23 de noviembre de 2013

Counting Sundays - Project euler, problema 19


El problema es el que sige:

You are given the following information, but you may prefer to do some research for yourself.
  • 1 Jan 1900 was a Monday.
  • Thirty days has September,
  • April, June and November.
  • All the rest have thirty-one,
  • Saving February alone,
  • Which has twenty-eight, rain or shine.
  • And on leap years, twenty-nine.
  • A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.
How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
Y la explicación, que es bastante sencilla, está en los comentarios del código:

%Pasan 100 años
%12 meses tiene cada año
%Hay un primer dia por mes
%=> Hay 12*100*1=1200 primeros dias del mes
%1 de cada 7 dias es domingo
%=> hay 1200*(1/7) domingos aprox.
floor(1200/7) %no contamos fracciones de domingo :P