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# Product of consecutive Fib numbers

## [Product of consecutive Fib numbers](https://www.codewars.com/kata/5541f58a944b85ce6d00006a)

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(m) verifying `F(m) * F(m+1) = prod`you will return

```
[F(m), F(m+1), false] or {F(n), F(n+1), 0} or (F(n), F(n+1), False)
```

F(m) being the smallest one such as `F(m) * F(m+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".

## Solutions

#### 🧠 C++

```cpp
#include <vector>
typedef unsigned long long ull;
class ProdFib
{
public:
  static std::vector<ull> productFib(ull prod)
  {
    return fib_till_max(0,1,prod);
  }

  static std::vector<ull> fib_till_max(ull x1, ull x2, ull n)
  {
    static ull a,b;

    a = x1; b = x2;

    if(x1*x2 < n)
      fib_till_max(x2, x1+x2, n);

    return {a,b, int(a*b == n)};

  }
};
```


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