مساله:
اعداد فیبوناچی اعدادی در دنباله صحیح زیر (Fn) هستند:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …
مانند زیر:
F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
عددی به شما داده می شود که prod نام دارد، ما باید دو عدد فیبوناچی را جستجو کنیم که شرایط زیر را داشته باشد:
F(n) * F(n+1) = prod.
تابع productFib شما یک عدد صحیح (prod) می گیرد و یک آرایه را برمی گرداند:
[F(n), F(n+1), true] or {F(n), F(n+1), 1} or (F(n), F(n+1), True)
F(n) کوچکترین F(n) * F(n+1)> prod است
چند مثال دیگر:
productFib(714) # should return (21, 34, true),
# since F(8) = 21, F(9) = 34 and 714 = 21 * 34
productFib(800) # should return (34, 55, false),
# since F(8) = 21, F(9) = 34, F(10) = 55 and 21 * 34 < 800 < 34 * 55
-----
productFib(714) # should return [21, 34, true],
productFib(800) # should return [34, 55, false],
-----
productFib(714) # should return {21, 34, 1},
productFib(800) # should return {34, 55, 0},
-----
productFib(714) # should return {21, 34, true},
productFib(800) # should return {34, 55, false},
Description:
The Fibonacci numbers are the numbers in the following integer sequence (Fn):
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, …
such as
F(n) = F(n-1) + F(n-2) with F(0) = 0 and F(1) = 1.
Given a number, say prod (for product), we search two Fibonacci numbers F(n) and F(n+1) verifying
F(n) * F(n+1) = prod.
Your function productFib takes an integer (prod) and returns an array:
[F(n), F(n+1), true] or {F(n), F(n+1), 1} or (F(n), F(n+1), True)
depending on the language if F(n) * F(n+1) = prod.
If you don’t find two consecutive F(n) verifying F(n) * F(n+1) = prodyou will return
[F(n), F(n+1), false] or {F(n), F(n+1), 0} or (F(n), F(n+1), False)
F(n) being the smallest one such as F(n) * F(n+1) > prod.
Some Examples of Return:
(depend on the language)
productFib(714) # should return (21, 34, true),
# since F(8) = 21, F(9) = 34 and 714 = 21 * 34
productFib(800) # should return (34, 55, false),
# since F(8) = 21, F(9) = 34, F(10) = 55 and 21 * 34 < 800 < 34 * 55
-----
productFib(714) # should return [21, 34, true],
productFib(800) # should return [34, 55, false],
-----
productFib(714) # should return {21, 34, 1},
productFib(800) # should return {34, 55, 0},
-----
productFib(714) # should return {21, 34, true},
productFib(800) # should return {34, 55, false},
Note:
You can see examples for your language in “Sample Tests”.
public class ProdFib {
public static long[] productFib(long prod) {
long a = 0L;
long b = 1L;
while (a * b < prod) {
long tmp = a;
a = b;
b = tmp + b;
}
return new long[] { a, b, a * b == prod ? 1 : 0 };
}
}public class ProdFib { // must be public for codewars
public static long[] productFib(long prod) {
long fibProd = 0;
int i = 1;
while (fibProd < prod) {
fibProd = fibNum(i) * fibNum(i + 1);
i++;
}
if (fibProd == prod) return new long[] {fibNum(i - 1),fibNum(i),1};
return new long[] {fibNum(i - 1),fibNum(i),0};
}
public static long fibNum(int n) {
double a = (Math.sqrt(5) + 1) / 2;
return (long) ((1 / Math.sqrt(5))*(Math.pow(a, n) + Math.pow(a-1, n)));
}
}public class ProdFib { // must be public for codewars
public static long[] productFib(long prod) {
long i = 1;
long j = 1;
while (i*j < prod) {long k = i; i=j; j=k+i; }
if (i*j == prod) return new long[] {i, j, 1};
return new long[] {i, j, 0};
}
}function productFib($prod) {
$a = 0; $b = 1;
while ($a * $b < $prod) {
$next = $a + $b;
$a = $b;
$b = $next;
}
return [$a, $b, $a * $b == $prod];
}function productFib($prod) {
$a = 0; $b = 1;
while ($a * $b < $prod) {
$next = $a + $b;
$a = $b;
$b = $next;
}
return [$a, $b, $a * $b == $prod];
}function productFib(prod){
let [a, b] = [0, 1];
while(a * b < prod) [a, b] = [b, a + b];
return [a, b, a * b === prod];
}function productFib(prod){
var a = 1
var b = 1;
while (a*b < prod) {
var next = a+b;
a = b;
b = next;
}
return [a, b, a*b===prod];
}
