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b3d9281591
* Added algorithm for creating Hamming numbers series in Python * Changed to f-string format. * Added modifications * Update and rename hamming.py to hamming_numbers.py * Update hamming_numbers.py * Update hamming_numbers.py * Rename maths/series/hamming_numbers.py to maths/hamming_numbers.py Co-authored-by: John Law <johnlaw.po@gmail.com>
52 lines
1.7 KiB
Python
52 lines
1.7 KiB
Python
"""
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A Hamming number is a positive integer of the form 2^i*3^j*5^k, for some
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non-negative integers i, j, and k. They are often referred to as regular numbers.
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More info at: https://en.wikipedia.org/wiki/Regular_number.
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"""
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def hamming(n_element: int) -> list:
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"""
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This function creates an ordered list of n length as requested, and afterwards
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returns the last value of the list. It must be given a positive integer.
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:param n_element: The number of elements on the list
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:return: The nth element of the list
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>>> hamming(5)
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[1, 2, 3, 4, 5]
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>>> hamming(10)
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[1, 2, 3, 4, 5, 6, 8, 9, 10, 12]
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>>> hamming(15)
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[1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24]
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"""
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n_element = int(n_element)
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if n_element < 1:
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my_error = ValueError("a should be a positive number")
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raise my_error
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hamming_list = [1]
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i, j, k = (0, 0, 0)
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index = 1
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while index < n_element:
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while hamming_list[i] * 2 <= hamming_list[-1]:
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i += 1
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while hamming_list[j] * 3 <= hamming_list[-1]:
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j += 1
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while hamming_list[k] * 5 <= hamming_list[-1]:
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k += 1
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hamming_list.append(
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min(hamming_list[i] * 2, hamming_list[j] * 3, hamming_list[k] * 5)
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)
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index += 1
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return hamming_list
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if __name__ == "__main__":
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n = input("Enter the last number (nth term) of the Hamming Number Series: ")
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print("Formula of Hamming Number Series => 2^i * 3^j * 5^k")
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hamming_numbers = hamming(int(n))
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print("-----------------------------------------------------")
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print(f"The list with nth numbers is: {hamming_numbers}")
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print("-----------------------------------------------------")
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