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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 "link/tangle.h"
#include "utilities/randutils.h"
// Affects the number of random type III moves attempted during simplification.
#define COEFF_TYPE_3 20
namespace regina {
bool Link::simplify() {
bool changed;
{ // Begin scope for change event group.
PacketChangeGroup span(*this);
// Reduce to a local minimum.
changed = simplifyToLocalMinimum(true);
// Clone to work with when we might want to roll back changes.
Link* use;
// Variables used for selecting random moves.
std::vector<std::pair<Crossing*, int>> type3Available;
std::pair<Crossing*, int> type3Choice;
size_t type3Attempts, type3Cap;
int side;
while (true) {
// Clone the link and start making moves that might
// or might not lead to a simplification.
// If we've already simplified then there's no need to use a
// separate clone since we won't need to undo further changes.
use = (changed ? this : new Link(*this, false));
// Make random type III Reidemeister moves.
type3Attempts = type3Cap = 0;
while (true) {
// Calculate the list of available type III moves.
type3Available.clear();
for (Crossing* c : use->crossings_)
for (side = 0; side < 2; ++side)
if (use->hasR3(c, side))
type3Available.emplace_back(c, side);
// Increment type3Cap if needed.
if (type3Cap < COEFF_TYPE_3 * type3Available.size())
type3Cap = COEFF_TYPE_3 * type3Available.size();
// Have we tried enough type III moves?
if (type3Attempts >= type3Cap)
break;
// Perform a random type III move on the clone.
type3Choice = type3Available[
RandomEngine::rand(type3Available.size())];
use->internalR3(type3Choice.first, type3Choice.second,
false /* do not check */, true);
// See if we can simplify now.
if (use->simplifyToLocalMinimum(true)) {
// We have successfully simplified!
// Start all over again.
type3Attempts = type3Cap = 0;
} else
++type3Attempts;
}
// Sync the real link with the clone if appropriate.
if (use != this) {
// At this point, changed == false.
if (use->size() < size()) {
// The type III moves were successful; accept them.
swap(*use);
changed = true;
}
delete use;
}
// Type III moves will help us no more for now.
break;
}
} // End scope for change event span.
return changed;
}
bool Link::simplifyToLocalMinimum(bool perform) {
if (! perform) {
// Look for type I or II Reidemeister moves.
for (Crossing* c : crossings_) {
if (hasR1(c))
return true;
if (hasR2(StrandRef(c, 1)))
return true;
}
return false;
}
PacketChangeGroup span(*this);
bool changed = false; // Has anything changed ever (for return value)?
bool changedNow = true; // Did we just change something (for loop control)?
while (changedNow) {
changedNow = false;
// Look for type I or II Reidemeister moves.
for (Crossing* c : crossings_) {
if (r1(c)) {
changedNow = changed = true;
break;
}
if (r2(StrandRef(c, 1))) {
changedNow = changed = true;
break;
}
}
if (changedNow)
continue;
}
return changed;
}
bool Tangle::simplifyToLocalMinimum(bool perform) {
if (! perform) {
// Look for type I or II Reidemeister moves.
for (Crossing* c : crossings_) {
if (hasR1(c))
return true;
if (hasR2(StrandRef(c, 1)))
return true;
}
return false;
}
bool changed = false; // Has anything changed ever (for return value)?
bool changedNow = true; // Did we just change something (for loop control)?
while (changedNow) {
changedNow = false;
// Look for type I or II Reidemeister moves.
for (Crossing* c : crossings_) {
if (r1(c)) {
changedNow = changed = true;
break;
}
if (r2(StrandRef(c, 1))) {
changedNow = changed = true;
break;
}
}
if (changedNow)
continue;
}
return changed;
}
} // namespace regina
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