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Update fast_fibonacci.py (#1889)

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* Update fast_fibonacci.py

* Update fast_fibonacci.py

Co-authored-by: Christian Clauss <cclauss@me.com>
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Sanders Lin 2020-05-20 01:31:52 +08:00 committed by GitHub
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commit 777ddca2e9
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1 changed files with 20 additions and 27 deletions
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dynamic_programming/fast_fibonacci.py
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@ -1,44 +1,37 @@
#!/usr/bin/python
#!/usr/bin/env python3
"""
This program calculates the nth Fibonacci number in O(log(n)).
It's possible to calculate F(1000000) in less than a second.
It's possible to calculate F(1_000_000) in less than a second.
"""
import sys
from typing import Tuple
# returns F(n)
def fibonacci(n: int): # noqa: E999 This syntax is Python 3 only
def fibonacci(n: int) -> int:
"""
return F(n)
>>> [fibonacci(i) for i in range(13)]
[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]
"""
if n < 0:
raise ValueError("Negative arguments are not supported")
return _fib(n)[0]
# returns (F(n), F(n-1))
def _fib(n: int): # noqa: E999 This syntax is Python 3 only
if n == 0:
# (F(0), F(1))
def _fib(n: int) -> Tuple[int, int]:
if n == 0: # (F(0), F(1))
return (0, 1)
else:
# F(2n) = F(n)[2F(n+1) − F(n)]
# F(2n+1) = F(n+1)^2+F(n)^2
a, b = _fib(n // 2)
c = a * (b * 2 - a)
d = a * a + b * b
if n % 2 == 0:
return (c, d)
else:
return (d, c + d)
return (d, c + d) if n % 2 else (c, d)
if __name__ == "__main__":
args = sys.argv[1:]
if len(args) != 1:
print("Too few or too much parameters given.")
exit(1)
try:
n = int(args[0])
except ValueError:
print("Could not convert data to an integer.")
exit(1)
print("F(%d) = %d" % (n, fibonacci(n)))
n = int(sys.argv[1])
print(f"fibonacci({n}) is {fibonacci(n)}")