/// Print solution
virtual void
print(std::ostream& os) const {
bool assigned = true;
for (int i=0; i<succ.size(); i++) {
if (!succ[i].assigned()) {
assigned = false;
break;
}
}
if (assigned) {
os << "\tTour: ";
int i=0;
do {
os << i << " -> ";
i=succ[i].val();
} while (i != 0);
os << 0 << std::endl;
os << "\tCost: " << total << std::endl;
} else {
os << "\tTour: " << std::endl;
for (int i=0; i<succ.size(); i++) {
os << "\t" << i << " -> " << succ[i] << std::endl;
}
os << "\tCost: " << total << std::endl;
}
}
virtual void print(std::ostream& os) const {
os << "queens\t";
for (int i = 0; i < q.size(); i++) {
os << q[i];
if ((i+1) % (int)sqrt(q.size()) == 0) {
os << std::endl << "\t";
}
}
os << std::endl;
}
/// Actual model
GolombRuler(const SizeOptions& opt)
: IntMinimizeScript(opt),
m(*this,opt.size(),0,
(opt.size() < 31) ? (1 << (opt.size()-1))-1 : Int::Limits::max) {
// Assume first mark to be zero
rel(*this, m[0], IRT_EQ, 0);
// Order marks
rel(*this, m, IRT_LE);
// Number of marks and differences
const int n = m.size();
const int n_d = (n*n-n)/2;
// Array of differences
IntVarArgs d(n_d);
// Setup difference constraints
for (int k=0, i=0; i<n-1; i++)
for (int j=i+1; j<n; j++, k++)
// d[k] is m[j]-m[i] and must be at least sum of first j-i integers
rel(*this, d[k] = expr(*this, m[j]-m[i]),
IRT_GQ, (j-i)*(j-i+1)/2);
distinct(*this, d, opt.icl());
// Symmetry breaking
if (n > 2)
rel(*this, d[0], IRT_LE, d[n_d-1]);
branch(*this, m, INT_VAR_NONE(), INT_VAL_MIN());
}
/// Print solution
virtual void
print(std::ostream& os) const {
os << "\t";
for (int i=0; i<x.size(); i++)
os << "(" << x[i] << "," << y[i] << ") ";
os << std::endl;
}
/// Print solution
virtual void
print(std::ostream& os) const {
const int n = x.size();
os << "\tx[" << n << "] = {";
for (int i = 0; i < n-1; i++)
os << x[i] << "(" << d[i] << "),";
os << x[n-1] << "}" << std::endl;
}
void among(Space& space, IntVarArray x, SetVar ss, IntVar a) {
int n = x.size();
BoolVarArgs b(space, n, 0, 1);
for(int i = 0; i < n; i++) {
rel(space, ss, SRT_SUP, x[i], b[i]);
}
rel(space, sum(b) == a);
}
/// Print solution
virtual void
print(std::ostream& os) const {
os << "queens\t";
for (int i = 0; i < q.size(); i++) {
os << q[i] << ", ";
if ((i+1) % 10 == 0)
os << std::endl << "\t";
}
os << std::endl;
}
/// Print solution
virtual void
print(std::ostream& os) const {
os << "\t";
int a, b;
a = b = 0;
for (int i = 0; i < x.size(); i++) {
a += x[i].val();
b += x[i].val()*x[i].val();
os << x[i] << ", ";
}
os << " = " << a << ", " << b << std::endl << "\t";
a = b = 0;
for (int i = 0; i < y.size(); i++) {
a += y[i].val();
b += y[i].val()*y[i].val();
os << y[i] << ", ";
}
os << " = " << a << ", " << b << std::endl;
}
/// Print the solution
virtual void
print(std::ostream& os) const {
os << "\tm = " << m << std::endl
<< "\tv[] = {";
for (int i = 0; i < v.size(); i++) {
os << v[i] << ", ";
