#include <stdio.h>

void print_valid(int a[9][9]){
	int x=1;
	int i,j,ii,jj;
	for (i = 0; i < 9; i++) {
		int count[10] = {0};
		for (j = 0; j < 9; j++) {
			if (a[i][j]!= 0) {
				if (count[a[i][j]] > 0) {
					x = 0;
					printf("False:Invalid initial Sudoku matrix!\n      The number %d in the row %d has been used!\n", a[i][j], i + 1);
					return;
				}
				count[a[i][j]]++;
			}
		}
	}
	int y=1;
	for (j = 0; j < 9; j++) {
		int count[10] = {0};
		for (i = 0; i <9; i++) {
			if (a[i][j]!= 0) {
				if (count[a[i][j]] > 0) {
					y = 0;
					printf("False:Invalid initial Sudoku matrix!\n      The number %d in the col %d has been used!\n", a[i][j], j + 1);
					return;
				}
				count[a[i][j]]++;
			}
		}
	}
	int z=1;
	for (i = 0; i <9; i += 3) {
		for (j = 0; j <9; j += 3) {
			int count[10] = {0};
			for (ii = i; ii < i + 3; ii++) {
				for (jj = j; jj < j + 3; jj++) {
					if (a[ii][jj]!= 0) {
						if (count[a[ii][jj]] > 0) {
							z = 0;
							printf("False:Invalid initial Sudoku matrix!\n      The number %d in the 3x3 submatrix starting at row %d, col %d has been used!\n", a[ii][jj], i + 1, j + 1);
							return;
						}
						count[a[ii][jj]]++;
					}
				}
			}
		}
	}
	if (x&&y&&z) {
	printf("True:Valid initial Sudoku matrix!\n");
	}
	return;
}

int is_valid(int a[9][9]){
	int x=1;
	int i,j,ii,jj;
	for (i = 0; i < 9; i++) {
		int count[10] = {0};
		for (j = 0; j < 9; j++) {
			if (a[i][j]!= 0) {
				if (count[a[i][j]] > 0) {
					x = 0;
					return 0;
				}
				count[a[i][j]]++;
			}
		}
	}
	int y=1;
	for (j = 0; j < 9; j++) {
		int count[10] = {0};
		for (i = 0; i <9; i++) {
			if (a[i][j]!= 0) {
				if (count[a[i][j]] > 0) {
					y = 0;
					return 0;
				}
				count[a[i][j]]++;
			}
		}
	}
	int z=1;
	for (i = 0; i <9; i += 3) {
		for (j = 0; j <9; j += 3) {
			int count[10] = {0};
			for (ii = i; ii < i + 3; ii++) {
				for (jj = j; jj < j + 3; jj++) {
					if (a[ii][jj]!= 0) {
						if (count[a[ii][jj]] > 0) {
							z = 0;
							return 0;
						}
						count[a[ii][jj]]++;
					}
				}
			}
		}
	}
	if (x&&y&&z) {
	}
	return 1;
}

int solve_sudoku(int a[9][9]) {
	int row,col,num;
    for (row = 0; row < 9; row++) {
        for (col = 0; col < 9; col++) {
            if (a[row][col] == 0) {
                for (num = 1; num <= 9; num++) {
                    if (is_valid(a)) {
                        a[row][col] = num;
                        if (solve_sudoku(a)) {
                            return 1;
                        }
                        a[row][col] = 0;
                    }
                }
                return 0;
            }
        }
    }
    return 1;
}

void print(int a[9][9]) {
	printf("|-----------------------|\n");
    int i,j;
	for(i=0;i<9;i++){
		printf("| ");
		for(j=0;j<9;j++){
			printf("%d ",a[i][j]);
			if(j==2||j==5) printf("| ");
			if(j==8) printf("|\n");
		}
		if(i==2||i==5) {
			int x=22;
			printf("|");
			while(x>=0) {
				printf("-");
				x--;
			}
			printf("|\n");
		}
	}
	printf("|-----------------------|\n");
}

void final(int a[9][9]) {
    printf("The original Sudoku matrix: \n");
    print(a);
    int valid=is_valid(a);
    print_valid(a);
    if(valid){
    	if (solve_sudoku(a)) {
            printf("The solution of Sudoku matrix:\n");
            print(a);
		}
		else printf("No solution!\n");
	}
	else printf("No solution!\n");
}

int main(){
	int board0[9][9] = {
	{5, 3, 0, 0, 7, 0, 0, 0, 0},
	{6, 0, 0, 1, 9, 5, 0, 0, 0},
	{0, 9, 8, 0, 0, 0, 0, 6, 0},
	{8, 0, 0, 0, 6, 0, 0, 0, 3},
	{4, 0, 0, 8, 0, 3, 0, 0, 1},
	{7, 0, 0, 0, 2, 0, 0, 0, 6},
	{0, 6, 0, 0, 0, 0, 2, 8, 0},
	{0, 0, 0, 4, 1, 9, 0, 0, 5},
	{0, 0, 0, 0, 8, 0, 0, 7, 9}
	};
	final(board0);
	int board1[9][9] = {
	{8, 3, 0, 0, 7, 0, 0, 0, 0},
	{6, 0, 0, 1, 9, 5, 0, 0, 0},
	{0, 9, 8, 0, 0, 0, 0, 6, 0},
	{8, 0, 0, 0, 6, 0, 0, 0, 3},
	{4, 0, 0, 8, 0, 3, 0, 0, 1},
	{7, 0, 0, 0, 2, 0, 0, 0, 6},
	{0, 6, 0, 0, 0, 0, 2, 8, 0},
	{0, 0, 0, 4, 1, 9, 0, 0, 5},
	{0, 0, 0, 0, 8, 0, 0, 7, 9}
	};
	final(board1);
	int board2[9][9] = {
	{5, 2, 0, 0, 7, 0, 0, 0, 0},
	{6, 0, 0, 1, 9, 5, 0, 0, 0},
	{0, 9, 8, 0, 0, 0, 0, 6, 0},
	{8, 0, 0, 0, 6, 0, 0, 0, 3},
	{4, 0, 0, 8, 0, 3, 0, 0, 1},
	{7, 0, 0, 0, 2, 0, 0, 0, 6},
	{0, 6, 0, 0, 0, 0, 2, 8, 0},
	{0, 0, 0, 4, 1, 9, 0, 0, 5},
	{0, 0, 0, 0, 8, 0, 0, 7, 9}
	};
	final(board2);
	return 0;
}