LPP* CnLPP::getLPP()
{
setComment("C(n) LPP " + gameId());
// each line is a structural variable
for (const Line& l: b.getLineList()) {
std::string v_name = to_string(l);
setVariableBounds(v_name, 0.0, 1.0);
}
// each dot is a structural variable
for (const Dot& d: b.getDotList()) {
std::string v_name = "dot_" + to_string(d);
setVariableBounds(v_name, 0.0, 1.0);
getObjective().push_back(std::pair<std::string, double>(v_name, -1.0));
// Constraint for exact problems.
//
// variables are either 0 or 1 (i.e. the move is either played or not)
if (getFlag("exact")) {
setVariableBoolean(v_name, true);
}
}
// constraints:
//
// (1) for each segment, sum of weights of moves that use this segment is <= 1
// (2) for each segment,
// dot_weight >= sum of weights of lines that use this segment
//
// (3) sum of line weights = n
//
// (4) dot_weight for dots from the cross is equal to 1
// (1) for each segment, sum of weights of moves that use this segment is <= 1
// (IT IS REDUNDANT TO (2) because dot_weight <= 1):
// (2) for each segment,
// dot_weight >= sum of weights of moves that remove this segment
for (const Segment& s: b.getSegmentList()) {
Constraint c;
c.setName("used_segment_" + to_string(s));
for (const Line& l: b.getLinesUsingSegment(s)) {
c.addVariable(to_string(l), -1.0);
}
c.addVariable("dot_" + to_string(s.first), 1.0);
c.setBound(0.0);
c.setType(Constraint::GT);
addConstraint(c);
}
// (3) sum of line weights = n
{
Constraint c;
c.setName("startingdots");
for (const Line& l: b.getLineList()) {
c.addVariable(to_string(l), 1.0);
}
c.setBound(n);
c.setType(Constraint::EQ);
addConstraint(c);
}
// (4) dot_weight for dots from the cross is equal to 1
for (const Dot& d: b.getDotList()) {
if (b.hasDot(d)) {
Constraint c;
c.setName("cross_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0);
c.setBound(1.0);
c.setType(Constraint::EQ);
addConstraint(c);
}
}
// symmetric solutions
if (getFlag("symmetric")) {
for (const Line&l: b.getLineList()) {
Line sl = b.centerSymmetry(l);
Constraint c;
c.addVariable(to_string(l), 1.0);
c.addVariable(to_string(sl), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("sym_" + to_string(l));
addConstraint(c);
}
}
return this;
}
LPP* PlusPlusLPP::getLPP()
{
setComment("++LPP " + gameId());
// each line is a structural variable
for (const Line& l: b.getLineList()) {
std::string v_name = to_string(l);
setVariableBounds(v_name, 0.0, 1.0);
getObjective().push_back(std::pair<std::string, double>(v_name, 1.0));
}
// each dot is a structural variable
for (const Dot& d: b.getDotList()) {
std::string v_name = "dot_" + to_string(d);
setVariableBounds(v_name, 0.0, 1.0);
// Constraint for exact problems.
