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#include <math.h>
#include <stdlib.h>
#include <stdio.h>
#define SOLVED 10
#define FULL 11
#define INVALID -1
#define VALID 0
#define BOARD_WIDTH 9
#define BOARD_HEIGHT 9
#define BOARD_LOW 1
#define BOARD_HIGH 9
#define EMPTY 0
int board[BOARD_WIDTH][BOARD_HEIGHT] = {
0, 2, 0, 7, 8, 9, 0, 0, 0,
0, 0, 7, 3, 2, 0, 0, 0, 0,
0, 8, 4, 5, 0, 0, 2, 0, 0,
8, 0, 0, 0, 9, 2, 0, 0, 6,
0, 1, 6, 0, 0, 0, 7, 4, 0,
4, 0, 0, 1, 7, 0, 0, 0, 8,
0, 0, 3, 0, 0, 8, 5, 7, 0,
0, 0, 0, 0, 5, 3, 4, 0, 0,
0, 0, 0, 9, 4, 7, 0, 2, 0
};
struct cell_position {
int x;
int y;
};
void printb()
{
int i, j;
printf("------------------------------\n");
for(i = 0; i < BOARD_HEIGHT; i++) {
for (j = 0; j < BOARD_WIDTH; j++) {
if ((j % 3) == 0)
printf("|");
printf(" %i ", board[i][j]);
}
if (((i + 1) % 3) == 0)
printf("\n------------------------------");
printf("|\n");
}
}
void get_next_empty(struct cell_position *p)
{
int i, j;
for(i = 0; i < BOARD_HEIGHT; i++) {
for(j = 0; j < BOARD_WIDTH; j++) {
if (board[i][j] == EMPTY) {
p->x = i;
p->y = j;
return;
}
}
}
p->x = FULL;
p->y = FULL;
}
//check row p->x and column p->y to see if num is already present
int column_row_valid(struct cell_position *p, int num)
{
int i;
for(i = 0; i < BOARD_WIDTH; i++) {
if (board[i][p->y] == num || board[p->x][i] == num)
return INVALID;
}
return VALID;
}
//block positions:
// (0,0), (1,0), (2,0)
// (0,1), (1,1), (2,1)
// (0,2), (1,2), (2,2)
int valid_for_block(struct cell_position *p, int num)
{
int block_x = floor(p->x / 3);
int block_y = floor(p->y / 3);
int row_start, row_end;
int column_start, column_end;
if (block_x == 0) {
column_start = 0;
column_end = 3;
}
else if (block_x == 1) {
column_start = 3;
column_end = 6;
}
else {
column_start = 6;
column_end = 9;
}
if (block_y == 0) {
row_start = 0;
row_end = 3;
}
else if (block_y == 1) {
row_start = 3;
row_end = 6;
}
else {
row_start = 6;
row_end = 9;
}
int i, j;
for(i = row_start; i < row_end; i++) {
for(j = column_start; j < column_end; j++) {
if (board[i][j] == num)
return INVALID;
}
}
return VALID;
}
int valid_for_empty(struct cell_position *p, int tried)
{
if (tried < BOARD_LOW || tried > BOARD_HIGH)
return INVALID;
if(column_row_valid(p, tried) != INVALID && valid_for_block(p, tried) != INVALID)
return VALID;
return INVALID;
}
int solve(int board[][BOARD_WIDTH], struct cell_position *p)
{
static int call_count = -1;
call_count++;
struct cell_position previous;
previous.x =p->x;
previous.y = p->y;
get_next_empty(p);
if (p->x == FULL && p->y == FULL)
return SOLVED;
int tried_number;
for(tried_number = BOARD_LOW; tried_number <= BOARD_HIGH; tried_number++) {
if (valid_for_empty(p, tried_number) == VALID) {
board[p->x][p->y] = tried_number;
printf("Set board posiiton (%i, %i) to %i for iteration %i\n", p->x, p->y, tried_number, call_count);
if (solve(board, p) == SOLVED) {
printf("YAY WE SOLVED THE PUZZLE\n");
printb();
return SOLVED;
}
//if the solve returns INVALID, we must reset the current board position to EMPTY
//to ensure that on the next iteration that the valid_for_empty will return our current
//board position.
printf("we have encountered an invalid number. reseting board position (%i, %i) whose number is %i to %i for interation %i\n",previous.x, previous.y, board[p->x][p->y], EMPTY, call_count);
board[p->x][p->y] = EMPTY;
p->x = previous.x;
p->y = previous.y;
}
}
//printf("We have exited the loop\n");
return INVALID;
}
int main(void)
{
printf("Unsolved Puzzle\n");
printb();
struct cell_position p;
p.x = EMPTY;
p.y = EMPTY;
solve(board, &p);
printf("\n");
printf("Solved Puzzle\n");
printb();
return 0;
}
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