mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-24 12:10:16 +00:00
5f4da5d616
* updating DIRECTORY.md
* isort --profile black .
* Black after
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
131 lines
3.5 KiB
Python
131 lines
3.5 KiB
Python
# fibonacci.py
|
|
"""
|
|
1. Calculates the iterative fibonacci sequence
|
|
|
|
2. Calculates the fibonacci sequence with a formula
|
|
an = [ Phin - (phi)n ]/Sqrt[5]
|
|
reference-->Su, Francis E., et al. "Fibonacci Number Formula." Math Fun Facts.
|
|
<http://www.math.hmc.edu/funfacts>
|
|
"""
|
|
import functools
|
|
import math
|
|
import time
|
|
from decimal import Decimal, getcontext
|
|
|
|
getcontext().prec = 100
|
|
|
|
|
|
def timer_decorator(func):
|
|
@functools.wraps(func)
|
|
def timer_wrapper(*args, **kwargs):
|
|
start = time.time()
|
|
func(*args, **kwargs)
|
|
end = time.time()
|
|
if int(end - start) > 0:
|
|
print(f"Run time for {func.__name__}: {(end - start):0.2f}s")
|
|
else:
|
|
print(f"Run time for {func.__name__}: {(end - start)*1000:0.2f}ms")
|
|
return func(*args, **kwargs)
|
|
|
|
return timer_wrapper
|
|
|
|
|
|
# define Python user-defined exceptions
|
|
class Error(Exception):
|
|
"""Base class for other exceptions"""
|
|
|
|
|
|
class ValueTooLargeError(Error):
|
|
"""Raised when the input value is too large"""
|
|
|
|
|
|
class ValueTooSmallError(Error):
|
|
"""Raised when the input value is not greater than one"""
|
|
|
|
|
|
class ValueLessThanZero(Error):
|
|
"""Raised when the input value is less than zero"""
|
|
|
|
|
|
def _check_number_input(n, min_thresh, max_thresh=None):
|
|
"""
|
|
:param n: single integer
|
|
:type n: int
|
|
:param min_thresh: min threshold, single integer
|
|
:type min_thresh: int
|
|
:param max_thresh: max threshold, single integer
|
|
:type max_thresh: int
|
|
:return: boolean
|
|
"""
|
|
try:
|
|
if n >= min_thresh and max_thresh is None:
|
|
return True
|
|
elif min_thresh <= n <= max_thresh:
|
|
return True
|
|
elif n < 0:
|
|
raise ValueLessThanZero
|
|
elif n < min_thresh:
|
|
raise ValueTooSmallError
|
|
elif n > max_thresh:
|
|
raise ValueTooLargeError
|
|
except ValueLessThanZero:
|
|
print("Incorrect Input: number must not be less than 0")
|
|
except ValueTooSmallError:
|
|
print(
|
|
f"Incorrect Input: input number must be > {min_thresh} for the recursive "
|
|
"calculation"
|
|
)
|
|
except ValueTooLargeError:
|
|
print(
|
|
f"Incorrect Input: input number must be < {max_thresh} for the recursive "
|
|
"calculation"
|
|
)
|
|
return False
|
|
|
|
|
|
@timer_decorator
|
|
def fib_iterative(n):
|
|
"""
|
|
:param n: calculate Fibonacci to the nth integer
|
|
:type n:int
|
|
:return: Fibonacci sequence as a list
|
|
"""
|
|
n = int(n)
|
|
if _check_number_input(n, 2):
|
|
seq_out = [0, 1]
|
|
a, b = 0, 1
|
|
for _ in range(n - len(seq_out)):
|
|
a, b = b, a + b
|
|
seq_out.append(b)
|
|
return seq_out
|
|
|
|
|
|
@timer_decorator
|
|
def fib_formula(n):
|
|
"""
|
|
:param n: calculate Fibonacci to the nth integer
|
|
:type n:int
|
|
:return: Fibonacci sequence as a list
|
|
"""
|
|
seq_out = [0, 1]
|
|
n = int(n)
|
|
if _check_number_input(n, 2, 1000000):
|
|
sqrt = Decimal(math.sqrt(5))
|
|
phi_1 = Decimal(1 + sqrt) / Decimal(2)
|
|
phi_2 = Decimal(1 - sqrt) / Decimal(2)
|
|
for i in range(2, n):
|
|
temp_out = ((phi_1 ** Decimal(i)) - (phi_2 ** Decimal(i))) * (
|
|
Decimal(sqrt) ** Decimal(-1)
|
|
)
|
|
seq_out.append(int(temp_out))
|
|
return seq_out
|
|
|
|
|
|
if __name__ == "__main__":
|
|
num = 20
|
|
# print(f'{fib_recursive(num)}\n')
|
|
# print(f'{fib_iterative(num)}\n')
|
|
# print(f'{fib_formula(num)}\n')
|
|
fib_iterative(num)
|
|
fib_formula(num)
|