//
// variables are either 0 or 1 (i.e. the move is either played or not)
if (getFlag("exact")) {
setVariableBoolean(v_name, true);
setVariableOrd(v_name, 1000-abs(b.getCRef().x - d.x) - abs(b.getCRef().y - d.y));
}
}
// constraints:
//
// (1) for each segment, sum of weights of moves that use this segment is <= 1
// (2) for each segment,
// dot_weight >= sum of weights of lines that use this segment
//
// (3) sum of dot weights = 36 + sum of line weights
//
// (4) dot_weight for dots from the cross is equal to 1
// (1) for each segment, sum of weights of moves that use this segment is <= 1
// (IT IS REDUNDANT TO (2) because dot_weight <= 1):
// (2) for each segment,
// dot_weight >= sum of weights of moves that remove this segment
for (const Segment& s: b.getSegmentList()) {
Constraint c;
c.setName("used_segment_" + to_string(s));
for (const Line& l: b.getLinesUsingSegment(s)) {
c.addVariable(to_string(l), -1.0);
}
c.addVariable("dot_" + to_string(s.first), 1.0);
c.setBound(0.0);
c.setType(Constraint::GT);
addConstraint(c);
}
// (3) sum of dot weights <= 36 + sum of line weights
{
Constraint c;
c.setName("startingdots");
for (const Dot& d: b.getDotList()) {
c.addVariable("dot_" + to_string(d), 1.0);
}
for (const Line& l: b.getLineList()) {
c.addVariable(to_string(l), -1.0);
}
c.setBound(36.0);
c.setType(Constraint::EQ);
addConstraint(c);
}
// (4) dot_weight for dots from the cross is equal to 1
for (const Dot& d: b.getDotList()) {
if (b.hasDot(d)) {
Constraint c;
c.setName("cross_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0);
c.setBound(1.0);
c.setType(Constraint::EQ);
addConstraint(c);
}
}
// symmetric solutions
if (getFlag("symmetric")) {
for (const Line&l: b.getLineList()) {
Line sl = b.centerSymmetry(l);
Constraint c;
c.addVariable(to_string(l), 1.0);
c.addVariable(to_string(sl), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("sym_" + to_string(l));
addConstraint(c);
}
for (const Dot&d: b.getDotList()) {
Dot sd = b.centerSymmetry(d);
Constraint c;
c.addVariable("dot_"+to_string(d), 1.0);
c.addVariable("dot_"+to_string(sd), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("dotsym_" + to_string(d));
addConstraint(c);
}
}
// exact hull
if (getFlag("hull")) {
// right side
addConstraint(getSideConstraint(1,0,true));
// left side
addConstraint(getSideConstraint(1,0,false));
// lower right side
addConstraint(getSideConstraint(1,-1,false));
// upper left side
addConstraint(getSideConstraint(1,-1,true));
// top side
addConstraint(getSideConstraint(0,1,true));
// bottom side
addConstraint(getSideConstraint(0,1,false));
// lower left side
addConstraint(getSideConstraint(1,1,false));
// upper right side
addConstraint(getSideConstraint(1,1,true));
}
// dots that are not placed have dot_ variable equal to 0
// this is important for --hull option
// and possibly for other reasons as well
for (const Dot& d: b.getDotList())
{
Constraint c;
c.setName("dotline_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0);
for (const Line& l: b.getLinesUsingDot(d)) {
c.addVariable(to_string(l), -1.0);
}
c.setType(Constraint::LT);
c.setBound(0.0);
addConstraint(c);
}
// extra constraints that remove small gaps from the solution
// there is always an optimal solution without 1-segment gaps
if (getFlag("extra")) {
for (const Line& l: b.getLineList()) {
{
Constraint c;
c.setName("smallgaps1_" + to_string(l));
c.addVariable(to_string(l), 1.0);
Line ol;
if (b.getVariant() == T5) {
ol = Line(l.st + direction[l.dir]*5, l.dir); if (b.validLine(ol)) { c.addVariable(to_string(ol), 1.0); }
} else {
ol = Line(l.st + direction[l.dir]*6, l.dir); if (b.validLine(ol)) { c.addVariable(to_string(ol), 1.0); }
}
c.setType(Constraint::LT);
c.setBound(1.0);
addConstraint(c);
}
{
Constraint c;
c.setName("smallgaps2_" + to_string(l));
c.addVariable(to_string(l), 1.0);
Line ol;
if (b.getVariant() == T5) {
ol = Line(l.st + direction[l.dir]*(-5), l.dir); if (b.validLine(ol)) { c.addVariable(to_string(ol), 1.0); }
} else {
ol = Line(l.st + direction[l.dir]*(-6), l.dir); if (b.validLine(ol)) { c.addVariable(to_string(ol), 1.0); }
}
c.setType(Constraint::LT);
c.setBound(1.0);
addConstraint(c);
}
}
}
return this;
}
LPP* MorpionLPP::getLPP()
{
setComment(gameId());
// each possible move is a structural variable
// our goal is to maximize sum over all variables
for (const Move& m: b.getMoveList()) {
std::string v_name = to_string(m);
setVariableBounds(v_name, 0.0, 1.0);
getObjective().push_back(std::pair<std::string, double>(v_name, 1.0));
// Constraint for exact problems.
