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(714) # should return {21, 34, 1},
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".
function productFib(prod){
// ...
const f = (n) => {
let phi = (1 + Math.sqrt(5)) / 2;
return Math.round(Math.pow(phi, n) / Math.sqrt(5))
}
for (let i = 0; i < Math.sqrt(prod)/2 ; i++) {
if (f(i) * f(i+1) === prod) return [f(i), f(i+1), true]
if (f(i) * f(i+1) < prod && f(i+1) * f(i+2) > prod) return [f(i+1), f(i+2), false]
}
return;
}