Correctness of Sakamoto's algorithm to find the day of week

Question

I am using Sakamoto\'s algorithm to find out the day of week from a given date. Can anybody tell me the correctness of this algorithm? I just want this from 2000 to 2099.

Answer 1

For Gregorian Calendar

int dayToWeekG(int d,int m,int y){
    int i;
    int t[12]={0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4};
            //{0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5};
    y-=m<3;
    i=(y+y/4-y/100+y/400 +t[m-1]+d)%7;
    return i;
}

Explanation:

• See the commented array for

 t[] = {0, 3, 3, 6, 1, 4, 6, 2, 5, 0, 3, 5};

and compare it with a calendar of a whole year (run cal 2to generate calendar in terminal in linux/unix) notice the starting day of the week of the day for each month.

• Every normal year shifting one day of the week and leap year shifting two days of the week. as (365%7)=1 and (366%7)=2

 i= y+y/4-y/100+y/400

• But we are should not calculate the extra day if y is a leap year for month 0 and 1

y-=m<3

• but by this way we are also removing the extra day from non-leap years too. so we will fill up the gap by subtracting 1 day for every month after February.

  int t[12]={0, 3, 2, 5, 0, 3, 5, 1, 4, 6, 2, 4};