if ((i+1) % 15 == 0)
os << std::endl << "\t ";
}
os << "};" << std::endl;
}
/// Actual model
Alpha(const Options& opt)
: Script(opt), le(*this,n,1,n) {
IntVar
a(le[ 0]), b(le[ 1]), c(le[ 2]), e(le[ 4]), f(le[ 5]),
g(le[ 6]), h(le[ 7]), i(le[ 8]), j(le[ 9]), k(le[10]),
l(le[11]), m(le[12]), n(le[13]), o(le[14]), p(le[15]),
q(le[16]), r(le[17]), s(le[18]), t(le[19]), u(le[20]),
v(le[21]), w(le[22]), x(le[23]), y(le[24]), z(le[25]);
rel(*this, b+a+l+l+e+t == 45, opt.icl());
rel(*this, c+e+l+l+o == 43, opt.icl());
rel(*this, c+o+n+c+e+r+t == 74, opt.icl());
rel(*this, f+l+u+t+e == 30, opt.icl());
rel(*this, f+u+g+u+e == 50, opt.icl());
rel(*this, g+l+e+e == 66, opt.icl());
rel(*this, j+a+z+z == 58, opt.icl());
rel(*this, l+y+r+e == 47, opt.icl());
rel(*this, o+b+o+e == 53, opt.icl());
rel(*this, o+p+e+r+a == 65, opt.icl());
rel(*this, p+o+l+k+a == 59, opt.icl());
rel(*this, q+u+a+r+t+e+t == 50, opt.icl());
rel(*this, s+a+x+o+p+h+o+n+e == 134, opt.icl());
rel(*this, s+c+a+l+e == 51, opt.icl());
rel(*this, s+o+l+o == 37, opt.icl());
rel(*this, s+o+n+g == 61, opt.icl());
rel(*this, s+o+p+r+a+n+o == 82, opt.icl());
rel(*this, t+h+e+m+e == 72, opt.icl());
rel(*this, v+i+o+l+i+n == 100, opt.icl());
rel(*this, w+a+l+t+z == 34, opt.icl());
distinct(*this, le, opt.icl());
switch (opt.branching()) {
case BRANCH_NONE:
branch(*this, le, INT_VAR_NONE(), INT_VAL_MIN());
break;
case BRANCH_INVERSE:
branch(*this, le.slice(le.size()-1,-1), INT_VAR_NONE(), INT_VAL_MIN());
break;
case BRANCH_SIZE:
branch(*this, le, INT_VAR_SIZE_MIN(), INT_VAL_MIN());
break;
}
}
/// Actual model
AllInterval(const SizeOptions& opt) :
x(*this, opt.size(), 0, opt.size()-1),
d(*this, opt.size()-1, 1, opt.size()-1) {
const int n = x.size();
// Set up variables for distance
for (int i=0; i<n-1; i++)
rel(*this, d[i] == abs(x[i+1]-x[i]), opt.icl());
distinct(*this, x, opt.icl());
distinct(*this, d, opt.icl());
// Break mirror symmetry
rel(*this, x[0], IRT_LE, x[1]);
// Break symmetry of dual solution
rel(*this, d[0], IRT_GR, d[n-2]);
branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
}
/// Print solution
virtual void
print(std::ostream& os) const {
#if 0
std::ostringstream outputstring1;
#endif
const int n = x.size();
os << "\tx[" << n << "] = {";
outputstring << "(";
for (int i = 0; i < n-1; i++)
{
os << x[i] << "(" << abs(x[i+1].val()-x[i].val()) << "),";
outputstring << x[i] << " ";
// outputstring << x[i] ;
}
outputstring << x[n-1] << ")";
os << x[n-1] << "}" << std::endl;
// strcpy(result,outputstring.str().c_str());
}
/// The actual problem
Queens(const SizeOptions& opt)
: q(*this,opt.size(),0,opt.size()-1) {
const int n = q.size();
switch (opt.propagation()) {
case PROP_BINARY:
for (int i = 0; i<n; i++)
for (int j = i+1; j<n; j++) {
rel(*this, q[i] != q[j]);
rel(*this, q[i]+i != q[j]+j);
rel(*this, q[i]-i != q[j]-j);
}
break;
case PROP_MIXED:
for (int i = 0; i<n; i++)
for (int j = i+1; j<n; j++) {
rel(*this, q[i]+i != q[j]+j);
rel(*this, q[i]-i != q[j]-j);
}
distinct(*this, q, opt.icl());
break;
case PROP_DISTINCT:
distinct(*this, IntArgs::create(n,0,1), q, opt.icl());
distinct(*this, IntArgs::create(n,0,-1), q, opt.icl());
distinct(*this, q, opt.icl());
break;
}
switch(opt.branching()) {
case BRANCH_MIN:
branch(*this, q, INT_VAR_SIZE_MIN(), INT_VAL_MIN());
break;
case BRANCH_MID:
branch(*this, q, INT_VAR_SIZE_MIN(), INT_VAL_MIN());
break;
case BRANCH_MAX_MAX:
branch(*this, q, INT_VAR_SIZE_MAX(), INT_VAL_MIN());
break;
case BRANCH_KNIGHT_MOVE:
branch(*this, q, INT_VAR_MIN_MIN(), INT_VAL_MED());
break;
}
}
/// Actual model
AllInterval(const SizeOptions& opt) :
x(*this, opt.size(), 0, opt.size() - 1) {
const int n = x.size();
IntVarArgs d(n-1);
// Set up variables for distance
for (int i=0; i<n-1; i++)
d[i] = expr(*this, abs(x[i+1]-x[i]), opt.icl());
// Constrain them to be between 1 and n-1
dom(*this, d, 1, n-1);
distinct(*this, x, opt.icl());
distinct(*this, d, opt.icl());
// Break mirror symmetry
rel(*this, x[0], IRT_LE, x[1]);
// Break symmetry of dual solution
rel(*this, d[0], IRT_GR, d[n-2]);
branch(*this, x, INT_VAR_SIZE_MIN, INT_VAL_SPLIT_MIN);
}
/// Construction of the model.
Pentominoes(const SizeOptions& opt)
: spec(examples[opt.size()]),
width(spec[0].width+1), // Add one for extra row at end.
height(spec[0].height),
filled(spec[0].amount),
nspecs(examples_size[opt.size()]-1),
ntiles(compute_number_of_tiles(spec+1, nspecs)),
board(*this, width*height, filled,ntiles+1) {
spec += 1; // No need for the specification-part any longer
// Set end-of-line markers
for (int h = 0; h < height; ++h) {
for (int w = 0; w < width-1; ++w)
rel(*this, board[h*width + w], IRT_NQ, ntiles+1);
rel(*this, board[h*width + width - 1], IRT_EQ, ntiles+1);
}
// Post constraints
if (opt.propagation() == PROPAGATION_INT) {
int tile = 0;
for (int i = 0; i < nspecs; ++i) {
for (int j = 0; j < spec[i].amount; ++j) {
// Color
int col = tile+1;
// Expression for color col
REG mark(col);
// Build expression for complement to color col
REG other;
bool first = true;
for (int j = filled; j <= ntiles; ++j) {
if (j == col) continue;
if (first) {
other = REG(j);
first = false;
} else {
other |= REG(j);
}
}
// End of line marker
REG eol(ntiles+1);
extensional(*this, board, get_constraint(i, mark, other, eol));
++tile;
}
}
} else { // opt.propagation() == PROPAGATION_BOOLEAN
int ncolors = ntiles + 2;
// Boolean variables for channeling
BoolVarArgs p(*this,ncolors * board.size(),0,1);
// Post channel constraints
for (int i=board.size(); i--; ) {
BoolVarArgs c(ncolors);
for (int j=ncolors; j--; )
c[j]=p[i*ncolors+j];
channel(*this, c, board[i]);
}
// For placing tile i, we construct the expression over
// 0/1-variables and apply it to the projection of
// the board on the color for the tile.