//
// mv_ variables are either 0 or 1 (i.e. the move is either played or not)
if (getFlag("exact") || getFlag("binary_moves")) {
setVariableBoolean(v_name, true);
}
}
// each segment gives us constraints:
// (1) if the segment is placed in the starting position
// (a) sum of weights of moves that place this segment <= 0
// (b) 1 - sum of weights of moves that remove this segment >= 0
// i.e. sum of weights of moves that remove this segment <= 1
// (2) if the segment is not placed in the starting position
// (a) sum of weights of moves that place this segment <= 1
// (b) sum of weights of moves that place this segment
// - sum of weights of moves that remove this segment >= 0
for (const Segment& s: b.getSegmentList()) {
int x = s.first.x;
int y = s.first.y;
int d = s.second;
std::string constr_name = "segment_" + to_string(x) + "_" + to_string(y) + "_" + to_string(d);
if (b.hasDot(Dot(x,y))) {
// (1a)
{
Constraint constr;
for (Move& pl: b.getMovesPlacingSegment(s)) {
constr.addVariable(to_string(pl), 1.0);
}
constr.setName("r1a_" + constr_name);
constr.setType(Constraint::LT);
constr.setBound(0.0);
addConstraint(constr);
}
// (1b)
{
Constraint constr;
for (Move& rm: b.getMovesRemovingSegment(s)) {
constr.addVariable(to_string(rm), 1.0);
}
constr.setName("r1b_" + constr_name);
constr.setType(Constraint::LT);
constr.setBound(1.0);
addConstraint(constr);
}
} else {
// (2a)
{
Constraint constr;
for (Move& pl: b.getMovesPlacingSegment(s)) {
constr.addVariable(to_string(pl), 1.0);
}
constr.setName("r2a_" + constr_name);
constr.setType(Constraint::LT);
constr.setBound(1.0);
addConstraint(constr);
}
// (2b)
{
Constraint constr;
for (Move& pl: b.getMovesPlacingSegment(s)) {
constr.addVariable(to_string(pl), 1.0);
}
for (Move& rm: b.getMovesRemovingSegment(s)) {
constr.addVariable(to_string(rm), -1.0);
}
constr.setName("r2b_" + constr_name);
constr.setType(Constraint::GT);
constr.setBound(0.0);
addConstraint(constr);
}
}
}
// EXTRA CONSTRAINTS:
//
// for each move m:
// for each dot d required by m:
// for each move n placing d that is consistent with m:
// weight_m <= sum of weights of n's
if (getFlag("extra")) {
for (const Move& m: b.getMoveList()) {
std::string constr_name = "_" + to_string(m);
for (const Dot& d: m.requiredDots(b.getVariant())) {
if (b.hasDot(d)) continue;
Constraint constr;
for (const Move& n: b.getMovesPlacingSegment(Segment(d,0))) {
if (m.consistentWith(n,b.getVariant())) {
constr.addVariable(to_string(n), -1.0);
}
}
constr.addVariable(to_string(m), 1.0);
constr.setName("extra_" + to_string(d) + constr_name);
constr.setType(Constraint::LT);
constr.setBound(0.0);
addConstraint(constr);
}
}
}
// Disallow cycles of length 3 from the solution.
// Improves fuzzy solutions
if (getFlag("short-cycles")) {
for (const Segment& s: b.getSegmentList()) {
int d = s.second;
if (d % 2 == 1) continue;
addConstraints(createCycleConstraints(s, d + 2, d + 5));
addConstraints(createCycleConstraints(s, d + 6, d + 1));
}
}
// Constraints for acyclic problems (explanation makes sense for exact problems):
//
// OBSOLETE
//
// 1. Each move mv_* has accompanying order variable order_*
// 2. Move that is not picked has always order 0,
// move that is picked has order between 1 and 675
//
// It is accomplished with the condition:
// mv_ <= order_ <= 675 * mv_
//
// 3. Assume that mv_1 removes segment s and mv_2 places segment s (mv_1 != mv_2).
