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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2025, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program 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 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program 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 this program. If not, see <https://www.gnu.org/licenses/>. *
* *
**************************************************************************/
#include <algorithm>
#include "split/sigcensus.h"
namespace regina {
size_t SigCensus::run() {
// Initialisations.
std::fill(sig.labelInv, sig.labelInv + 2 * sig.order_, false);
sig.nCycles = 0;
sig.nCycleGroups = 0;
nextLabel = 0;
std::fill(used, used + sig.order_, 0);
totalFound = 0;
// Try creating a first cycle.
extendAutomorphisms();
for (unsigned i = 2 * sig.order_; i > 0; i--)
tryCycle(i, true, 0);
automorph[sig.nCycleGroups].clear();
return totalFound;
}
bool SigCensus::extendAutomorphisms() {
if (sig.nCycleGroups == 0) {
automorph[0].push_back(SigPartialIsomorphism(1));
automorph[0].push_back(SigPartialIsomorphism(-1));
return true;
}
unsigned firstLabel;
int result;
unsigned i;
for (const SigPartialIsomorphism& base : automorph[sig.nCycleGroups - 1]) {
// Try extending this automorphism.
SigPartialIsomorphism iso(base, nextLabel, sig.nCycles);
firstLabel = base.nLabels;
if (firstLabel == nextLabel) {
iso.makeCanonical(sig, sig.nCycleGroups - 1);
result = iso.compareWithIdentity(sig, sig.nCycleGroups - 1);
if (result == 0)
automorph[sig.nCycleGroups].push_back(std::move(iso));
else if (result < 0)
return false;
} else {
for (i = firstLabel; i < nextLabel; i++)
iso.labelImage[i] = i;
do {
iso.makeCanonical(sig, sig.nCycleGroups - 1);
result = iso.compareWithIdentity(sig, sig.nCycleGroups - 1);
if (result < 0)
return false;
else if (result == 0)
automorph[sig.nCycleGroups].push_back(
SigPartialIsomorphism(iso));
} while (std::next_permutation(iso.labelImage + firstLabel,
iso.labelImage + nextLabel));
}
}
return true;
}
void SigCensus::tryCycle(unsigned cycleLen, bool newCycleGroup,
unsigned startPos) {
// Are we finished?
if (startPos == 2 * sig.order_) {
++totalFound;
action_(sig, automorph[sig.nCycleGroups]);
return;
}
// Prepare the signature for the forthcoming cycle.
sig.nCycles++;
if (newCycleGroup)
sig.nCycleGroups++;
// Insert the cycleStart sentinel.
unsigned endPos = startPos + cycleLen;
sig.cycleStart[sig.nCycles] = endPos;
// We won't insert the cycleGroupStart sentinel until we know where
// the group will finish.
// Generate all possibilities for this cycle.
unsigned tryPos = startPos;
sig.label[tryPos] = 0;
unsigned lowerBnd, upperBnd;
bool avoid;
unsigned i;
while(true) {
if (tryPos == endPos) {
// Found a complete cycle.
avoid = false;
if (startPos == 0 && used[sig.label[startPos]] == 2) {
// We run the risk of having a cycle that could be
// made lexicographically smaller simply by rotating it.
i = 1;
while (sig.label[startPos + i] != sig.label[startPos])
i++;
if (sig.cycleCmp(
sig.nCycles - 1, 0, 1, nullptr,
sig.nCycles - 1, i, 1, nullptr) > 0)
avoid = true;
}
if (! avoid) {
if (endPos == 2 * sig.order_) {
// Found a complete cycle set.
sig.cycleGroupStart[sig.nCycleGroups] = sig.nCycles;
if (extendAutomorphisms())
tryCycle(0, true, endPos);
automorph[sig.nCycleGroups].clear();
} else {
// Move on to create the next cycle.
// The next cycle will have length i.
if (endPos + cycleLen <= 2 * sig.order_)
tryCycle(cycleLen, false, endPos);
sig.cycleGroupStart[sig.nCycleGroups] = sig.nCycles;
if (extendAutomorphisms())
for (i = (endPos + cycleLen - 1 <= 2 * sig.order_ ?
cycleLen - 1 : 2 * sig.order_ - endPos);
i > 0; i--)
tryCycle(i, true, endPos);
automorph[sig.nCycleGroups].clear();
}
}
// Step back again.
tryPos--;
used[sig.label[tryPos]]--;
if (sig.label[tryPos] == nextLabel - 1 &&
used[sig.label[tryPos]] == 0)
nextLabel--;
sig.label[tryPos]++;
} else {
// Find the next viable possibility for this position.
if (tryPos == startPos) {
if (newCycleGroup)
lowerBnd = 0;
else
lowerBnd = sig.label[startPos - cycleLen];
upperBnd = (startPos == 0 ? 1 : nextLabel);
} else {
lowerBnd = (startPos == 0 ? sig.label[startPos] :
sig.label[startPos] + 1);
upperBnd = nextLabel + 1;
}
if (upperBnd >= sig.order_)
upperBnd = sig.order_;
if (sig.label[tryPos] < lowerBnd)
sig.label[tryPos] = lowerBnd;
while (sig.label[tryPos] < upperBnd) {
if (used[sig.label[tryPos]] < 2)
break;
sig.label[tryPos]++;
}
if (sig.label[tryPos] >= upperBnd) {
// We've run out of ideas for this position.
// Step back and undo the previous position.
if (tryPos == startPos)
break;
tryPos--;
used[sig.label[tryPos]]--;
if (sig.label[tryPos] == nextLabel - 1 &&
used[sig.label[tryPos]] == 0)
nextLabel--;
sig.label[tryPos]++;
} else {
// We've found a value to try.
used[sig.label[tryPos]]++;
if (sig.label[tryPos] == nextLabel)
nextLabel++;
tryPos++;
if (tryPos < endPos)
sig.label[tryPos] = 0;
}
}
}
sig.nCycles--;
if (newCycleGroup)
sig.nCycleGroups--;
}
} // namespace regina
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