REG other(0), mark(1);
int tile = 0;
for (int i = 0; i < nspecs; ++i) {
for (int j = 0; j < spec[i].amount; ++j) {
int col = tile+1;
// Projection for color col
BoolVarArgs c(board.size());
for (int k = board.size(); k--; ) {
c[k] = p[k*ncolors+col];
}
extensional(*this, c, get_constraint(i, mark, other, other));
++tile;
}
}
}
if (opt.symmetry() == SYMMETRY_FULL) {
// Remove symmetrical boards
IntVarArgs orig(board.size()-height), symm(board.size()-height);
int pos = 0;
for (int i = 0; i < board.size(); ++i) {
if ((i+1)%width==0) continue;
orig[pos++] = board[i];
}
int w2, h2;
bsymmfunc syms[] = {flipx, flipy, flipd1, flipd2, rot90, rot180, rot270};
int symscnt = sizeof(syms)/sizeof(bsymmfunc);
for (int i = 0; i < symscnt; ++i) {
syms[i](orig, width-1, height, symm, w2, h2);
if (width-1 == w2 && height == h2)
rel(*this, orig, IRT_LQ, symm);
}
}
// Install branching
branch(*this, board, INT_VAR_NONE, INT_VAL_MIN);
}
/// Actual model
AllInterval(const SizeOptions& opt) :
Script(opt),
x(*this, opt.size(), 0, 66) { // 66 or opt.size() - 1
const int n = x.size();
IntVarArgs d(n-1);
IntVarArgs dd(66);
IntVarArgs xx_(n); // pitch class for AllInterval Chords
IntVar douze;
Rnd r(1U);
if ((opt.model() == MODEL_SET) || (opt.model() == MODEL_SET_CHORD) || (opt.model() == MODEL_SSET_CHORD) ||(opt.model() == MODEL_SYMMETRIC_SET)) // Modele original : serie
{
// Set up variables for distance
for (int i=0; i<n-1; i++)
d[i] = expr(*this, abs(x[i+1]-x[i]), opt.ipl());
// Constrain them to be between 1 and n-1
dom(*this, d, 1, n-1);
dom(*this, x, 0, n-1);
if((opt.model() == MODEL_SET_CHORD) || (opt.model() == MODEL_SSET_CHORD))
{
/*expr(*this,dd[0]==0);
// Set up variables for distance
for (int i=0; i<n-1; i++)
{
expr(*this, dd[i+1] == (dd[i]+d[i])%12, opt.icl());
}
// Constrain them to be between 1 and n-1
dom(*this, dd,0, n-1);
distinct(*this, dd, opt.icl());
*/
rel(*this, abs(x[0]-x[n-1]) == 6, opt.ipl());
}
if(opt.symmetry())
{
// Break mirror symmetry (renversement)
rel(*this, x[0], IRT_LE, x[1]);
// Break symmetry of dual solution (retrograde de la serie) -> 1928 solutions pour accords de 12 sons
rel(*this, d[0], IRT_GR, d[n-2]);
}
//series symetriques
if ((opt.model() == MODEL_SYMMETRIC_SET)|| (opt.model() == MODEL_SSET_CHORD))
{
rel (*this, d[n/2 - 1] == 6); // pivot = triton
for (int i=0; i<(n/2)-2; i++)
rel(*this,d[i]+d[n-i-2]==12);
}
}
else
{
for (int j=0; j<n; j++)
xx_[j] = expr(*this, x[j] % 12);
dom(*this, xx_, 0, 11);
distinct(*this, xx_, opt.ipl());
//intervalles
for (int i=0; i<n-1; i++)
d[i] = expr(*this,x[i+1] - x[i],opt.ipl());
dom(*this, d, 1, n-1);
dom(*this, x, 0, n * (n - 1) / 2.);
//d'autres choses dont on est certain (contraintes redondantes) :
rel(*this, x[0] == 0);
rel(*this, x[n-1] == n * (n - 1) / 2.);
// break symmetry of dual solution (renversement de l'accord)
if(opt.symmetry())
rel(*this, d[0], IRT_GR, d[n-2]);
//accords symetriques
if (opt.model() == MODEL_SYMMETRIC_CHORD)
{
rel (*this, d[n/2 - 1] == 6); // pivot = triton
for (int i=0; i<(n/2)-2; i++)
rel(*this,d[i]+d[n-i-2]==12);
}
if (opt.model() == MODEL_PARALLEL_CHORD)
{
rel (*this, d[n/2 - 1] == 6); // pivot = triton
for (int i=0; i<(n/2)-2; i++)
rel(*this,d[i]+d[n/2 + i]==12);
}
}
distinct(*this, x, opt.ipl());
distinct(*this, d, opt.ipl());
#if 0
//TEST
IntVarArray counter(*this,12,0,250);
IntVar testcounter(*this,0,250);
for (int i=1; i<11; i++) {
count(*this, d, i,IRT_EQ,testcounter,opt.icl()); // OK
}
