Calculating future occurences of Friday the 13th

Question

I'd like to be able to start with a year, and calculate occurrences of Friday the 13th. A brute force solution is easy and obvious. I have something slightly better, but I have no doubt that someone else can come up with an elegant algorithm for this.

Perhaps a little trickier, I'd be interested in giving the program a month, and have it find the next year in which that month has a Friday the 13th.

Feel free to use pseudo code, but I expect people will vote more for working code samples in you favorite language.

Answer 1

initialize startDate to 13th of the month given in the current year
while (true) {
    if (startDate.dayOfWeek == Date.FRIDAY)
         break;
    else
         startDate.year ++;
}
return startDate.year;

Answer 2

http://javascript.internet.com/time-date/find-friday-the-13th%27s!.html

Answer 3

Since your brute force algorithm is apparently the intuitive day-by-day iteration option, perhaps you haven't considered the Doomsday Algorithm. It would allow you to simply check if that 13th is a Friday. As far as I know, it is the most efficient solution to the problem.

Answer 4

Any month that starts with a Sunday has a Friday on the thirteenth. There are only 14 combinations possible knowing what day the first of the year is on (with or without leap year, and sun-sat). You should just calculate it once and get it over with. You'd only check 14*12 possible months to start out with, well with in reason.

resultant table element (from 2009, 2010):

[Thursday,false] => Feb, March, Nov
[Friday,false] => Aug

to fill the table you have a generic month Jan(31),Feb(28).. and then iterate with a seed of each day of the week, noting months that start with sunday, and also with a leap year and without. Pretty straight forward, and once done, you can share it with us :)

Answer 5

One thing I noticed is that the first of the month falls on a Sunday during months with a Friday the 13th. You can probably leverage this to make it easier to calculate.

Answer 6

This is how I would do it:

• Assume year is known and is an integer.

• Loop from 1 to 12

  • Create date with loop index, year and 13 for the day

    • Determine day of week as per established algorithms

    • If day of week calculated above is Friday, do your work

If you want to start with a month and year (you have to assume some sort of year), your algorithm becomes

• Assume year is known and an integer

• Assume month is known and is an integer

• Loop

  • Create date with index of loop as year, known month variable, and 13 for the day

  • Determine day of week as per established algorithms

  • If day of week calculate above is Friday, return date, else

  • Else increment year by 1

Answer 7

Here's some example PHP code that goes through a pretty straight forward loop of the dates in a range. I would modify this to check the 13th of each month for Fridayness, rather than checking every Friday for 13thness, as they do in the example.