Day of the week P18777

Write a function that, given a valid date made with a day @d@, a month @m@ and a year @y@, returns its day of the week, that is, “Monday”, or “Tuesday”, or …

To compute it, use the congruence of Zeller. Let $d$ be the day, $m$ be the month, and $y$ be the year. Then,

1. Subtract two from the month $m$, and if the result is zero or less, add 12 to the month and subtract one from the year. Call $m'$ the new month and call $y'$ the new year.

2. Compute the century $c$ (the first two digits of the year) from the year $y'$.

3. Compute the year $a$ inside the century (the two last digits of the year) from the year $y'$.

4. Compute $$f = \lfloor 2.6m' - 0.2 \rfloor + d + a + \lfloor a/4 \rfloor + \lfloor c/4 \rfloor - 2c.$$

5. Finally, $f$ modulo 7 gives us the desired result, taking into account that 0 represents Sunday, 1 represents Monday, 2 represents Tuesday, …, and 6 represents Saturday.

Interface

string day_of_the_week (int d, int m, int y);

char* day_of_the_week (int d, int m, int y);

public static String day_of_the_week (int d, int m, int y);

day_of_the_week (d, m, y)  # returns str

day_of_the_week (d: int, m: int, y: int) -> str

dayOfTheWeek :: Int -> Int -> Int -> String

Precondition

The parameter @y@ is between 1800 and 9999, both included. The date is valid.

Hint

Watch out for modulos of negative numbers!

Observation

You only need to submit the required procedure; your main program will be ignored.