Problem 19

Counting Sundays

Problem 19

14 June 2002

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)?

 

Answer:

171

 

 

#include "pub.h"

int count=0;
void ct(int y, int m, int week_day)
{
    //y:year
    //m:month
    //week_day: 0-monday,1-tuesday,...6-sunday
    if(y==2000 && m==12)
    {
        if(week_day==6)
            count++;
        return;
    }
    else
    {
        if(week_day==6)
            count++;
        if(m==12)
        {
            week_day = (week_day+31%7)%7;
            //the next year
            return ct(y+1, 1,week_day);
        }
        else
        {
            if(m==2)
            {
                if(y%400==0 || y%4==0&&y%100!=0)
                    week_day = (week_day+29%7)%7;
                else
                    week_day = (week_day+28%7)%7;
            }
            else if(m==1 || m==3 ||m==5 ||m==7 ||m==8 ||m==10|| m==12)
                week_day = (week_day+31%7)%7;
            else
                week_day = (week_day+30%7)%7;
            //next month
            return ct(y, m+1,week_day);
        }
    }
}

void p19()
{
    //1901.1.1 is tuesday
    ct(1901, 1,1);
    cout<<count<<endl;
}