeniusStrategy : public Strategy {
public:
FrobeniusStrategy(const vector<mpz_class>& degrees,
mpz_class* frobeniusNumber,
TermHandler& handler):
_dimension(handler.getDimension()),
_partialDegrees(handler.getDimension()),
_degreeMultiples(0),
_initialDegree(degrees[0]),
_handler(handler),
_frobeniusNumber(frobeniusNumber) {
ASSERT(_dimension >= 3); // TODO: handle the case _dimension == 3
ASSERT(degrees.size() == _dimension + 1);
ASSERT(frobeniusNumber != 0);
createDegreeMultiples(degrees);
}
virtual ~FrobeniusStrategy() {
ASSERT(_degreeMultiples != 0);
for (unsigned int i = 0; i < _dimension; ++i)
delete[] _degreeMultiples[i];
delete[] _degreeMultiples;
*_frobeniusNumber = _maximumDegreeSeen;
}
virtual bool consideringCall(const ExternalTerm& b,
SortedTermList::iterator it,
const SortedTermList& terms) {
return true;
}
virtual bool startingCall(const ExternalTerm& b,
const SortedTermList& terms) {
int position = terms.position();
if (position == 0)
_partialDegrees[0] = -_initialDegree;
else {
const Degree& degree = _degreeMultiples[position - 1][b[position - 1]];
_partialDegrees[position] = _partialDegrees[position - 1] + degree;
}
return !canSkipDueToUpperBound(terms, _partialDegrees[position]);
}
virtual void endingCall(const ExternalTerm& b,
const SortedTermList& terms) {
}
virtual void foundSolution(const ExternalTerm& b) {
Degree degree = _partialDegrees[_dimension - 2] +
_degreeMultiples[_dimension - 2][b[_dimension - 2]] +
_degreeMultiples[_dimension - 1][b[_dimension - 1]];
if (degree > _maximumDegreeSeen)
_maximumDegreeSeen = degree;
}
private:
bool canSkipDueToUpperBound(const SortedTermList& terms, const Degree& degree) {
unsigned int position = terms.position();
if (position > _dimension - 3)
return false;
ExternalTerm lcm(_handler);
SortedTermList::iterator end = terms.end();
for (SortedTermList::iterator it = terms.begin(); it != end; ++it)
_handler.lcm(lcm, lcm, &*it, position);
Degree upperBound = degree;
for (unsigned int i = position; i < _dimension; ++i) {
ASSERT(lcm[i] > 0);
upperBound += _degreeMultiples[i][lcm[i] - 1];
}
if (upperBound <= _maximumDegreeSeen)
return true;
if (false) { // too expensive to compute
Degree maxMinLoss = 0; // loss of degree
for (SortedTermList::iterator it = terms.begin(); it != end; ++it) {
Degree minLoss = -1;
for (unsigned int i = position; i < _dimension; ++i) {
Degree loss = _degreeMultiples[i][lcm[i] - 1] - _degreeMultiples[i][_handler.getExponent(&*it, i)];
if (minLoss == -1 || loss < minLoss)
minLoss = loss;
}
if (minLoss > maxMinLoss)
maxMinLoss = minLoss;
}
if (upperBound - maxMinLoss <= _maximumDegreeSeen)
return true;
}
// This works almost as well while being much faster to compute.
// It is still too expensive a bound.
if (false) {
SortedTermList::iterator bestCandidate = end;
int maxMinValue = -1;
for (SortedTermList::iterator it = terms.begin(); it != end; ++it) {
int minValue = -1;
for (unsigned int i = position; i < _dimension; ++i) {
int value = lcm[i] - _handler.getExponent(&*it, i);
if (minValue == -1 || value < minValue) {
minValue = value;
}
}
if (maxMinValue == -1 || minValue > maxMinValue) {
maxMinValue = minValue;
bestCandidate = it;
}
}
ASSERT(bestCandidate != end);
Degree minLoss = -1;
for (unsigned int i = position; i < _dimension; ++i) {
Degree loss = _degreeMultiples[i][lcm[i] - 1] -
_degreeMultiples[i][_handler.getExponent(&*bestCandidate, i)];
if (minLoss == -1 || loss < minLoss)
minLoss = loss;
}
if (upperBound - minLoss <= _maximumDegreeSeen)
return true;
}
return false;
}
void createDegreeMultiples(const vector<mpz_class>& degrees) {
ASSERT(_degreeMultiples == 0);
ASSERT(degrees.size() == _dimension + 1);
_degreeMultiples = new Degree*[_dimension];
for (unsigned int position = 0; position < _dimension; ++position) {
const vector<mpz_class>& decompressionMap = _handler.getDecompressionMap(position);
_degreeMultiples[position] = new Degree[decompressionMap.size()];
for (Exponent exponent = 0;
exponent < decompressionMap.size(); ++exponent)
_degreeMultiples[position][exponent] =
_handler.getDecompressionMap(position)[exponent] * degrees[position + 1];
}
}
unsigned int _dimension;
vector<Degree> _partialDegrees;
Degree** _degreeMultiples;
Degree _initialDegree;
Degree _maximumDegreeSeen;
TermHandler& _handler;
mpz_class* _frobeniusNumber;
};
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