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// Copyright 2008, 2009 Brady J. Garvin
// This file is part of Covering Arrays by Simulated Annealing (CASA).
// CASA is free software: you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// CASA is distributed in the hope that it will be useful, but
// WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with CASA. If not, see <http://www.gnu.org/licenses/>.
#include <cassert>
#include "Combinadic.H"
using namespace std;
static double TWO_PI = 2 * M_PI;
static double INVERSE_E = 1 / M_E;
// We want result to approximately satisfy
// cardinality! * encoding = result * (result-1) * ... * (result-(cardinality-1))
// The right-hand side usually has degree >= 5, so we need to trivialize it a bit.
// It can be replaced with the overapproximation:
// cardinality! * encoding = (result - (cardinality-1) / 2) ^ cardinality
// Factorials are also expensive, so we use Stirling's approximation:
// sqrt(TWO_PI * cardinality) * ((cardinality / e) ^ cardinality) * encoding =
// (result - (cardinality-1) / 2) ^ cardinality
// Now, to solve for result, take the cardinality'th root of both sides:
// (cardinality / e) *
// (encoding * sqrt(TWO_PI * cardinality)) ^ (1 / cardinality) =
// result - (cardinality - 1)/2
// And then rearrange that and add a half to make the flooring round to nearest:
// result =
// (cardinality / e) *
// (encoding * sqrt(TWO_PI * cardinality)) ^ (1 / cardinality) +
// cardinality / 2 =
// ((1 / e) *
// (encoding * sqrt(TWO_PI * cardinality)) ^ (1 / cardinality) + 0.5) *
// cardinality
unsigned Combinadic::guessLastMember(unsigned encoding, unsigned cardinality) {
double scaledEncoding = encoding * sqrt(TWO_PI * cardinality);
double rootOfEncoding = pow(scaledEncoding, 1.0 / cardinality);
return (unsigned)((INVERSE_E * rootOfEncoding + 0.5) * (double)cardinality);
}
pair<unsigned, unsigned>Combinadic::getLastMemberAndContribution
(unsigned encoding, unsigned cardinality) {
unsigned member = guessLastMember(encoding, cardinality);
unsigned contribution = triangle.nCr(member, cardinality);
if (contribution > encoding) {
do {
contribution = triangle.nCr(--member, cardinality);
} while (contribution > encoding);
} else {
unsigned nextContribution = triangle.nCr(member + 1, cardinality);
while (nextContribution <= encoding) {
++member;
contribution = nextContribution;
nextContribution = triangle.nCr(member + 1, cardinality);
}
}
return pair<unsigned, unsigned>(member, contribution);
}
unsigned Combinadic::encode(Array<unsigned>sortedSubset) {
unsigned result = 0;
for (unsigned i = 0; i < sortedSubset.getSize(); ++i) {
result += triangle.nCr(sortedSubset[i], i + 1);
}
return result;
}
Array<unsigned>Combinadic::decode(unsigned encoding, unsigned cardinality) {
Array<unsigned>result(cardinality);
for (unsigned i = cardinality; i;) {
pair<unsigned, unsigned>memberAndContribution =
getLastMemberAndContribution(encoding, i);
result[--i] = memberAndContribution.first;
encoding -= memberAndContribution.second;
}
return result;
}
Array<unsigned>Combinadic::begin(unsigned size) const {
Array<unsigned>result(size);
for(unsigned i = size; i-- ;) {
result[i]=i;
}
return result;
}
void Combinadic::previous(Array<unsigned>sortedSubset) const {
assert(sortedSubset.getSize());
unsigned limit = sortedSubset.getSize();
for(unsigned i = 0; i < limit; ++i) {
unsigned entry = sortedSubset[i];
if (entry > i) {
do {
sortedSubset[i] = --entry;
} while (i-- > 0);
return;
}
}
}
void Combinadic::next(Array<unsigned>sortedSubset) const {
assert(sortedSubset.getSize());
unsigned limit = sortedSubset.getSize() - 1, ceiling = sortedSubset[0];
for (unsigned i = 0; i < limit; ++i) {
unsigned entry = ceiling + 1;
ceiling = sortedSubset[i + 1];
if (entry < ceiling) {
sortedSubset[i] = entry;
return;
}
sortedSubset[i] = i;
}
++sortedSubset[limit];
}
Combinadic combinadic;
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