static bddp hit_z2b_rec(zddp f, my_hash *h)
{
if(f == zdd_top()) return bdd_bot();
if(f == zdd_bot()) return bdd_top();
bddp r;
if(ht_search((uintptr_t)f, (uintptr_t*)&r, h)) return r;
INC_RECDEPTH(recdepth);
bddp r0 = hit_z2b_rec(zdd_lo(f), h);
bddp r1 = hit_z2b_rec(zdd_hi(f), h);
DEC_RECDEPTH(recdepth);
bddp t = bdd_node(zdd_itemval(f), r1, bdd_top());
ENSURE_TRUE_MSG(t != BDD_NULL, "BDD operation failed");
r = bdd_and(r0, t);
ENSURE_TRUE_MSG(r != BDD_NULL, "BDD operation failed");
ht_insert((uintptr_t)f, (uintptr_t)r, h);
#ifdef SIZE_LOG
const uintmax_t insize = zdd_size(f);
const uintmax_t outsize = bdd_size(r);
fprintf(sizelog, "%ju\t%ju\n", insize, outsize);
if(maxsize < outsize) maxsize = outsize;
#endif /*SIZE_LOG*/
return r;
}
// Construct ZDD of sets containing exactly 1 occurrence of digit d in row r.
// For instance, if d = 3, r = 0:
//
// 1 === 2 === 3
// 3 ... 4a, --- 4b
// 4a === 5a === ... === 9a === ... === 11a === 12
// 4b === 5b === ... === 9b === ... === 11b === 13b
// 12 ... 13a, --- 13b
// 13a === ... === 20a === 21
// 13b === ... === 20b === 22b
// and so on until:
// 74a === 75 ... F, --- 76
// 74b === 76
// 76 === ... === 729 === T
//
// This ZDD has 9*2^720 members.
// When intersected with the one-digit-per-box set, the result has
// 9*8^8*9^72 members. (Pick 1 of 9 positions ford, leaving 8 possible choices
// forthe remaining 8 boxes in that row. The other 81 - 9 boxes can contain
// any single digitS.)
// The intersection forall d and a fixed r has 9!*9^72 members.
// The intersection forall r and a fixed d has 9^9*8^72 members.
void unique_digit_per_row(int d, int r) {
zdd_push();
// The order is determined by sorting by number, then by letter.
int next = 81 * r + d; // The next node involving the digit d.
int v = 1;
int state = 0;
while (v <= 729) {
if (v == next) {
next += 9;
state++;
if (state == 1) {
// The first split in the ZDD.
zdd_add_node(v, 1, 2);
} else if (state < 9) {
// Fix previous node. We must not have a second occurrence of d.
uint32_t n = zdd_last_node();
zdd_set_hilo(n, n + 3);
// If this is the first occurrence of d, we're on notice.
zdd_add_node(v, 1, 2);
} else {
// If we never saw d, then branch to FALSE.
// Otherwise reunite the branches.
zdd_add_node(v, 0, 1);
next = -1;
}
} else if (state == 0 || state == 9) {
zdd_add_node(v, 1, 1);
} else {
zdd_add_node(v, 2, 2);
zdd_add_node(v, 2, 2);
}
v++;
}
// Fix last nodes.
uint32_t n = zdd_last_node();
if (zdd_lo(n - 1) > n) zdd_set_lo(n - 1, 1);
if (zdd_hi(n - 1) > n) zdd_set_hi(n - 1, 1);
if (zdd_lo(n) > n) zdd_set_lo(n, 1);
if (zdd_hi(n) > n) zdd_set_hi(n, 1);
}
// Construct ZDD of sets containing all elements in the given list.
// The list is terminated by -1.
void contains_all(int *list) {
zdd_push();
int v = 1;
int *next = list;
while (v <= 729) {
if (v == *next) {
next++;
zdd_add_node(v, 0, 1);
} else {
zdd_add_node(v, 1, 1);
}
v++;
}
// Fix 729.
uint32_t n = zdd_last_node();
if (zdd_lo(n) > n) zdd_set_lo(n, 1);
if (zdd_hi(n) > n) zdd_set_hi(n, 1);
}
static zddp minhit_nonsup_rec(zddp f, my_hash *h)
{
if(f == zdd_bot()) return zdd_top();
if(f == zdd_top()) return zdd_bot();
zddp r;
if(ht_search((uintptr_t)f, (uintptr_t*)&r, h)) return r;
zddp t = zdd_union(zdd_lo(f), zdd_hi(f));
ENSURE_TRUE_MSG(t != BDD_NULL, "ZDD operation failed");
INC_RECDEPTH(recdepth);
zddp r0 = minhit_nonsup_rec(t, h);
zddp tt = minhit_nonsup_rec(zdd_lo(f), h);
DEC_RECDEPTH(recdepth);
zddp r1 = nonsup(tt, r0);
ENSURE_TRUE_MSG(r1 != BDD_NULL, "ZDD extra operation failed");
r = zdd_node(zdd_itemval(f), r0, r1);
ENSURE_TRUE_MSG(r != BDD_NULL, "ZDD operation failed");
ht_insert((uintptr_t)f, (uintptr_t)r, h);
return r;
}
