Can someone please explain this code to me?

Question

If num = 8 how would the process go?

num = int(input())

def fibonacci(n):
if n <= 1:
return n
else:
return fibonacci(n-1) + fibonacci(n-2)
for i in range(num):
print(fibonacci(i))

Answer 1

Ava Alford

For ex: n=5.
fib(5)
=>fib(5-2) +fib(5-1)
=> fib(3) + fib(4)
👇 👇
=>[ fib(3-2) + fib(3-1) ] + [ fib(4-2)+fib(4-1) ]

= >[ fib(1) + fib(2) ] + [ fib(2) +fib(3) ]

=>1 + fib(2-2)+ fib(2-1) +fib(2-2)+fib(2-1) +[ fib(1) + fib(2)]

=>1+fib(0)+fib(1)+ fib(0)+fib(1) + [ 1 + fib(2-2)+ fib(2-1)]

=>1+1+1+1+1+ [ 1+ fib(0)+ fib(1)]

=>5+ [ 1+1+1]

=> 5+3 = 8.

Here
5th number is 8 . Also you can see that 4th number is 5 and 3th number is 3

This is the way it been evaluted by code..

I had posted this in link earlier,
https://www.sololearn.com/discuss/2125616/?ref=app
Links have some other example, may help to understand I think.

Hope it helps..

Answer 2

If do it on paper you start with 1,1

1+1 = 2

1,1,2

1+2 = 3

1,1,2,3

2+3=5

1,1,2,3,5

3+5=8

1,1,2,3,5,8

And so on...

Hope this helps you.

Answer 3

Ava Alford

num = 8
fibonnaci(n) = F(n)

F(8)
/ \
F(7) F(6)
/ \ / \
F(6) F(5) F(5) F(4)

You can continue this tree until you get F(1) and F(0) on each branch.

F(0) returns 0 and F(1) returns 1
F(0) + F(1) = F(2) = 1
F(1) + F(2) = F(3) = 2
F(2) + F(3) = F(4) = 3
F(3) + F(4) = F(5) = 5
F(4) + F(5) = F(6) = 8
F(5) + F(6) = F(7) = 13
F(6) + F(7) = F(8) = 21

If n = 8 then you get 21 because 21 is the 8th fibonacci number.

n 0 1 2 3 4 5 6 7 8....
f 0 1 1 2 3 5 8 13 21....

Answer 4

Jayakrishna🇮🇳 thank you

Answer 5

Ava Alford

The other way around would be to say okay I want fibonacci(8) so let's start at 1,1 until I have 8 fibonacci numbers.
You would do this with a normal loop.

But here you say I want fibonacci(8), I don't know fibonacci(7) and fibonacci(6) but I know that f(8) is the sum of f(7) and f(6) (that's how fibonacci works f(n) = f(n-2) + f(n-1))
So each function call needs another function call until fibonacci(0) and fibonacci(1) are called. They return their values to the other function calls until fibonacci(8) get its value.
And this is how recursion works.

Answer 6

Jayakrishna🇮🇳 so I almost understand it. Can you please run me through how the code would work if num = 8? I'm having issues with that.

Answer 7

https://www.sololearn.com/discuss/2125616/?ref=app
https://www.sololearn.com/discuss/2222560/?ref=app
https://www.sololearn.com/discuss/2389918/?ref=app

Ava Alford
hope these helps.. go through ones.. I have already added explaination in those for some samples.. with step by steps..
hope it helps to understand it..

Answer 8

For 8:
1, 1, 2, 3, 5, 8, 13, 21
21 you get.

Ava Alford You're welcome..

Answer 9

Jayakrishna🇮🇳 I mean how do you 8 from 3 and 5 with the code? When I work through it on paper I always get 7 which I know is incorrect

Answer 10

How 7 ?

3+5 = 8 Is not it?

Answer 11

I understand the math behind it. I'm trying to work through how the code does that math

Answer 12

Fibonacci Sequence starts with n = 0, 1, 2, 3, 4, 5, 6, 7, 8,...
this then gives:
0, 1, 1, 2, 3, 5, 8, 13, 21,...

That is at:

n = 0, it has 0
n = 1, it has 1
n = 2, it has 1
n = 3, it has 2
n = 4, it has 3
n = 5, it has 5
n = 6, it has 8

This shows that from n = 3 upward, the current no is the sum of the two preceding nos.

Also, setting the initial condition is also important as the sequence starts from n = 0.

Hence the initial conditions of

If n = 0: return 0;
if n = 1: return 1; and
if n = 2: return 1;
ought to be set as displayed below:

n = int(input("Enter the n value: "));
def fib(n):
if n == 0:
return 0;
elif n == 1 or n == 2:
return 1;
else:
y = fib(n-1) + fib(n-2);
return y;
print(fib(n));

Answer 13

Why your expectation is 0110 ? Can you explain your understandings..!!

Fibonachi series is " curent value is sum of precious two terms...
1 1 2 3...
1 1 are initial values and
2 is 1+1
3 is 2+1 .. Sum of privious 2 terms...
Hope it helps...