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* add a yiled method to fibonaci * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * fibonaci * Update fibonacci.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update fibonacci.py --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
245 lines
6.6 KiB
Python
245 lines
6.6 KiB
Python
"""
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Calculates the Fibonacci sequence using iteration, recursion, memoization,
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and a simplified form of Binet's formula
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NOTE 1: the iterative, recursive, memoization functions are more accurate than
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the Binet's formula function because the Binet formula function uses floats
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NOTE 2: the Binet's formula function is much more limited in the size of inputs
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that it can handle due to the size limitations of Python floats
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See benchmark numbers in __main__ for performance comparisons/
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https://en.wikipedia.org/wiki/Fibonacci_number for more information
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"""
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import functools
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from collections.abc import Iterator
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from math import sqrt
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from time import time
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def time_func(func, *args, **kwargs):
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"""
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Times the execution of a function with parameters
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"""
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start = time()
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output = func(*args, **kwargs)
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end = time()
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if int(end - start) > 0:
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print(f"{func.__name__} runtime: {(end - start):0.4f} s")
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else:
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print(f"{func.__name__} runtime: {(end - start) * 1000:0.4f} ms")
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return output
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def fib_iterative_yield(n: int) -> Iterator[int]:
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"""
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Calculates the first n (1-indexed) Fibonacci numbers using iteration with yield
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>>> list(fib_iterative_yield(0))
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[0]
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>>> tuple(fib_iterative_yield(1))
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(0, 1)
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>>> tuple(fib_iterative_yield(5))
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(0, 1, 1, 2, 3, 5)
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>>> tuple(fib_iterative_yield(10))
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(0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55)
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>>> tuple(fib_iterative_yield(-1))
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Traceback (most recent call last):
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...
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ValueError: n is negative
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"""
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if n < 0:
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raise ValueError("n is negative")
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a, b = 0, 1
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yield a
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for _ in range(n):
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yield b
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a, b = b, a + b
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def fib_iterative(n: int) -> list[int]:
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"""
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Calculates the first n (0-indexed) Fibonacci numbers using iteration
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>>> fib_iterative(0)
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[0]
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>>> fib_iterative(1)
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[0, 1]
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>>> fib_iterative(5)
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[0, 1, 1, 2, 3, 5]
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>>> fib_iterative(10)
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> fib_iterative(-1)
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Traceback (most recent call last):
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...
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ValueError: n is negative
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"""
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if n < 0:
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raise ValueError("n is negative")
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if n == 0:
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return [0]
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fib = [0, 1]
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for _ in range(n - 1):
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fib.append(fib[-1] + fib[-2])
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return fib
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def fib_recursive(n: int) -> list[int]:
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"""
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Calculates the first n (0-indexed) Fibonacci numbers using recursion
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>>> fib_iterative(0)
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[0]
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>>> fib_iterative(1)
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[0, 1]
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>>> fib_iterative(5)
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[0, 1, 1, 2, 3, 5]
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>>> fib_iterative(10)
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> fib_iterative(-1)
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Traceback (most recent call last):
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...
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ValueError: n is negative
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"""
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def fib_recursive_term(i: int) -> int:
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"""
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Calculates the i-th (0-indexed) Fibonacci number using recursion
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>>> fib_recursive_term(0)
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0
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>>> fib_recursive_term(1)
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1
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>>> fib_recursive_term(5)
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5
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>>> fib_recursive_term(10)
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55
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>>> fib_recursive_term(-1)
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Traceback (most recent call last):
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...
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Exception: n is negative
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"""
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if i < 0:
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raise ValueError("n is negative")
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if i < 2:
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return i
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return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)
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if n < 0:
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raise ValueError("n is negative")
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return [fib_recursive_term(i) for i in range(n + 1)]
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def fib_recursive_cached(n: int) -> list[int]:
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"""
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Calculates the first n (0-indexed) Fibonacci numbers using recursion
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>>> fib_iterative(0)
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[0]
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>>> fib_iterative(1)
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[0, 1]
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>>> fib_iterative(5)
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[0, 1, 1, 2, 3, 5]
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>>> fib_iterative(10)
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> fib_iterative(-1)
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Traceback (most recent call last):
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...
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ValueError: n is negative
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"""
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@functools.cache
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def fib_recursive_term(i: int) -> int:
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"""
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Calculates the i-th (0-indexed) Fibonacci number using recursion
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"""
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if i < 0:
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raise ValueError("n is negative")
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if i < 2:
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return i
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return fib_recursive_term(i - 1) + fib_recursive_term(i - 2)
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if n < 0:
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raise ValueError("n is negative")
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return [fib_recursive_term(i) for i in range(n + 1)]
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def fib_memoization(n: int) -> list[int]:
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"""
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Calculates the first n (0-indexed) Fibonacci numbers using memoization
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>>> fib_memoization(0)
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[0]
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>>> fib_memoization(1)
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[0, 1]
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>>> fib_memoization(5)
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[0, 1, 1, 2, 3, 5]
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>>> fib_memoization(10)
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> fib_iterative(-1)
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Traceback (most recent call last):
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...
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ValueError: n is negative
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"""
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if n < 0:
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raise ValueError("n is negative")
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# Cache must be outside recursuive function
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# other it will reset every time it calls itself.
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cache: dict[int, int] = {0: 0, 1: 1, 2: 1} # Prefilled cache
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def rec_fn_memoized(num: int) -> int:
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if num in cache:
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return cache[num]
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value = rec_fn_memoized(num - 1) + rec_fn_memoized(num - 2)
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cache[num] = value
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return value
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return [rec_fn_memoized(i) for i in range(n + 1)]
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def fib_binet(n: int) -> list[int]:
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"""
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Calculates the first n (0-indexed) Fibonacci numbers using a simplified form
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of Binet's formula:
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https://en.m.wikipedia.org/wiki/Fibonacci_number#Computation_by_rounding
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NOTE 1: this function diverges from fib_iterative at around n = 71, likely
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due to compounding floating-point arithmetic errors
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NOTE 2: this function doesn't accept n >= 1475 because it overflows
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thereafter due to the size limitations of Python floats
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>>> fib_binet(0)
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[0]
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>>> fib_binet(1)
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[0, 1]
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>>> fib_binet(5)
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[0, 1, 1, 2, 3, 5]
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>>> fib_binet(10)
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
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>>> fib_binet(-1)
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Traceback (most recent call last):
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...
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ValueError: n is negative
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>>> fib_binet(1475)
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Traceback (most recent call last):
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...
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ValueError: n is too large
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"""
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if n < 0:
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raise ValueError("n is negative")
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if n >= 1475:
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raise ValueError("n is too large")
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sqrt_5 = sqrt(5)
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phi = (1 + sqrt_5) / 2
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return [round(phi**i / sqrt_5) for i in range(n + 1)]
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if __name__ == "__main__":
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from doctest import testmod
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testmod()
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# Time on an M1 MacBook Pro -- Fastest to slowest
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num = 30
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time_func(fib_iterative_yield, num) # 0.0012 ms
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time_func(fib_iterative, num) # 0.0031 ms
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time_func(fib_binet, num) # 0.0062 ms
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time_func(fib_memoization, num) # 0.0100 ms
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time_func(fib_recursive_cached, num) # 0.0153 ms
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time_func(fib_recursive, num) # 257.0910 ms
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