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I am trying to find the fourth Thursday of November (thanksgiving day) of any user inputted year. I used the following function to find the day of December 31'st of the previous year of user inputted year.

int yr;
int lastDayofDecember;
scanf("%i",&yr);
lastDayofDecember = (((yr-1)*365)+((yr-1)/4)-((yr-1)/100)+((yr-1)/400))%7;

where, lastDayofDecember = 0 : Sunday, 1 : Monday,......6:Saturday;

Now for year 2016, the last day was a Saturday i.e lastDayofDecember = 6, I added 5 to it to find the first thursday of January and added 304 to it to find the first Thursday of November (January 1 - November 1 is 304 days for non-leap year) to which I added 21 to find the fourth thursday of November, but now I am confused about what to do next. I can not use loops

    int txDay = 5 + 304 + 21;
San Mo
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  • I would construct the date November 1 (for whatever year) in a `struct tm`, then call `mktime` to fill in `tm_wday`, then work from there. – Steve Summit Oct 23 '17 at 11:26
  • @SteveSummit: I'd do similar, but using November 21. – Brendan Oct 23 '17 at 11:28
  • @SteveSummit I can not use `struct` since it is a school assignment. But I am using user defined functions to work this problem out. – San Mo Oct 23 '17 at 11:29
  • `int thanksGivingDayOfMonth=28-(5+year+year/4-year/100+year/400)%7;` (now you only need to explain this) –  Oct 23 '17 at 12:26
  • @FelixPalmen this calculates what day is the last day of the given `year`. `0=Sunday`,`1=Monday` and so on till `6=Saturday`. – San Mo Oct 23 '17 at 12:32
  • @SanMo I think you didn't understand my comment. –  Oct 23 '17 at 12:33
  • @FelixPalmen Oh I got it now, sorry been up all night trying to figure this out haha – San Mo Oct 23 '17 at 12:35
  • @SanMo still it only helps you when you **can** explain it. It's not that hard though. –  Oct 23 '17 at 12:47
  • @FelixPalmen Yes I am trying to figure out the logic behind the code you gave me. Thanks a lot. – San Mo Oct 23 '17 at 12:50
  • @SanMo I added an explanation –  Oct 23 '17 at 13:40

1 Answers1

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Breaking this down, although it's not directly about programming, it's an interesting topic -- assuming the gregorian calendar only *):

As the week day advances by one per year, it can be calculated using a simple modulo 7 of the year. The only problem here are leap years, and you already have the formula to accomodate for these.

You're effectively doing calculations in the Ring ℤ7 so you just have to add the number of leap years until your current year. Exploiting integer division, this number is

year/4 - year/100 + year/400

So, to get a unique number between 0 and 7 corresponding to one day of week each, you just do (year + year/4 - year/100 + year/400) % 7. This would be a bit more complicated for dates early in the year, but as we're interested in November, for leap years, the 29. February has already passed -> nothing more to do.

The latest possible date for thanksgiving day is the 28, when the 1. November is a Friday. So you want your calculated value to be 0 for years when November starts on a Friday. You can find by experimentation that you need to add an offset of 5 inside your Ring to achieve that. With that, you just need to subtract that value from this latest possible date, 28. This gives the complete formula:

int thanksGivingDate = 28 - (5 + year + year/4 - year/100 + year/400) % 7;

*) As this uses the rules of the gregorian calendar, the result will be incorrect for older dates still using the julian calendar. (e.g. 1752 and earlier for the U.S.)