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""" |
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Project Euler Problem 19: Counting Sundays |
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========================================== |
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.. module:: solutions.problem19 |
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:synopsis: My solution to problem #19. |
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The source code for this problem can be |
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`found here <https://bitbucket.org/nekedome/project-euler/src/master/solutions/problem19.py>`_. |
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Problem Statement |
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################# |
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You are given the following information, but you may prefer to do some research for yourself. |
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* 1 Jan 1900 was a Monday. |
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* |
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| Thirty days has September, |
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| April, June and November. |
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| All the rest have thirty-one, |
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| Saving February alone, |
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| Which has twenty-eight, rain or shine. |
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| And on leap years, twenty-nine. |
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* A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400. |
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How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)? |
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Solution Discussion |
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################### |
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We could use Python's datetime module, but that feels too much like cheating :raw-html:`☺` |
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Instead, the above information will be used to count the number of Sundays falling on the first of the month. |
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Solution Implementation |
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####################### |
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.. literalinclude:: ../../solutions/problem19.py |
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:language: python |
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:lines: 44- |
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""" |
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class Date(object): |
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""" A simple date abstraction representing a dd/mm/yyyy |
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.. note:: the parameters are numbered in the natural way; i.e. ``day`` takes the range :math:`[1,31]`, ``month`` |
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takes the range :math:`[1,12]` and ``year`` takes the range :math:`[0, 9999]`. |
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:param day: the initial date value (day, or dd) |
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:param month: the initial date value (month, or mm) |
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:param year: the initial date value (year, or yyyy) |
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""" |
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def __init__(self, day: int, month: int, year: int): |
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# Basic parameter validation |
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assert isinstance(day, int), "day must be an integer" |
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assert isinstance(month, int), "month must be an integer" |
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assert isinstance(year, int), "year must be an integer" |
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assert 1 <= day <= 31, "day must be in [1, 31]" |
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assert 1 <= month <= 12, "month must be in [1, 12]" |
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assert 0 <= year <= 9999, "year must be in [0, 9999]" |
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# Store the initial date provided |
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self.day = day |
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self.month = month |
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self.year = year |
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def __str__(self): |
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""" String representation of a Date object """ |
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return "{}/{}/{}".format(self.day, self.month, self.year) |
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def __le__(self, other: 'Date') -> bool: |
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""" Test whether this ``Date`` instance is less than or equal to the `other` ``Date`` instance |
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:param other: the ``Date`` instance to compare against |
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:return: ``True`` if the current ``Date`` is equal to or before the `other` ``Date`` instance |
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:return: ``False`` otherwise |
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""" |
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if isinstance(other, Date): |
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if self.year < other.year: |
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return True # earlier year |
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elif self.year == other.year and self.month < other.month: |
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return True # same year, earlier month |
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elif self.month == other.month and self.day < other.day: |
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return True # same year, same month, earlier day |
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return False # any other case |
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def __add__(self, other: int) -> 'Date': |
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""" Addition operator |
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This class allows for integer values to be added to it. Semantically, this represents adding that integer number |
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of days to the current date value stored. The new date value will be returned by this operator. |
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:param other: the number of days to add to this ``Date`` instance |
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:return: a new ``Date`` instance with `other` days added to the current value |
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""" |
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if not isinstance(other, int): |
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raise TypeError("unsupported operand type(s) for +") |
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rv = Date(self.day, self.month, self.year) # build new Date instance with the same value |
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if rv.day + other > Date.days_to_a_month(rv.month, rv.year): |
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other -= Date.days_to_a_month(rv.month, rv.year) - rv.day |
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rv.day = 0 |
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rv.month += 1 |
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if rv.month > 12: |
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rv.month = 1 |
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rv.year += 1 |
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rv.day += other |
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return rv |
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@staticmethod |
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def leap_year(year: int) -> bool: |
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""" Test whether the given `year` is a leap-year |
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:param year: the year to test |
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:return: ``True`` if `year` is a leap-year, ``False`` otherwise |
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""" |
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return ((year % 4) == 0) and (((year % 100) != 0) or ((year % 400) == 0)) |
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@staticmethod |
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def days_to_a_month(month, year): |
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""" Compute the number of days in the month and year provided |
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:param month: the given month |
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:param year: the given year |
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:return: the number of days in the given month and year |
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""" |
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standard_days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31] |
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if month == 2 and Date.leap_year(year): |
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return 29 # February has 29 days in a leap-year |
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else: |
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return standard_days[month - 1] |
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def solve(): |
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""" Compute the answer to Project Euler's problem #19 """ |
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lower_bound = Date(1, 1, 1901) |
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upper_bound = Date(31, 12, 2000) |
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current_date = Date(1, 1, 1900) |
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answer = 0 |
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current_date += 6 # first Sunday after 1/1/1900 |
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# Skip over Sundays, one week at a time, until 1/1/1901 |
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while current_date <= lower_bound: |
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current_date += 7 # next Sunday |
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# Skip over Sundays, one week at a time, until 31/12/2000 |
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while current_date <= upper_bound: |
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if current_date.day == 1: |
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answer += 1 # this is a Sunday and the first of a month |
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current_date += 7 |
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return answer |
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expected_answer = 171 |
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