sol1 Algorithm

The sol1 Algorithm, also known as "Squaring the Circle" algorithm, is a mathematical technique that aims to solve the ancient geometrical problem of constructing a square with the same area as a given circle using only compass and straightedge. This algorithm is based on the approximation of the value of Pi (π), which is the ratio of the circumference of a circle to its diameter. The main idea behind the sol1 Algorithm is to find the side length of a square that, when multiplied by itself, gives the same area as that of a circle with a given radius. The sol1 Algorithm begins by drawing a circle with the desired radius, followed by constructing an inscribed square within the circle. The next step involves dividing the circle's circumference into a number of equal segments, which are then used to create a polygon that approximates the circle. The area of this polygon can be easily calculated using basic trigonometry, and as the number of segments increases, the approximation of the circle's area becomes more accurate. Finally, the side length of the square is determined by finding the square root of the approximated circle's area, and a square with this side length is constructed using a compass and straightedge. Although the sol1 Algorithm provides an approximation to the problem of squaring the circle, it has been proven mathematically impossible to achieve an exact solution using only compass and straightedge due to the transcendental nature of the number π.
"""
Counting Sundays
Problem 19

You are given the following information, but you may prefer to do some research
for yourself.

1 Jan 1900 was a Monday.
Thirty days has September,
April, June and November.
All the rest have thirty-one,
Saving February alone,
Which has twenty-eight, rain or shine.
And on leap years, twenty-nine.

A leap year occurs on any year evenly divisible by 4, but not on a century
unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century
(1 Jan 1901 to 31 Dec 2000)?
"""


def solution():
    """Returns the number of mondays that fall on the first of the month during
    the twentieth century (1 Jan 1901 to 31 Dec 2000)?

    >>> solution()
    171
    """
    days_per_month = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]

    day = 6
    month = 1
    year = 1901

    sundays = 0

    while year < 2001:
        day += 7

        if (year % 4 == 0 and not year % 100 == 0) or (year % 400 == 0):
            if day > days_per_month[month - 1] and month != 2:
                month += 1
                day = day - days_per_month[month - 2]
            elif day > 29 and month == 2:
                month += 1
                day = day - 29
        else:
            if day > days_per_month[month - 1]:
                month += 1
                day = day - days_per_month[month - 2]

        if month > 12:
            year += 1
            month = 1

        if year < 2001 and day == 1:
            sundays += 1
    return sundays


if __name__ == "__main__":
    print(solution())

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