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* Add solution to problem 74 * Fix typo * Edit unnecessary comment * Rename folder, add default params in solution() * Rename file to solve conflicts * Fix doctests
117 lines
3.1 KiB
Python
117 lines
3.1 KiB
Python
"""
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Project Euler Problem 074: https://projecteuler.net/problem=74
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Starting from any positive integer number
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it is possible to attain another one summing the factorial of its digits.
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Repeating this step, we can build chains of numbers.
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It is not difficult to prove that EVERY starting number
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will eventually get stuck in a loop.
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The request is to find how many numbers less than one million
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produce a chain with exactly 60 non repeating items.
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Solution approach:
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This solution simply consists in a loop that generates
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the chains of non repeating items.
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The generation of the chain stops before a repeating item
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or if the size of the chain is greater then the desired one.
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After generating each chain, the length is checked and the counter increases.
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"""
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def factorial(a: int) -> int:
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"""Returns the factorial of the input a
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>>> factorial(5)
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120
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>>> factorial(6)
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720
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>>> factorial(0)
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1
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"""
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# The factorial function is not defined for negative numbers
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if a < 0:
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raise ValueError("Invalid negative input!", a)
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# The case of 0! is handled separately
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if a == 0:
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return 1
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else:
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# use a temporary support variable to store the computation
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temporary_computation = 1
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while a > 0:
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temporary_computation *= a
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a -= 1
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return temporary_computation
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def factorial_sum(a: int) -> int:
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"""Function to perform the sum of the factorial
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of all the digits in a
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>>> factorial_sum(69)
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363600
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"""
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# Prepare a variable to hold the computation
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fact_sum = 0
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""" Convert a in string to iterate on its digits
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convert the digit back into an int
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and add its factorial to fact_sum.
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"""
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for i in str(a):
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fact_sum += factorial(int(i))
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return fact_sum
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def solution(chain_length: int = 60, number_limit: int = 1000000) -> int:
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"""Returns the number of numbers that produce
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chains with exactly 60 non repeating elements.
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>>> solution(60,1000000)
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402
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>>> solution(15,1000000)
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17800
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"""
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# the counter for the chains with the exact desired length
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chain_counter = 0
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for i in range(1, number_limit + 1):
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# The temporary list will contain the elements of the chain
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chain_list = [i]
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# The new element of the chain
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new_chain_element = factorial_sum(chain_list[-1])
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""" Stop computing the chain when you find a repeating item
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or the length it greater then the desired one.
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"""
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while not (new_chain_element in chain_list) and (
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len(chain_list) <= chain_length
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):
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chain_list += [new_chain_element]
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new_chain_element = factorial_sum(chain_list[-1])
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""" If the while exited because the chain list contains the exact amount of elements
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increase the counter
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"""
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chain_counter += len(chain_list) == chain_length
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return chain_counter
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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print(f"{solution()}")
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