965dadaa
 Salvador Abreu
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/* knapsack2(X, Y, Z) == min(Z) <= sum(X . Y) <= max(Z) */
// XXX: assumes all values are non-negative
static int fd_knapsack2_filter(fd_constraint this)
{
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965dadaa
Salvador Abreu
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int ub, lb;
int min, max;
int terms = (this->nvariables - 1) / 2;
int *mins, *maxs; // XXX: trouble possible if a variable appears repeated
int i;
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eef94371
 Vasco Pedro
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#ifdef CONSTRAINT_TEMPS
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965dadaa
Salvador Abreu
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int *base;
assert(!fd__constraint_data_valid(this));
if (!constraint_memory[this->index])
constraint_memory[this->index] = malloc((2 * 2 * terms + 4) * sizeof(int));
base = constraint_memory[this->index];
mins = base + 4;
maxs = mins + 2 * terms;
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eef94371
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#else
mins = alloca(2 * terms * sizeof(*mins));
maxs = alloca(2 * terms * sizeof(*maxs));
#endif
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965dadaa
Salvador Abreu
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lb = _fd_var_min(VAR(this, this->nvariables - 1)); // lower bound
ub = _fd_var_max(VAR(this, this->nvariables - 1)); // upper bound
// sum the minima of the terms
min = 0;
for (i = 0; i < terms; ++i)
{
mins[i] = _fd_var_min(VAR(this, i));
mins[terms + i] = _fd_var_min(VAR(this, terms + i));
min += mins[i] * mins[terms + i];
if (min > ub)
return FD_NOSOLUTION;
}
// sum the maxima of the terms
max = 0;
for (i = 0; i < terms; ++i)
{
maxs[i] = _fd_var_max(VAR(this, i));
maxs[terms + i] = _fd_var_max(VAR(this, terms + i));
max += maxs[i] * maxs[terms + i];
}
if (max < lb)
return FD_NOSOLUTION;
// XXX: poor man's propagation
if (min == ub)
for (i = 0; i < terms; ++i)
{
int min_x = mins[i];
int min_y = mins[terms + i];
if (min_x != 0 || min_y != 0)
{
if (min_y != 0 && _fd_var_del_gt(min_x, VAR(this, i)))
_fd_revise_connected(this, VAR(this, i));
if (min_x != 0 && _fd_var_del_gt(min_y, VAR(this, terms + i)))
_fd_revise_connected(this, VAR(this, terms + i));
}
}
else if (max == lb)
for (i = 0; i < terms; ++i)
{
int max_x = maxs[i];
int max_y = maxs[terms + i];
if (max_x != 0 && max_y != 0)
{
if (_fd_var_del_lt(max_x, VAR(this, i)))
_fd_revise_connected(this, VAR(this, i));
if (_fd_var_del_lt(max_y, VAR(this, terms + i)))
_fd_revise_connected(this, VAR(this, terms + i));
}
}
else if (max > ub)
for (i = 0; i < terms; ++i)
{
int min_x = mins[i];
int max_x = maxs[i];
int min_y = mins[terms + i];
int max_y = maxs[terms + i];
if (min_x * (max_y - min_y) > ub - min)
{
max_y = (ub - min + min_x * min_y) / min_x;
_fd_var_del_gt(max_y, VAR(this, terms + i));
_fd_revise_connected(this, VAR(this, terms + i));
}
if ((max_x - min_x) * min_y > ub - min)
{
max_x = (ub - min + min_x * min_y) / min_y;
_fd_var_del_gt(max_x, VAR(this, i));
_fd_revise_connected(this, VAR(this, i));
}
}
if ((min > lb && _fd_var_del_lt(min, VAR(this, this->nvariables - 1))) |
(max < ub && _fd_var_del_gt(max, VAR(this, this->nvariables - 1))))
_fd_revise_connected(this, VAR(this, this->nvariables - 1));
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eef94371
Vasco Pedro
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#ifdef CONSTRAINT_TEMPS
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965dadaa
Salvador Abreu
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// save values
*base = lb;
*(base + 1) = ub;
*(base + 2) = min;
*(base + 3) = max;
fd__constraint_remember(this);
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eef94371
Vasco Pedro
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#endif
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965dadaa
Salvador Abreu
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return FD_OK;
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Salvador Abreu
