Zeller's Congruence - Find the Day for a Date in Python

An Introduction to Zeller's Congruence

A technique called Zeller's Congruence can be used to determine the day of the week for any given Julian or Gregorian calendar date. This formula uses integer calculations based on the year, month, and day to calculate which day of the week a given date falls on.

Christian Zeller developed a technique known as Zeller's congruence, which allows one to determine the day of the week for any date in the Julian or Gregorian calendar. One may argue that it is predicated on the conversion of the calendar date to Julian's day.

The day of the week for every given date may be found using an algorithm.

It is as follows for the Gregorian calendar:

In terms of the Julian calendar, it's

Where:

• The day of the week is represented by h (0 = Saturday, 1 = Sunday, 2 = Monday,..., 6 = Friday).
• The day of the month is q.
• 3 = March, 4 = April, 5 = May,..., 14 = February is the month m.
• The year K is the century year (year % 100).
• J is the century that is zero-based (actually,? year/100?) To distinguish them from the standard ordinal century enumeration, which shows the twentieth century in both situations, the zero-based centuries for 1995 and 2000 are, for instance, 19 and 20, respectively.

NOTE: In this procedure, January and February are accounted for as months 13 and 14 of the preceding year. For instance, on February 2, 2010, the date is calculated by the algorithm as the second day of the fourteenth month of 2009 (02/14/2009 in DD/MM/YYYY format).
Day-of-Week d (1 = Monday to 7 = Sunday) for an ISO week date, use d = ((h + 5) % 7) + 1

Implementation of Zeller's Congruence in Python

We will now look at some of the examples illustrating the implementation of Zeller's Congruence in Python:

Example 1:

Output:

 
Sunday

Explanation:

The Python application uses Zeller's Congruence to determine the day of the week for a given date, modifying the month and year for January and February. The weekday name is created from the index by the get_day_name function, which then prints it.

• Time Complexity: O(1)
• Auxiliary Space: O(1)

An additional Zeller's Congruence formula variation:

Example 2:

Output:

 
Friday

Explanation:

The application computes the day of the week for any date with the Doomsday Algorithm; this date maps on to the doomsday of the month. The day names ("Sunday" through "Saturday") are hitched to the result.

Conclusion:

Zeller's Congruence is an efficient and accurate device to compute the day of the week for dates in both Julian and Gregorian calendars, using integer arithmetic.