#include<stdio.h>
#include<stdlib.h>
#include<time.h>
#define range9(x) for(int x = 0; x < 9; x ++)

struct Sudoku{
    int inc[9][9];
};

#define MAXSIZE 1000
struct Sudoku *M_PtrReg[MAXSIZE];
int PRtp = 0;
void ptrInit(){
    for(int i = 0; i < MAXSIZE; i ++)
        M_PtrReg[i] = (struct Sudoku *)malloc(sizeof(struct Sudoku));
}
void ptrClear(){
    for(int i = 0; i < MAXSIZE; i ++)
        free(M_PtrReg[i]);
}
struct Sudoku *ptrReg(){return M_PtrReg[PRtp++];}
void ptrFree(){--PRtp;}

void sudokuClear(struct Sudoku *a){
    range9(i)
        range9(j)
            a->inc[i][j] = 0;
}
void sudokuCopy(struct Sudoku src, struct Sudoku *dst){
    range9(i)
        range9(j)
            dst->inc[i][j] = src.inc[i][j];
}
void sudokufromArray(int src[9][9], struct Sudoku *dst){
    range9(i)
        range9(j)
            dst->inc[i][j] = src[i][j];
}
void sudokuPrint(struct Sudoku a){
    range9(i){
        if(!(i % 3)) putchar('\n');
        range9(j){
            if(!(j % 3)) putchar(' ');
            if(!a.inc[i][j])
                putchar('.');
            else 
                // putchar(a.inc[i][j] + 48);
                printf("%d", a.inc[i][j]);
            putchar(' ');
        }
        putchar('\n');
    }
}
void initRandomSeed(){srand(time(NULL));}
struct Sudoku sudokuRandomGenerate(unsigned int fill){// %
    fill %= 101;
    struct Sudoku *res = ptrReg();
    range9(i)
        range9(j)
            if(rand()%100 <= fill)
                res->inc[i][j] = rand() % 9 + 1;
            else 
                res->inc[i][j] = 0;
    return *res;
}
struct Sudoku tags;
int tag(struct Sudoku *a, int i, int j, int x, int y, struct Sudoku *tags){
    if(i == x && j == y) return 0;
    if(a->inc[i][j] == a->inc[x][y]){
        printf("False:repetition found in (%d,%d) and (%d,%d) with the number {%d}\n", i+1, j+1, x+1, y+1, a->inc[x][y]);
        return 1;
    }
    tags->inc[x][y] |= (1 << a->inc[i][j]);
    return 0;
}
int tagPoint(struct Sudoku *a, int i, int j, struct Sudoku *tags){
    range9(k)
        if(tag(a, i, j, i, k, tags)||tag(a, i, j, k, j, tags)||tag(a, i, j, i/3*3+k/3, j/3*3+k%3, tags))
        return 1;
    return 0;
}
int tagsInit(struct Sudoku *a, struct Sudoku *tags){
    range9(i)
        range9(j)
            tags->inc[i][j] |= (1 << a->inc[i][j]);
    range9(i)
        range9(j)
            if(a->inc[i][j] && tagPoint(a, i, j, tags))
                return 1;
}
int sudokuJudge(struct Sudoku a){
    struct Sudoku tags;
    sudokuClear(&tags);
    if(tagsInit(&a, &tags)) return 1;
    printf("True:Valid initial Sudoku matrix!\n");
    return 0;
}
void tagFindLeast(struct Sudoku *a, int *x, int *y, struct Sudoku *tags){
    int minv = 10;
    int mini=0, minj=0;
    range9(i)
        range9(j)
            if(!a->inc[i][j]){
                int cnt = 0;
                range9(k)
                    cnt += (tags->inc[i][j] >> k) & 1;
                if(cnt < minv && cnt != 0){
                    minv = cnt;
                    mini = i;
                    minj = j;
                }
            }
    *x = mini;
    *y = minj;
}
struct Sudoku *sudokuFill__(struct Sudoku *a, int unfillednum, struct Sudoku *tags){
    struct Sudoku *pres, *t_tags;
    if(!unfillednum){
        pres = ptrReg();
        sudokuCopy(*a, pres);
        sudokuPrint(*tags);
        return pres;
    }
    int m=0, n=0;
    tagFindLeast(a, &m, &n, tags);
    range9(i)
        if(!((tags->inc[m][n] >> i) & 1)){
            a->inc[m][n] = i;
            t_tags = ptrReg();
            sudokuCopy(*tags, t_tags);
            tagPoint(a, m, n, t_tags);
            // sudokuPrint(*a);
            // getchar();
            pres = sudokuFill__(a, unfillednum - 1, t_tags);
            if(pres)
                return pres;
            a->inc[m][n] = 0;
            ptrFree();
        }
    return NULL;
}
struct Sudoku *sudokuFill(struct Sudoku *a){
    struct Sudoku tags, res, *pres;
    sudokuClear(&tags);
    if(tagsInit(a, &tags)) return NULL;
    int unfillednum = 0;
    range9(i)
        range9(j)
            if(!a->inc[i][j])
                unfillednum ++;
    printf("%d", unfillednum);
    return sudokuFill__(a, unfillednum, &tags);
}