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#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>
#define SUDOKU_N 3
#define BLOCK_N (SUDOKU_N * SUDOKU_N)
#define DIGITS_N BLOCK_N
#define PLACE_BIT_N (BLOCK_N * BLOCK_N)
#define BLOCK_BIT_N (BLOCK_N * DIGITS_N)
#define ROW_BIT_N BLOCK_BIT_N
#define COL_BIT_N ROW_BIT_N
#define SET_COVER_ROW (BLOCK_N * BLOCK_N * DIGITS_N)
#define SET_COVER_COL (PLACE_BIT_N + BLOCK_BIT_N + ROW_BIT_N + COL_BIT_N)
typedef struct DNode {
struct DNode *left, *right, *up, *down;
struct DNode *ctl;
uint32_t size, row;
} DNode; /* the node of dlx */
int bitmap[SET_COVER_ROW][SET_COVER_COL];
int row_seq[SET_COVER_ROW];
int puzzle[BLOCK_N][BLOCK_N];
int backref[SET_COVER_ROW][3];
DNode *dnode_new() {
return (DNode *)malloc(sizeof(DNode));
}
void dnode_free(DNode *p) {
free(p);
}
DNode *build_dlx(int nrow, int ncol) {
DNode *head = dnode_new();
DNode *chead[SET_COVER_COL];
head->left = head->right = head;
head->up = head->down = head;
int i, j;
/* build the guard chain */
for (j = 0; j < ncol; j++)
{
DNode *p = chead[j] = dnode_new();
(p->left = head->left)->right = p;
(p->right = head)->left = p;
p->up = p->down = p;
p->size = 0;
}
DNode *rhead = dnode_new(); /* helper node */
for (i = 0; i < nrow; i++)
{
rhead->left = rhead->right = rhead;
for (j = 0; j < ncol; j++)
if (bitmap[i][j])
{
DNode *p = dnode_new();
p->ctl = chead[j];
p->ctl->size++;
p->row = i;
(p->left = rhead->left)->right = p;
(p->right = rhead)->left = p;
(p->up = p->ctl->up)->down = p;
(p->down = p->ctl)->up = p;
}
rhead->left->right = rhead->right;
rhead->right->left = rhead->left;
}
dnode_free(rhead);
return head;
}
#define LOOP(q, p, d) for (q = p->d; q != p; q = q->d)
void set_cover(DNode *pctl) {
DNode *q, *r;
pctl->left->right = pctl->right;
pctl->right->left = pctl->left;
LOOP(q, pctl, down)
LOOP(r, q, right)
{
r->up->down = r->down;
r->down->up = r->up;
r->ctl->size--;
}
}
void set_uncover(DNode *pctl) {
DNode *q, *r;
pctl->left->right = pctl;
pctl->right->left = pctl;
LOOP(q, pctl, up)
LOOP(r, q, left)
{
r->up->down = r;
r->down->up = r;
r->ctl->size++;
}
}
void dlx_print(int step) {
int i;
for (i = 0; i < step; i++)
printf("%d ", row_seq[i]);
puts("");
}
void sudoku_print(int step) {
int i, j;
for (i = 0; i < step; i++)
{
int *t = backref[row_seq[i]];
puzzle[t[0]][t[1]] = t[2];
}
for (i = 0; i < BLOCK_N; i++, puts(""))
for (j = 0; j < BLOCK_N; j++)
printf("%d ", puzzle[i][j]);
puts("");
}
void search(DNode *head, int step) {
DNode *p, *q, *lp;
uint32_t least_value = -1U;
if (head->left == head)
{
sudoku_print(step);
/* dlx_print(step); */
return;
}
LOOP(p, head, right)
if (p->size < least_value)
{
least_value = p->size;
lp = p;
}
set_cover(lp);
LOOP(p, lp, down)
{
LOOP(q, p, right) set_cover(q->ctl);
row_seq[step] = p->row;
search(head, step + 1);
LOOP(q, p, left) set_uncover(q->ctl);
}
set_uncover(lp);
}
void test_dlx() {
int nrow, ncol, i, j;
DNode *head;
scanf("%d %d", &nrow, &ncol);
for (i = 0; i < nrow; i++)
for (j = 0; j < ncol; j++)
scanf("%d", bitmap[i] + j);
head = build_dlx(nrow, ncol);
search(head, 0);
}
void sudoku() {
int i, j, d, nrow = 0;
DNode *head;
for (i = 0; i < BLOCK_N; i++)
for (j = 0; j < BLOCK_N; j++)
scanf("%d", puzzle[i] + j);
for (i = 0; i < BLOCK_N; i++)
for (j = 0; j < BLOCK_N; j++)
for (d = 0; d < DIGITS_N; d++)
if (!puzzle[i][j] || puzzle[i][j] == d + 1)
{
int *b = bitmap[nrow];
b[i * BLOCK_N + j] = 1;
b += PLACE_BIT_N;
b[((i / SUDOKU_N) * SUDOKU_N + j / SUDOKU_N) * BLOCK_N + d] = 1;
b += BLOCK_BIT_N;
b[i * BLOCK_N + d] = 1;
b += ROW_BIT_N;
b[j * BLOCK_N + d] = 1;
backref[nrow][0] = i;
backref[nrow][1] = j;
backref[nrow][2] = d + 1;
nrow++;
}
printf("%d\n", nrow);
head = build_dlx(nrow, SET_COVER_COL);
search(head, 0);
}
int main() {
/* test_dlx(); */
sudoku();
return 0;
}
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