// Then
// order_1 + (1 - mv_1) * 1000 >= order_2 + 1
//
// The (1-mv_1)*1000 term assures that the condition is not enforced
// for moves that are not picked (i.e. have mv_1 = 0)
if (getFlag("acyclic")) {
throw std::string("not implemented");
}
// Constraints for symmetric problems.
//
// Moves that are symmetric by central symmetry
// with center at ref + (1.5,1.5) have to have equal weights
if (getFlag("symmetric")) {
for (const Move&m: b.getMoveList()) {
Move sm = b.centerSymmetry(m);
Constraint c;
c.addVariable(to_string(m), 1.0);
c.addVariable(to_string(sm), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("sym_" + to_string(m));
addConstraint(c);
}
}
// dot-acyclic - better implementation of acyclic problems
// dots that are not placed have dot_ variable equal to 0
// this is important for --hull option
// use this not only for dot-acyclic problems
for (const Dot& d: b.getDotList())
{
if (b.hasDot(d)) continue;
Constraint c;
c.setName("dotmove_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0);
for (const Move& m: b.getMovesPlacingDot(d)) {
c.addVariable(to_string(m), -b.bound());
}
c.setType(Constraint::LT);
c.setBound(0.0);
addConstraint(c);
}
if (getFlag("dot-acyclic")) {
for (int x = 0; x < b.getWidth(); x++) {
for (int y= 0; y < b.getHeight(); y++) {
if (b.infeasibleDot(Dot(x,y)) || b.hasDot(Dot(x,y))) continue;
setVariableBounds("dot_" + to_string(Dot(x,y)), 0, b.bound());
if (getFlag("symmetric")) {
Constraint c;
if (b.infeasibleDot(b.centerSymmetry(Dot(x,y)))) continue;
c.setName("dotsym_");
c.addVariable("dot_" + to_string(Dot(x,y)), 1.0);
c.addVariable("dot_" + to_string(b.centerSymmetry(Dot(x,y))), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
addConstraint(c);
}
}
}
for (const Move& m: b.getMoveList()) {
for (const Dot& rq: m.requiredDots(b.getVariant())) {
if (b.hasDot(rq)) continue;
Constraint c;
// dot_placed >= dot_required + 1 - (1 - m) * bound
// i.e. dot_placed - dot_required - bound * m >= 1 - bound
c.setName("dot_");
c.addVariable("dot_" + to_string(m.placedDot()), 1.0);
c.addVariable("dot_" + to_string(rq), -1.0);
c.addVariable(to_string(m), -b.bound());
c.setBound(1 - b.bound());
c.setType(Constraint::GT);
addConstraint(c);
}
}
}
// Constraints that enforce that the board (if it is rectangle) is
// the convex hull of the solution
if (getFlag("rhull")) {
// right side
addConstraint(getSideConstraint(1,0,true));
// left side
addConstraint(getSideConstraint(1,0,false));
// top side
addConstraint(getSideConstraint(0,1,true));
// bottom side
addConstraint(getSideConstraint(0,1,false));
}
// Constraints that enforce that the board (if it is octagon) is
// the convex hull of the solution
if (getFlag("hull")) {
// right side
addConstraint(getSideConstraint(1,0,true));
// left side
addConstraint(getSideConstraint(1,0,false));
// lower right side
addConstraint(getSideConstraint(1,-1,false));
// upper left side
addConstraint(getSideConstraint(1,-1,true));
// top side
addConstraint(getSideConstraint(0,1,true));
// bottom side
addConstraint(getSideConstraint(0,1,false));
// lower left side
addConstraint(getSideConstraint(1,1,false));
// upper right side
