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Create cached fibonacci algorithm (#8084)

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* feat: Add `fib_recursive_cached` func

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* doc: Show difference in time when caching algorithm

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Caeden Perelli-Harris 2023-01-07 16:56:39 +00:00 committed by GitHub
parent 32a1ff9359
commit 4939e8463f
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1 changed files with 37 additions and 2 deletions
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maths/fibonacci.py
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@ -16,6 +16,7 @@ fib_memoization runtime: 0.0107 ms
fib_binet runtime: 0.0174 ms
"""
from functools import lru_cache
from math import sqrt
from time import time
@ -92,6 +93,39 @@ def fib_recursive(n: int) -> list[int]:
return [fib_recursive_term(i) for i in range(n + 1)]
def fib_recursive_cached(n: int) -> list[int]:
"""
Calculates the first n (0-indexed) Fibonacci numbers using recursion
>>> fib_iterative(0)
[0]
>>> fib_iterative(1)
[0, 1]
>>> fib_iterative(5)
[0, 1, 1, 2, 3, 5]
>>> fib_iterative(10)
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
>>> fib_iterative(-1)
Traceback (most recent call last):
...
Exception: n is negative
"""
@lru_cache(maxsize=None)
def fib_recursive_term(i: int) -> int:
"""
Calculates the i-th (0-indexed) Fibonacci number using recursion
"""
if i < 0:
raise Exception("n is negative")
if i < 2:
return i
return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)
if n < 0:
raise Exception("n is negative")
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
@ -163,8 +197,9 @@ def fib_binet(n: int) -> list[int]:
if __name__ == "__main__":
num = 20
num = 30
time_func(fib_iterative, num)
time_func(fib_recursive, num)
time_func(fib_recursive, num) # Around 3s runtime
time_func(fib_recursive_cached, num) # Around 0ms runtime
time_func(fib_memoization, num)
time_func(fib_binet, num)