Python/maths/fibonacci.py
Christian Clauss 5f4da5d616
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Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
2020-07-06 09:44:19 +02:00

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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)