addConstraint(getSideConstraint(1,1,true));
}
return this;
}
LPP* PotentialLPP::getLPP()
{
setComment("PotentialLPP " + gameId());
// each move is a structural variable
for (const Move& l: b.getMoveList()) {
std::string v_name = to_string(l);
setVariableBounds(v_name, 0.0, 1.0);
if (getFlag("exact") && getFlag("dot-acyclic")) {
setVariableBoolean(v_name, true);
setVariableOrd(v_name, 0);
}
}
// each dot is a structural variable
for (Dot d: b.getDotList()) {
std::string v_name = "dot_" + to_string(d);
if (!b.hasDot(d)) {
getObjective().push_back(std::pair<std::string, double>(v_name, 1.0));
}
// dots are the only boolean variables
if (getFlag("exact")) {
setVariableBoolean(v_name, true);
if (b.infeasibleDot(d + Dot(1,0)) ||
b.infeasibleDot(d + Dot(1,1)) ||
b.infeasibleDot(d + Dot(0,1)) ||
b.infeasibleDot(d + Dot(1,-1)) ||
b.infeasibleDot(d + Dot(0,-1)) ||
b.infeasibleDot(d + Dot(-1,-1)) ||
b.infeasibleDot(d + Dot(-1,0)) ||
b.infeasibleDot(d + Dot(-1,1)))
{
Dot n = d - b.getCRef();
setVariableOrd(v_name, 1 + abs(n.x) + abs(n.y));
} else {
setVariableOrd(v_name, -1);
}
}
// dots that are placed on board have dot variable equal to 1
if (b.hasDot(d)) {
setVariableBounds(v_name, 1.0, 1.0);
} else {
setVariableBounds(v_name, 0.0, 1.0);
}
}
// constraints:
//
// (1) dot at beginning of segment - moves removing segment starting from dot >= 0
//
// (2) dot == sum of weights of moves that place dot
//
// (3) sum of weights of dots - sum of weights of moves <= 36
// (1)
// L4
for (const Segment& s: b.getSegmentList()) {
Constraint c;
c.setName("sgm_" + to_string(s));
c.addVariable("dot_" + to_string(s.first), 1.0);
for (const Move& m: b.getMovesRemovingSegment(s)) {
c.addVariable(to_string(m), -1.0);
}
c.setType(Constraint::GT);
c.setBound(0.0);
addConstraint(c);
}
// L3
for (const Dot& d: b.getDotList()) {
if (b.hasDot(d)) continue;
Constraint c;
c.setName("L3_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0f);
for (const Move& m: b.getMovesPlacingDot(d)) {
c.addVariable(to_string(m), -1.0f);
}
c.setBound(0.0f);
c.setType(Constraint::EQ);
addConstraint(c);
}
/*
// (2)
for (const Dot &d: b.getDotList()) {
if (b.hasDot(d)) continue;
Constraint c;
c.setName("dotmv_" + to_string(d));
for (const Move &m: b.getMovesPlacingDot(d)) {
c.addVariable(to_string(m), -1.0);
}
c.addVariable("dot_" + to_string(d), 1.0);
c.setBound(0.0);
c.setType(Constraint::EQ);
addConstraint(c);
}
*/
/*
// (3)
{
Constraint c;
c.setName("dots_moves");
for (const Dot &d: b.getDotList()) {
c.addVariable("dot_"+to_string(d), 1.0);
}
for (const Move &m: b.getMoveList()) {
c.addVariable(to_string(m), -1.0);
}
c.setBound(36.0);
c.setType(Constraint::LT);
addConstraint(c);
}
*/
// dots that are not placed have dot_ variable equal to 0
// this is important for --hull option
// use this not only for dot-acyclic problems
/*
for (const Dot& d: b.getDotList())
{
if (b.hasDot(d)) continue;
Constraint c;
c.setName("dotmove_" + to_string(d));
c.addVariable("dot_" + to_string(d), 1.0);
for (const Move& m: b.getMovesPlacingDot(d)) {
c.addVariable(to_string(m), -b.bound());
}
c.setType(Constraint::LT);
c.setBound(0.0);
addConstraint(c);
