algorithm - Calculating future occurrences 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

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 :)