Recursion tree with Fibonacci -Python-

Question

I'm learning about recursion and I wrote this (inefficient) n'th Fibonacci number calculator:

def fibonacci(n):
    if n == 0:
        return 0
    elif n == 1:
        return 1
    else:
        return fibonacci(n-1) + fibonacci(n-2)

I know that in recursion, you can draw so called 'recursion trees'. When I made this simple binary generator:

def binary(length, outstr=""):
    if len(outstr) == length:
        print(outstr)
    else:
        for i in ["0", "1"]:
            binary(length, outstr + i)

I could figure out what this tree looks like:

But I cannot figure out the tree of the Fibonacci function! What would that tree look like?

Thanks in advance,

You can easily visualize recursive function using recursion-visualiser package in Python. Here is how to do it: stackoverflow.com/a/60126148/7552117 — Bishal Sarang
– Bishal Sarang, Commented Feb 8, 2020 at 11:26

k4ppa · Accepted Answer · 2015-11-19 16:15:08Z

4

For example fibonacci(4) gives the following recursive tree, because require two function call: fibonacci(3) and fibonacci(2), so every call to the function, call other two functions, until you reach the exit conditions.

            4
           / \
          /   \
         /     \
        3       2
       / \     / \
      /   \   /   \
     2     1 1     0
    / \
   /   \
  1     0

answered Nov 19, 2015 at 16:15

k4ppa

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1 Comment

user2092743 Over a year ago

Thanks, just what I needed!

Bishal Sarang · Accepted Answer · 2020-05-13 05:53:30Z

1

You can easily visualize any recursive function using recursion-visualiser package in Python. You just need to add decorator to your function and it does the rest.

Binary String

Let's do it for binary string first.

from visualiser.visualiser import Visualiser as vs

"""
Problem Link: https://stackoverflow.com/questions/33808653/recursion-tree- 
with-fibonacci-python/60126306#60126306
"""

@vs(node_properties_kwargs={"shape":"record", "color":"#f57542","style":"filled", "fillcolor":"grey"})
def binary(length, outstr=""):
     if len(outstr) == length:
          print(outstr)
     else:
          for i in ["0", "1"]:
               binary(length=length, outstr=outstr + i)

binary(length=3,outstr="")
vs.make_animation("binary_string.gif", delay=2)

Here is how output animation looks like

Also the final tree is saved as :

Fibonacci: Let's visualise it for fib(6)

# Import Visualiser class from module visualiser
from visualiser.visualiser import Visualiser as vs

# Add decorator
@vs(node_properties_kwargs={"shape":"record", "color":"#f57542", "style":"filled", "fillcolor":"grey"})
def fib(n):
    if n <= 1:
        return n
    return fib(n=n - 1) + fib(n=n-2)

def main():
    print(fib(n=6))
    vs.make_animation("fibonacci.gif", delay=2)

if __name__ == "__main__":
    main()

Here is the output which looks much better:

Here is the final image of the recursion tree:

Check out more examples at here

edited May 13, 2020 at 5:53

answered Feb 8, 2020 at 12:17

Bishal Sarang

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3 Comments

mLstudent33 Over a year ago

links are broken

mLstudent33 Over a year ago

Do I just need to put this anywhere on the script or in main? os.environ["PATH"] += os.pathsep + 'C:/Program Files (x86)/Graphviz2.38/bin/'

Bishal Sarang Over a year ago

You are required to download graphviz and add graphviz executable to PATH. You can do it manually from environment variables or alternatively add it using the above script . If you are installing from pip then the above process may not work. You may have to do it manually . Here is the link that can help you setup graphviz bobswift.atlassian.net/wiki/spaces/GVIZ/pages/20971549/… Feel free to open issue on github if any problem arises.

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