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267b5eff40
* Added doctest and more explanation about Dijkstra execution. * tests were not passing with python2 due to missing __init__.py file at number_theory folder * Removed the dot at the beginning of the imported modules names because 'python3 -m doctest -v data_structures/hashing/*.py' and 'python3 -m doctest -v data_structures/stacks/*.py' were failing not finding hash_table.py and stack.py modules. * Moved global code to main scope and added doctest for project euler problems 1 to 14. * Added test case for negative input. * Changed N variable to do not use end of line scape because in case there is a space after it the script will break making it much more error prone. * Added problems description and doctests to the ones that were missing. Limited line length to 79 and executed python black over all scripts. * Changed the way files are loaded to support pytest call. * Added __init__.py to problems to make them modules and allow pytest execution. * Added project_euler folder to test units execution * Changed 'os.path.split(os.path.realpath(__file__))' to 'os.path.dirname()'
74 lines
1.9 KiB
Python
74 lines
1.9 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Problem Statement:
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The following iterative sequence is defined for the set of positive integers:
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n → n/2 (n is even)
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n → 3n + 1 (n is odd)
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Using the rule above and starting with 13, we generate the following sequence:
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13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
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It can be seen that this sequence (starting at 13 and finishing at 1) contains
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10 terms. Although it has not been proved yet (Collatz Problem), it is thought
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that all starting numbers finish at 1.
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Which starting number, under one million, produces the longest chain?
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"""
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from __future__ import print_function
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try:
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raw_input # Python 2
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except NameError:
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raw_input = input # Python 3
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def solution(n):
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"""Returns the number under n that generates the longest sequence using the
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formula:
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n → n/2 (n is even)
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n → 3n + 1 (n is odd)
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>>> solution(1000000)
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{'counter': 525, 'largest_number': 837799}
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>>> solution(200)
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{'counter': 125, 'largest_number': 171}
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>>> solution(5000)
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{'counter': 238, 'largest_number': 3711}
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>>> solution(15000)
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{'counter': 276, 'largest_number': 13255}
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"""
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largest_number = 0
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pre_counter = 0
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for input1 in range(n):
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counter = 1
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number = input1
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while number > 1:
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if number % 2 == 0:
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number /= 2
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counter += 1
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else:
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number = (3 * number) + 1
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counter += 1
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if counter > pre_counter:
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largest_number = input1
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pre_counter = counter
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return {"counter": pre_counter, "largest_number": largest_number}
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if __name__ == "__main__":
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result = solution(int(raw_input().strip()))
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print(
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(
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"Largest Number:",
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result["largest_number"],
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"->",
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result["counter"],
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"digits",
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)
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)
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