count(*this, d, counter,opt.icl()); // OK
#endif
//END TEST
if(opt.branching() == 0)
branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
else
branch(*this, x, INT_VAR_RND(r), INT_VAL_RND(r));
}
void print(std::ostream& os) const {
for (int index = 0; index < q.size(); ++index) {
os << q[index] << " ";
}
os << endl << endl;
}
/// Print solution
virtual void
print(std::ostream& os) const {
os << "\tm[" << m.size() << "] = " << m << std::endl;
}
/// Return cost
virtual IntVar cost(void) const {
return m[m.size()-1];
}
/// The model of the problem
CrowdedChess(const SizeOptions& opt)
: n(opt.size()),
s(*this, n*n, 0, PMAX-1),
queens(*this, n, 0, n-1),
rooks(*this, n, 0, n-1),
knights(*this, n*n, 0, 1) {
const int nkval = sizeof(kval)/sizeof(int);
const int nn = n*n, q = n, r = n, b = (2*n)-2,
k = n <= nkval ? kval[n-1] : kval[nkval-1];
const int e = nn - (q + r + b + k);
assert(nn == (e + q + r + b + k));
Matrix<IntVarArray> m(s, n);
// ***********************
// Basic model
// ***********************
count(*this, s, E, IRT_EQ, e, opt.icl());
count(*this, s, Q, IRT_EQ, q, opt.icl());
count(*this, s, R, IRT_EQ, r, opt.icl());
count(*this, s, B, IRT_EQ, b, opt.icl());
count(*this, s, K, IRT_EQ, k, opt.icl());
// Collect rows and columns for handling rooks and queens
for (int i = 0; i < n; ++i) {
IntVarArgs aa = m.row(i), bb = m.col(i);
count(*this, aa, Q, IRT_EQ, 1, opt.icl());
count(*this, bb, Q, IRT_EQ, 1, opt.icl());
count(*this, aa, R, IRT_EQ, 1, opt.icl());
count(*this, bb, R, IRT_EQ, 1, opt.icl());
// Connect (queens|rooks)[i] to the row it is in
element(*this, aa, queens[i], Q, ICL_DOM);
element(*this, aa, rooks[i], R, ICL_DOM);
}
// N-queens constraints
distinct(*this, queens, ICL_DOM);
distinct(*this, IntArgs::create(n,0,1), queens, ICL_DOM);
distinct(*this, IntArgs::create(n,0,-1), queens, ICL_DOM);
// N-rooks constraints
distinct(*this, rooks, ICL_DOM);
// Collect diagonals for handling queens and bishops
for (int l = n; l--; ) {
const int il = (n-1) - l;
IntVarArgs d1(l+1), d2(l+1), d3(l+1), d4(l+1);
for (int i = 0; i <= l; ++i) {
d1[i] = m(i+il, i);
d2[i] = m(i, i+il);
d3[i] = m((n-1)-i-il, i);
d4[i] = m((n-1)-i, i+il);
}
count(*this, d1, Q, IRT_LQ, 1, opt.icl());
count(*this, d2, Q, IRT_LQ, 1, opt.icl());
count(*this, d3, Q, IRT_LQ, 1, opt.icl());
count(*this, d4, Q, IRT_LQ, 1, opt.icl());
if (opt.propagation() == PROP_DECOMPOSE) {
count(*this, d1, B, IRT_LQ, 1, opt.icl());
count(*this, d2, B, IRT_LQ, 1, opt.icl());
count(*this, d3, B, IRT_LQ, 1, opt.icl());
count(*this, d4, B, IRT_LQ, 1, opt.icl());
}
}
if (opt.propagation() == PROP_TUPLE_SET) {
IntVarArgs b(s.size());
for (int i = s.size(); i--; )
b[i] = channel(*this, expr(*this, (s[i] == B)));
extensional(*this, b, bishops, EPK_DEF, opt.icl());
}
// Handle knigths
// Connect knigths to board
for(int i = n*n; i--; )
knights[i] = expr(*this, (s[i] == K));
knight_constraints();
// ***********************
// Redundant constraints
// ***********************
// Queens and rooks not in the same place
// Faster than going through the channelled board-connection
for (int i = n; i--; )
rel(*this, queens[i], IRT_NQ, rooks[i]);
// Place bishops in two corners (from Schimpf and Hansens solution)
// Avoids some symmetries of the problem
rel(*this, m(n-1, 0), IRT_EQ, B);
rel(*this, m(n-1, n-1), IRT_EQ, B);
// ***********************
// Branching
// ***********************
// Place each piece in turn
branch(*this, s, INT_VAR_MIN_MIN(), INT_VAL_MIN());
}