/* retorna TRUE cuando encuentra una solucion valida */
int backtrack(int a[], int n, int k) {
if (n == k) {
if (is_valid_solution(a, n)) {
print_solution(a, n);
return TRUE;
}
else
return FALSE;
}
else {
int nr_candidates;
int candidates[N];
find_candidates(a, n, k, candidates, &nr_candidates);
int found;
int i;
for (i = 0; i < nr_candidates; ++i) {
a[k] = candidates[i];
found = backtrack(a, n, k + 1);
if (found)
return TRUE;
}
return FALSE;
}
}
long long min_x_solution(long long d)
{
number_t num;
fraction_t x_over_y;
long long * seq; // expansion sequence for sqrt(d)
long long seq_size, seq_cap;
// num = a * (sqrt(b) - c) / d
num.a = 1;
num.b = d;
num.c = 0;
num.d = 1;
seq_size = 0;
seq_cap = 4;
seq = (long long *) malloc(seq_cap * sizeof(seq[0]));
do
{
if(seq_size >= seq_cap)
{
seq_cap *= 2;
seq = (long long *) realloc(seq, seq_cap * sizeof(seq[0]));
}
seq[seq_size] = next_num(&num);
seq_size++;
x_over_y = expanded_sequence(seq, seq_size);
} while(!is_valid_solution(d, x_over_y.num, x_over_y.denom));
free(seq);
return x_over_y.num;
}
int main(int argc, char ** argv)
{
INT d, x, j, sqrt_d;
INT max_x, max_d;
max_d = 0;
max_x = 0;
for(d = 2; d <= 1000; d++)
{
if(is_square(d))
continue;
for(j = 1; j > 0; j++)
{
if(is_valid_solution(d, d * j - 1))
{
x = d * j - 1;
break;
}
if(is_valid_solution(d, d * j + 1))
{
x = d * j + 1;
break;
}
}
printf("%Ld ^ 2 - %Ld * %Ld ^ 2 == 1\n", x, d, dx_to_y(d, x));
if(max_x < x)
{
max_x = x;
max_d = d;
}
}
printf("Largest minimal x for x^2-D*y^2=1 for 1 <= D <= 1000: %Ld\n", max_x);
return 0;
}
