@@ -1,13 +1,19 @@
# fibonacci.py
"""
Calculates the Fibonacci sequence using iteration, recursion, and a simplified
form of Binet's formula
Calculates the Fibonacci sequence using iteration, recursion, memoization,
and a simplified form of Binet's formula
NOTE 1: the iterative and recursive functions are more accurate than the Binet's
formula function because the iterative function doesn't use floats
NOTE 1: the iterative, recursive, memoization functions are more accurate than
the Binet's formula function because the Binet formula function uses floats
NOTE 2: the Binet's formula function is much more limited in the size of inputs
that it can handle due to the size limitations of Python floats
RESULTS: (n = 20)
fib_iterative runtime: 0.0055 ms
fib_recursive runtime: 6.5627 ms
fib_memoization runtime: 0.0107 ms
fib_binet runtime: 0.0174 ms
"""
from math import sqrt
@@ -86,6 +92,39 @@ def fib_recursive_term(i: int) -> int:
return [fib_recursive_term (i ) for i in range (n + 1 )]
def fib_memoization (n : int ) -> list [int ]:
"""
Calculates the first n (0-indexed) Fibonacci numbers using memoization
>>> fib_memoization(0)
[0]
>>> fib_memoization(1)
[0, 1]
>>> fib_memoization(5)
[0, 1, 1, 2, 3, 5]
>>> fib_memoization(10)
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
>>> fib_iterative(-1)
Traceback (most recent call last):
...
Exception: n is negative
"""
if n < 0 :
raise Exception ("n is negative" )
# Cache must be outside recursuive function
# other it will reset every time it calls itself.
cache : dict [int , int ] = {0 : 0 , 1 : 1 , 2 : 1 } # Prefilled cache
def rec_fn_memoized (num : int ) -> int :
if num in cache :
return cache [num ]
value = rec_fn_memoized (num - 1 ) + rec_fn_memoized (num - 2 )
cache [num ] = value
return value
return [rec_fn_memoized (i ) for i in range (n + 1 )]
def fib_binet (n : int ) -> list [int ]:
"""
Calculates the first n (0-indexed) Fibonacci numbers using a simplified form
@@ -127,4 +166,5 @@ def fib_binet(n: int) -> list[int]:
num = 20
time_func (fib_iterative , num )
time_func (fib_recursive , num )
time_func (fib_memoization , num )
time_func (fib_binet , num )
