/**
* use the index of each slot, together with constraints only one queen in each row from different
* angle e.g for var at position [0][0] has index 0, bdd && (NOT0 v NOT1) && (NOT0 v NOT2) &&
* (NOT0 v NOT3) && (NOT0 v NOT4) horizontal && (NOT0 v NOT5) && (NOT0 v NOT10) && (NOT0 v NOT15)
* && (NOT0 v NOT20) vertical && (NOT0 v NOT6) && (NOT0 v NOT12) && (NOT0 v NOT18) && (NOT0 v
* NOT24) diagonal && one queen per row rule oneQueen
*
* @return BDD
*/
public BDD build() {
BDD bdd = factory.one();
for (int x = 0; x < size; x++) {
BDD oneQueen = factory.zero();
for (int y = 0; y < size; y++) {
oneQueen.orWith(factory.ithVar(idx(x, y)));
BDD var = factory.nithVar(idx(x, y)); // get negated index value
// horizontal
for (int i = (y + 1); i < size; i++) {
bdd.andWith(var.or(factory.nithVar(idx(x, i))));
}
// vertical
for (int i = (x + 1); i < size; i++) {
bdd.andWith(var.or(factory.nithVar(idx(i, y))));
}
// diagonal
for (int i = 1; (y + i) < size; i++) {
if ((x - i) >= 0) {
bdd.andWith(var.or(factory.nithVar(idx(x - i, y + i))));
}
if ((x + i) < size) {
bdd.andWith(var.or(factory.nithVar(idx(x + i, y + i))));
}
}
}
bdd.andWith(oneQueen); // one row has to/only can have one queen
}
return bdd;
}