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Merge maths/fibonacci.py and maths/fibonacci_sequence_recursion.py (#5738)
* Rewrite parts of Vector and Matrix methods * Refactor determinant method and add unit tests Refactor determinant method to create separate minor and cofactor methods. Add respective unit tests for new methods. Rename methods using snake case to follow Python naming conventions. * Reorganize Vector and Matrix methods * Update linear_algebra/README.md Co-authored-by: John Law <johnlaw.po@gmail.com> * Fix punctuation and wording * Apply suggestions from code review Co-authored-by: John Law <johnlaw.po@gmail.com> * Deduplicate euclidean length method for Vector * Add more unit tests for Euclidean length method * Fix bug in unit test for euclidean_length * Remove old comments for magnitude method * Rewrite maths/fibonacci.py * Rewrite timer and add unit tests * Fix typos in fib_binet unit tests * Fix typos in fib_binet unit tests * Clean main method * Merge fibonacci.py and fibonacci_sequence_recursion.py * Fix fib_binet unit test Co-authored-by: John Law <johnlaw.po@gmail.com>
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Tianyi Zheng
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# fibonacci.py
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"""
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1. Calculates the iterative fibonacci sequence
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Calculates the Fibonacci sequence using iteration, recursion, and a simplified
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form of Binet's formula
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2. Calculates the fibonacci sequence with a formula
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an = [ Phin - (phi)n ]/Sqrt[5]
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reference-->Su, Francis E., et al. "Fibonacci Number Formula." Math Fun Facts.
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<http://www.math.hmc.edu/funfacts>
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NOTE 1: the iterative and recursive functions are more accurate than the Binet's
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formula function because the iterative function doesn't use 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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"""
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import functools
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import math
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import time
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from decimal import Decimal, getcontext
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getcontext().prec = 100
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from math import sqrt
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from time import time
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def timer_decorator(func):
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@functools.wraps(func)
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def timer_wrapper(*args, **kwargs):
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start = time.time()
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func(*args, **kwargs)
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end = time.time()
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if int(end - start) > 0:
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print(f"Run time for {func.__name__}: {(end - start):0.2f}s")
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else:
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print(f"Run time for {func.__name__}: {(end - start)*1000:0.2f}ms")
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return func(*args, **kwargs)
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return timer_wrapper
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# define Python user-defined exceptions
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class Error(Exception):
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"""Base class for other exceptions"""
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class ValueTooLargeError(Error):
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"""Raised when the input value is too large"""
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class ValueTooSmallError(Error):
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"""Raised when the input value is not greater than one"""
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class ValueLessThanZero(Error):
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"""Raised when the input value is less than zero"""
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def _check_number_input(n, min_thresh, max_thresh=None):
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def time_func(func, *args, **kwargs):
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"""
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:param n: single integer
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:type n: int
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:param min_thresh: min threshold, single integer
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:type min_thresh: int
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:param max_thresh: max threshold, single integer
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:type max_thresh: int
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:return: boolean
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Times the execution of a function with parameters
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"""
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try:
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if n >= min_thresh and max_thresh is None:
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return True
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elif min_thresh <= n <= max_thresh:
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return True
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elif n < 0:
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raise ValueLessThanZero
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elif n < min_thresh:
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raise ValueTooSmallError
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elif n > max_thresh:
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raise ValueTooLargeError
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except ValueLessThanZero:
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print("Incorrect Input: number must not be less than 0")
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except ValueTooSmallError:
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print(
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f"Incorrect Input: input number must be > {min_thresh} for the recursive "
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"calculation"
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)
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except ValueTooLargeError:
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print(
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f"Incorrect Input: input number must be < {max_thresh} for the recursive "
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"calculation"
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)
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return False
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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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@timer_decorator
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def fib_iterative(n):
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def fib_iterative(n: int) -> list[int]:
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"""
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:param n: calculate Fibonacci to the nth integer
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:type n:int
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:return: Fibonacci sequence as a list
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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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Exception: n is negative
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"""
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n = int(n)
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if _check_number_input(n, 2):
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seq_out = [0, 1]
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a, b = 0, 1
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for _ in range(n - len(seq_out)):
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a, b = b, a + b
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seq_out.append(b)
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return seq_out
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if n < 0:
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raise Exception("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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@timer_decorator
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def fib_formula(n):
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def fib_recursive(n: int) -> list[int]:
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"""
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:param n: calculate Fibonacci to the nth integer
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:type n:int
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:return: Fibonacci sequence as a list
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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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Exception: n is negative
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"""
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seq_out = [0, 1]
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n = int(n)
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if _check_number_input(n, 2, 1000000):
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sqrt = Decimal(math.sqrt(5))
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phi_1 = Decimal(1 + sqrt) / Decimal(2)
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phi_2 = Decimal(1 - sqrt) / Decimal(2)
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for i in range(2, n):
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temp_out = ((phi_1 ** Decimal(i)) - (phi_2 ** Decimal(i))) * (
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Decimal(sqrt) ** Decimal(-1)
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)
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seq_out.append(int(temp_out))
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return seq_out
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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 Exception("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 Exception("n is negative")
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return [fib_recursive_term(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 overflows on n >= 1475 because of the size limitations
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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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Exception: 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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Exception: n is too large
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"""
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if n < 0:
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raise Exception("n is negative")
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if n >= 1475:
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raise Exception("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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num = 20
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# print(f'{fib_recursive(num)}\n')
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# print(f'{fib_iterative(num)}\n')
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# print(f'{fib_formula(num)}\n')
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fib_iterative(num)
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fib_formula(num)
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time_func(fib_iterative, num)
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time_func(fib_recursive, num)
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time_func(fib_binet, num)
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@ -1,22 +0,0 @@
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# Fibonacci Sequence Using Recursion
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def recur_fibo(n: int) -> int:
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"""
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>>> [recur_fibo(i) for i in range(12)]
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[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
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"""
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return n if n <= 1 else recur_fibo(n - 1) + recur_fibo(n - 2)
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def main() -> None:
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limit = int(input("How many terms to include in fibonacci series: "))
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if limit > 0:
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print(f"The first {limit} terms of the fibonacci series are as follows:")
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print([recur_fibo(n) for n in range(limit)])
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else:
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print("Please enter a positive integer: ")
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if __name__ == "__main__":
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main()
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