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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;