What is the easiest algorithm to find the day of week of day zero of a given year?

Question

I am trying to figure out what the day of the week of day zero (January 1st) of a given year.

So far I have looked at the Wikipedia page 'Calculating the day of the week' but I was wondering if there is an easiest algorithm if you're just trying to find day zero.

Answer 1

The bottom of the Wikipedia page on "Calculating the day of the week" gives the rules you'd need. You could also simplify Zeller's congruence by hardcoding the month and day of the month.

Answer 2

I find this a bit more practical than the article on Wikipedia, but it is still generic:

http://stason.org/TULARC/society/calendars/2-5-What-day-of-the-week-was-2-August-1953.html

Answer 3

Most languages provide facilities for representing and manipulating dates... I would rely on those instead of implementing some (probably incomplete) algorithm.

Answer 4

You could always keep a reference date, and then add days of the year (mod 7) to keep a running tally, but like Zach said, using built-in functions is going to be way easier.

Answer 5

Years repeat on a 28 year cycle. Divide the year by 28 and return the respective day-of-the-week (the day-of-the-week values being stored in an array/vector). This would be the fastest and simplest algorithm. But this algorithm would not be at all clear to someone reading the code. Your choice depends on whether you want fast, simple or "clearly correct".

Answer 6

Here's a simple one-liner. I've verified this for all the years 1901-2200 using Excel.

dayOfWeek = (year*365 + trunc((year-1) / 4) - trunc((year-1) / 100) + trunc((year-1) / 400)) % 7

This will give the day of the week as 0=Sunday, 6=Saturday. This result can easily be adjusted by adding a constant before or after the modulus 7.

Answer 7

int dayofweek(y, m, d) /* 0 = Sunday / int y, m, d; / 1 <= m <= 12, y > 1752 or so */ { static int t[] = {0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4}; y -= m < 3; return (y + y/4 - y/100 + y/400 + t[m-1] + d) % 7; }