8-Queens snippet - c

Question

I have currently learning backtracking and got stuck on the 8-queen problem, I am using a 8x8 matrix and I think I've got some problems regarding the matrix passing to functions, any help would be highly apreciated.I wouldn't mind if anyone would bring any optimisation to the code, thanks.
here is my code.
#include <stdio.h>
#include <stdlib.h>
#define MAX 7
//void azzera(int **mat);
void posiziona(int **mat, int r,int c);
void stampa(int **mat);
int in_scacchi(int **mat,int r ,int c);
int main(int argc, char *argv[])
{
int i=0,j=0;
int **mat=(int **)malloc(sizeof(int *)*MAX);
for(i=0;i<=MAX;i++){
mat[i]=(int *)malloc(MAX*sizeof(int));
for(j=0;j<=MAX;j++){
mat[i][j]=-1;
}
}
printf("insert pos of the first queen on the first row (1-8) :");
scanf("%d",&i);
i-=1;
mat[0][i]=1;
posiziona(mat,1,0);
stampa(mat);
system("PAUSE");
return 0;
}
/*void azzera(int **mat){
int i=0,j=0;
for(i=0;i<=MAX;i++){
for(j=0;j<=MAX;j++){
mat[i][j]=-1;
}
}
}*/
void stampa(int **mat){
int i,j;
for(i=0;i<=MAX;i++){
for(j=0;j<=MAX;j++){
printf(" %d",mat[i][j]);
}
printf("\n");
}
}
void posiziona(int **mat, int r,int c){
int i=0,riga=1,flag_col=-1,flag_riga=-1;
if(riga<=7&&flag_riga!=1){
if(flag_riga==1){
flag_riga=-1;
posiziona(mat,r+1,0);
}
else if(in_scacchi(mat,r,c)==1){
if(c==MAX)
posiziona(mat,r-1,0);
posiziona(mat,r,c+1);
}
else{
flag_riga=1;
}
}
}
int in_scacchi(int **mat,int r ,int c){
int i,j,k,m;
int flag=0;
//col
for(i=0;i<r;i++){
for(j=0;j<=c;j++){
if(((mat[i][j]==1)&&(c==j)))
return 1;
}
}
//diag \
for(i=0;i<MAX-r;i++){
for(j=0;j<=MAX-c;j++){
if(mat[MAX-r-i][MAX-c-j]==1)
return 1;
}
}
//antidiag
for(i=r+1;i<=MAX;i++){
for(j=c+1;j<=MAX;j++){
if(mat[r-i][c+j]==1) {
return 1;
}
}
}
return 0;
}

Answer 1

1. One glaring problem is the memory allocation:
int **mat=(int **)malloc(sizeof(int *)*MAX);
for(i=0;i<=MAX;i++){
mat[i]=(int *)malloc(MAX*sizeof(int));
Given that MAX is 7, both mallocs are allocating too little memory for the matrix (seven elements instead of eight).
To be honest, I'd rename MAX to SIZE or something similar, and change all your loops to use strict less-than, i.e.
for(i = 0; i < SIZE; i++) {
I would argue that this is slightly more idiomatic and less prone to errors.
2. I haven't tried to debug the logic (I don't think it's fair to expect us to do that). However, I have noticed that nowhere except in main do you assign to elements of mat. To me this suggests that the code can't possibly be correct.
3. Beyond that, it may be useful to observe that in a valid solution every row of the chessboard contains exactly one queen. This means that you don't really need an 8x8 matrix to represent the solution: an 8-element array of column positions will do.
edit In response to your question in the comments, here is a complete Python implementation demonstrating point 3 above:
def can_place(col_positions, col):
row = len(col_positions)
for r, c in enumerate(col_positions):
if c == col or abs(c - col) == abs(r - row): return False
return True
def queens(n, col_positions = []):
if len(col_positions) >= n:
pretty_print(n, col_positions)
return True
for col in xrange(n):
if can_place(col_positions, col):
if queens(n, col_positions + [col]):
return True
return False
def pretty_print(n, col_positions):
for col in col_positions:
print '.' * col + 'X' + '.' * (n - 1 - col)
queens(8)

Answer 2

Your matrix must iterate from 0 to MAX-1,
i.e
int **mat= malloc(sizeof(int *)*MAX);
for(i=0;i< MAX;i++){ //see for i<MAX
mat[i]= malloc(MAX*sizeof(int));
for(j=0;j<MAX;j++){ //see for j<MAX
mat[i][j]=-1;
}
}

Answer 3

malloc must be called with sizeof(...) * (MAX+1) in both the i- and j-loop.
Moreover, when I ran your program I got an access violation in the antidiag portion of in_scacchi(...) due to the fact that the code tries to access mat[r-i][c+j] which evaluates to mat[-1][1] because r==1 and i==2.
So there seems to be a logical error in your description of the anti-diagonal of the matrix.