Project Euler 19

Counting Sundays

How many Sundays fell on the first of the month during the 20th century (1 January 1901 to 31 December 2000)?

Approach 1

In Python, if we create a datetime variable y then, y.strftime("%a") will return the weekday of the date.

 y=datetime(year,month,date)
 weekday = y.strftime("%a")

Using the function above, we can loop from 1901 to 2000, and for each year, we will check the 1st of every month.
If we find the 1st of a month to be Sunday, we increment sunday_count by 1.

Approach 2

A slightly better approach would be this.

Weekcode = { 0=Sunday, 1=Monday, 2=Tuesday, 3=Wednesday, 4=Thrusday, 5=Friday, 6=Saturday}

Generalized formula:

Weekcode on 1st of nth month of yth year = [ ( Weekcode on 1st of (n-1)th month of yth year ) + ( No. of Days in (n-1)th month ) ] % 7

We make a for loop from 1900 to 2000 and for every year.
We calculate the day on the 1st of each month by the generalized formula above.
When we find the 1st of a month to be Sunday, we increment our sunday_count by 1.

Weekcode = 1
# Weekcode of 1st Jan 1900 is i.e. Monday
months = [31,28,31,30,31,30,31,31,30,31,30,31]
# no. of days in each month ordered as they occurence in a year.
sunday_count = 0
# This is the sundays counter
for cur_year in range(1900,2000+1) :
    # for loop from 1900 to 2000
    # updating day count of Feb month according to the year
    if (cur_year%4==0 and cur_year%100!=0) or (cur_year%400==0):
        months[1] = 29
    else:
        months[1] = 28
    
    for y in months:
        Weekcode = (Weekcode + y)%7
        if Weekcode==0 and cur_year>1900:
            sunday_count+=1
        
print(sunday_count)