void Fibonacci(__int64 n, BIGNUM &rez)
{
BIGNUM f1, f2;
if (n < HASH)
memcpy(rez, Table[n], sizeof(Table[n]));
else
{
memset(rez, 0, sizeof(rez));
if (n & 1) // f[2n-1] = f^2[n] + f^2[n-1]
{
Fibonacci((n + 1) / 2, f1);
Fibonacci(n / 2, f2);
BigMul(rez, f1, f1);
memset(f1, 0, sizeof(f1));
BigMul(f1, f2, f2);
BigAdd(rez, f1);
} else // f[2n] = f[n]*(f[n-1] + f[n+1])
{
Fibonacci(n / 2 - 1, f1);
Fibonacci(n / 2 + 1, f2);
BigAdd(rez, f1);
BigAdd(rez, f2);
Fibonacci(n / 2, f1);
BigMul(rez, rez, f1);
}
}
}
int main (int argc, char *argv[])
{
int n, x, a1, b1, t, mn;
struct BigNum p[3], q[3], mx, my;
BigInit(&mx, 0);
BigInit(&my, 0);
for (n = 2; n < MAX_N; n++) {
a1 = 1;
x = b1 = sqrt(n);
if (x*x == n)
continue;
BigInit(&p[0], 1);
BigInit(&q[0], 0);
BigInit(&p[1], x);
BigInit(&q[1], 1);
if (check_xy(n, &p[1], &q[1])) {
printf("N = %d, x = %I64u, y = %I64u\n", n, p[1], q[1]);
fflush(stdout);
continue;
}
do {
x = get_next_coeff(n, &a1, &b1);
BigMultiplyConst(&p[2], &p[1], x);
BigAdd(&p[2], &p[2], &p[0]);
BigMultiplyConst(&q[2], &q[1], x);
BigAdd(&q[2], &q[2], &q[0]);
if (check_xy(n, &p[2], &q[2])) {
break;
}
BigAssign(&p[0], &p[1]);
BigAssign(&p[1], &p[2]);
BigAssign(&q[0], &q[1]);
BigAssign(&q[1], &q[2]);
} while (1);
if (BigCompare(&mx, &p[2]) < 0) {
BigAssign(&mx, &p[2]);
BigAssign(&my, &q[2]);
mn = n;
}
}
printf("\n===== Maximum at N = %d\n", mn);
printf("X: "); BigPrint(&mx, mx.n);
printf("Y: "); BigPrint(&my, my.n);
return 0;
}
void BuildTable(int n)
{
int i;
Table[0][0] = Table[1][0] = 1;
Table[0][1] = 0;
Table[1][1] = 1;
for (i = 2; i <= n; i++)
{
BigAdd(Table[i], Table[i - 1]);
BigAdd(Table[i], Table[i - 2]);
}
}
int main()
{
scanf("%d", &N);
//clock_t start = clock();
BuildTable(HASH - 1);
Fibonacci(N - 1, rez1);
Fibonacci(N + 1, rez2);
BigAdd(rez1, rez2);
printf("%d", rez1[rez1[0]]);
for (int i = rez1[0] - 1; i > 0; i--)
printf(FMT, rez1[i]);
printf("\n");
//clock_t end = clock();
//printf("Time = %.4lf\n", (double)(end - start)/CLK_TCK);
return 0;
}