}
*/
// Constraints that enforce that the board (if it is an octagon) is
// the convex hull of the solution
if (getFlag("hull")) {
// right side
addConstraint(getSideConstraint(1,0,true));
// left side
addConstraint(getSideConstraint(1,0,false));
// lower right side
addConstraint(getSideConstraint(1,-1,false));
// upper left side
addConstraint(getSideConstraint(1,-1,true));
// top side
addConstraint(getSideConstraint(0,1,true));
// bottom side
addConstraint(getSideConstraint(0,1,false));
// lower left side
addConstraint(getSideConstraint(1,1,false));
// upper right side
addConstraint(getSideConstraint(1,1,true));
}
if (getFlag("rhull")) {
// right side
addConstraint(getSideConstraint(1,0,true));
// left side
addConstraint(getSideConstraint(1,0,false));
// top side
addConstraint(getSideConstraint(0,1,true));
// bottom side
addConstraint(getSideConstraint(0,1,false));
}
if (getFlag("rside")) {
// right side
addConstraint(getSideConstraint(1,0,true));
}
if (getFlag("symmetric")) {
for (const Move&m: b.getMoveList()) {
Move sm = b.centerSymmetry(m);
Constraint c;
c.addVariable(to_string(m), 1.0);
c.addVariable(to_string(sm), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("sym_" + to_string(m));
addConstraint(c);
}
for (const Dot& d: b.getDotList()) {
std::string v_name = "symdot_" + to_string(d);
Dot sd = b.centerSymmetry(d);
if (b.hasDot(d) || b.hasDot(sd)) {
continue;
}
Constraint c;
c.addVariable("dot_" + to_string(d), 1.0);
c.addVariable("dot_" + to_string(sd), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
c.setName("symdot_" + to_string(d));
addConstraint(c);
}
}
// create only acyclic solutions
if (getFlag("dot-acyclic")) {
for (int x = 0; x < b.getWidth(); x++) {
for (int y= 0; y < b.getHeight(); y++) {
if (b.infeasibleDot(Dot(x,y)) || b.hasDot(Dot(x,y))) continue;
setVariableBounds("ord_" + to_string(Dot(x,y)), 0, b.bound());
if (getFlag("symmetric")) {
Constraint c;
if (b.infeasibleDot(b.centerSymmetry(Dot(x,y)))) continue;
c.setName("ordsym_"+to_string(Dot(x,y)));
c.addVariable("ord_" + to_string(Dot(x,y)), 1.0);
c.addVariable("ord_" + to_string(b.centerSymmetry(Dot(x,y))), -1.0);
c.setType(Constraint::EQ);
c.setBound(0.0);
addConstraint(c);
}
}
}
for (const Move& m: b.getMoveList()) {
for (const Dot& rq: m.requiredDots(b.getVariant())) {
if (b.hasDot(rq)) continue;
Constraint c;
// dot_placed >= dot_required + 1 - (1 - m) * bound
// i.e. dot_placed - dot_required - bound * m >= 1 - bound
c.setName("ord_" + to_string(m) + "_" + to_string(rq));
c.addVariable("ord_" + to_string(m.placedDot()), 1.0);
c.addVariable("ord_" + to_string(rq), -1.0);
c.addVariable(to_string(m), -b.bound());
c.setBound(1 - b.bound());
c.setType(Constraint::GT);
addConstraint(c);
}
}
}
/*
enum { R = 0, D = 2, L = 4, U = 6 };
std::vector<int> inside_path = { R, U, U, R, D, D, D, R, R, R, D, L, L, L,
D, D, D, L, U, U, U, L, L, L, U, R, R, R };
Dot r = b.getReference();
for (auto & d: inside_path) {
r = r + direction[d];
Constraint c;
c.setName("inside_" + to_string(r));
c.addVariable("dot_" + to_string(r), 1.0f);
c.setBound(1.0f);
c.setType(Constraint::EQ);
addConstraint(c);
}
*/
return this;
}