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}
static int fd_knapsack2_propagate2(fd_constraint this, fd_int culprit)
{
#ifdef CONSTRAINT_TEMPS
int ub, lb;
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eef94371
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int min, max;
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965dadaa
Salvador Abreu
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int terms = (this->nvariables - 1) / 2;
int *mins, *maxs; // XXX: trouble possible if a variable appears repeated
int i;
int *base;
int x, y;
int nmin, nmin_x, nmax, nmax_x;
if (!fd__constraint_data_valid(this))
return fd_knapsack2_filter(this); // ignores culprit
// bounds filtering
base = constraint_memory[this->index];
mins = base + 4;
maxs = mins + 2 * terms;
lb = *base;
ub = *(base + 1);
min = *(base + 2);
max = *(base + 3);
if (culprit == VAR(this, this->nvariables - 1))
{
// the culprit is the sum variable
int nlb, nub;
nlb = _fd_var_min(culprit);
nub = _fd_var_max(culprit);
if (nlb == lb && nub == ub)
return FD_OK;
if (nlb != lb)
{
if (max < nlb)
return FD_NOSOLUTION;
if (max == nlb)
for (i = 0; i < terms; ++i)
{
int max_x = maxs[i];
int max_y = maxs[terms + i];
if (max_x != 0 && max_y != 0)
{
if (_fd_var_del_lt(max_x, VAR(this, i)))
{
if (fd_domain_empty(VAR(this, i)))
return FD_NOSOLUTION;
_fd_revise_connected(this, VAR(this, i));
}
if (_fd_var_del_lt(max_y, VAR(this, terms + i)))
{
if (fd_domain_empty(VAR(this, terms + i)))
return FD_NOSOLUTION;
_fd_revise_connected(this, VAR(this, terms + i));
}
}
}
*base = nlb;
}
if (nub != ub)
{
if (min > nub)
return FD_NOSOLUTION;
if (min == nub)
for (i = 0; i < terms; ++i)
{
int min_x = mins[i];
int min_y = mins[terms + i];
if (min_x != 0 || min_y != 0)
{
if (min_y != 0 && _fd_var_del_gt(min_x, VAR(this, i)))
{
if (fd_domain_empty(VAR(this, i)))
return FD_NOSOLUTION;
_fd_revise_connected(this, VAR(this, i));
}
if (min_x != 0 && _fd_var_del_gt(min_y, VAR(this, terms + i)))
{
if (fd_domain_empty(VAR(this, terms + i)))
return FD_NOSOLUTION;
_fd_revise_connected(this, VAR(this, terms + i));
}
}
}
*(base + 1) = nub;
}
return FD_OK;
}
// the culprit appears in one of the terms, find out which one
for (x = 0; culprit != VAR(this, x); ++x)
;
y = (x < terms) ? x + terms : x - terms; // the other variable in the term
nmin_x = _fd_var_min(VAR(this, x));
nmin = min + (nmin_x - mins[x]) * mins[y];
nmax_x = _fd_var_max(VAR(this, x));
nmax = max - (maxs[x] - nmax_x) * maxs[y];
if (nmin > ub || nmax < lb)
return FD_NOSOLUTION;
if ((nmin > lb && _fd_var_del_lt(nmin, VAR(this, this->nvariables - 1))) |
(nmax < ub && _fd_var_del_gt(nmax, VAR(this, this->nvariables - 1))))
{
if (fd_domain_empty(VAR(this, this->nvariables - 1)))
return FD_NOSOLUTION;
_fd_revise_connected(this, VAR(this, this->nvariables - 1));
}
mins[x] = nmin_x;
maxs[x] = nmax_x;
*(base + 2) = nmin;
*(base + 3) = nmax;
return FD_OK;
#else /* CONSTRAINT_TEMPS */
return fd_knapsack2_filter(this); // ignores culprit
#endif /* CONSTRAINT_TEMPS */
}
fd_constraint fd_knapsack2(fd_int xs[], fd_int ys[], int nvariables, fd_int limits)
{
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eef94371
Vasco Pedro
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fd_constraint c = fd__constraint_new(2 * nvariables + 1, 0);
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965dadaa
Salvador Abreu
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int i;
if (c)
{
for (i = 0; i < nvariables; ++i)
c->variables[i] = FD_INT2C_VAR(xs[i]);
for (; i < 2 * nvariables; ++i)
c->variables[i] = FD_INT2C_VAR(ys[i - nvariables]);
c->variables[2 * nvariables] = FD_INT2C_VAR(limits);
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Vasco Pedro
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965dadaa
Salvador Abreu
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c->kind = FD_CONSTR_KNAPSACK2;
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Salvador Abreu
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for (i = 0; i < c->nvariables; ++i)
_fd_var_add_constraint(VAR(c, i), c);
_fd_add_constraint(c);
}
return c;
}
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