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75 lines
2.3 KiB
Python
75 lines
2.3 KiB
Python
"""
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This is a pure Python implementation of the Geometric Series algorithm
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https://en.wikipedia.org/wiki/Geometric_series
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Run the doctests with the following command:
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python3 -m doctest -v geometric_series.py
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or
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python -m doctest -v geometric_series.py
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For manual testing run:
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python3 geometric_series.py
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"""
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from __future__ import annotations
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def geometric_series(
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nth_term: float,
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start_term_a: float,
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common_ratio_r: float,
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) -> list[float]:
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"""
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Pure Python implementation of Geometric Series algorithm
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:param nth_term: The last term (nth term of Geometric Series)
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:param start_term_a : The first term of Geometric Series
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:param common_ratio_r : The common ratio between all the terms
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:return: The Geometric Series starting from first term a and multiple of common
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ration with first term with increase in power till last term (nth term)
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Examples:
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>>> geometric_series(4, 2, 2)
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[2, 4.0, 8.0, 16.0]
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>>> geometric_series(4.0, 2.0, 2.0)
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[2.0, 4.0, 8.0, 16.0]
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>>> geometric_series(4.1, 2.1, 2.1)
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[2.1, 4.41, 9.261000000000001, 19.448100000000004]
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>>> geometric_series(4, 2, -2)
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[2, -4.0, 8.0, -16.0]
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>>> geometric_series(4, -2, 2)
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[-2, -4.0, -8.0, -16.0]
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>>> geometric_series(-4, 2, 2)
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[]
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>>> geometric_series(0, 100, 500)
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[]
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>>> geometric_series(1, 1, 1)
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[1]
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>>> geometric_series(0, 0, 0)
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[]
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"""
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if not all((nth_term, start_term_a, common_ratio_r)):
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return []
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series: list[float] = []
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power = 1
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multiple = common_ratio_r
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for _ in range(int(nth_term)):
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if not series:
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series.append(start_term_a)
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else:
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power += 1
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series.append(float(start_term_a * multiple))
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multiple = pow(float(common_ratio_r), power)
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return series
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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nth_term = float(input("Enter the last number (n term) of the Geometric Series"))
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start_term_a = float(input("Enter the starting term (a) of the Geometric Series"))
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common_ratio_r = float(
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input("Enter the common ratio between two terms (r) of the Geometric Series")
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)
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print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
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print(geometric_series(nth_term, start_term_a, common_ratio_r))
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