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Added memoization function in fibonacci (#5856)

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* Added memoization function in fibonacci

* Minor changes
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Jaydeep Das 2021-11-28 23:50:18 +05:30 committed by GitHub
parent f4a16f607b
commit 65d3cfff2f
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1 changed files with 44 additions and 4 deletions
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maths/fibonacci.py
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@ -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(n: int) -> list[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 @@ if __name__ == "__main__":
num = 20
time_func(fib_iterative, num)
time_func(fib_recursive, num)
time_func(fib_memoization, num)
time_func(fib_binet, num)