HaimLeshem - 2 months ago 13

Python Question

I have a function that is defined in this way:

`F(n) = n`

`if n<=3`

`F(n) = F(n-1) + 2 * F(n-2) + 3 * F(n-3)`

`if n>3`

Now, I've written it as a recursive function and it works fine.

I'm trying to write it as an iterative function but i cant seem to make it happen.

The output should be, for example:

`print(FRec(5)) => 22`

print(FRec(10)) => 1657

print(FRec(15)) => 124905

Any tips?

Here is my recursive implementation:

`def FRec(n):`

if(n <= 3):

return n

if(n > 3):

return FRec(n - 1) + 2 * FRec(n - 2) + 3 * FRec(n - 3)

Answer

All you need is keep the last 3 results:

```
from collections import deque
def F_iter(n):
if n <= 3:
return n
prev = deque([1, 2, 3], maxlen=3)
for i in range(4, n + 1):
result = prev[-1] + 2 * prev[-2] + 3 * prev[-3]
prev.append(result)
return prev[-1]
```

If a `deque`

is not 'available' to you, then you can inefficiently replace that with some list slicing and concatenation:

```
prev = [1, 2, 3]
for i in range(4, n + 1):
result = prev[-1] + 2 * prev[-2] + 3 * prev[-3]
prev = prev[1:] + [result]
```

Demo:

```
>>> F_iter(5)
22
>>> F_iter(10)
1657
>>> F_iter(15)
124905
```