Zeller’s congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date. It can be considered to be based on the conversion between Julian’s day and the calendar date.
It is an algorithm to find the day of the week for any date.
For the Gregorian calendar it is:
![h=\left ( q + [ \frac{13(m+1)}{5} ]+K +\left [ \frac{K}{4}\right ]+\left [ \frac{J}{4}\right ]+5J\right )mod7](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-1ffa544afc1ba0e6d37617f0cc241efd_l3.png "Rendered by QuickLaTeX.com")
For the Julian calendar it is:
![h=\left ( q + \left [ \frac{13(m+1)}{5} \right ]+K +\left [ \frac{K}{4}\right ]+5-J\right )mod7](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-a36b8578bee24e1dd40a760b0a430697_l3.png "Rendered by QuickLaTeX.com")
where,
- h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, …, 6 = Friday)
- q is the day of the month
- m is the month (3 = March, 4 = April, 5 = May, …, 14 = February)
- K is the year of the century (year % 100).
- J is the zero-based century (actually ⌊ year/100 ⌋) For example, the zero-based centuries for 1995 and 2000 are 19 and 20 respectively (to not be confused with the common ordinal century enumeration which indicates 20th for both cases).
NOTE: In this algorithm January and February are
counted as months 13 and 14 of the previous
year.E.g. if it is 2 February 2010, the
algorithm counts the date as the second day
of the fourteenth month of 2009 (02/14/2009
in DD/MM/YYYY format)
For an ISO week date Day-of-Week d (1 = Monday to 7 = Sunday), use
d = ((h+5)%7) + 1
C++
#include <cmath>
#include <cstring>
#include <iostream>
using namespace std;
int Zellercongruence(int day, int month, int year)
{
if (month == 1) {
month = 13;
year--;
}
if (month == 2) {
month = 14;
year--;
}
int q = day;
int m = month;
int k = year % 100;
int j = year / 100;
int h
= q + 13 * (m + 1) / 5 + k + k / 4 +
j / 4 + 5 * j;
h = h % 7;
switch (h) {
case 0:
cout << "Saturday \n";
break;
case 1:
cout << "Sunday \n";
break;
case 2:
cout << "Monday \n";
break;
case 3:
cout << "Tuesday \n";
break;
case 4:
cout << "Wednesday \n";
break;
case 5:
cout << "Thursday \n";
break;
case 6:
cout << "Friday \n";
break;
}
return 0;
}
int main()
{
Zellercongruence(22, 10, 2017);
return 0;
}
|
Java
import java.util.*;
class GFG
{
static void Zellercongruence(int day, int month,
int year)
{
if (month == 1)
{
month = 13;
year--;
}
if (month == 2)
{
month = 14;
year--;
}
int q = day;
int m = month;
int k = year % 100;
int j = year / 100;
int h = q + 13*(m + 1) / 5 + k + k / 4 + j / 4 + 5 * j;
h = h % 7;
switch (h)
{
case 0 : System.out.println("Saturday"); break;
case 1 : System.out.println("Sunday"); break;
case 2 : System.out.println("Monday"); break;
case 3 : System.out.println("Tuesday"); break;
case 4 : System.out.println("Wednesday"); break;
case 5 : System.out.println("Thursday"); break;
case 6 : System.out.println("Friday"); break;
}
}
public static void main(String[] args)
{
Zellercongruence(22, 10, 2017);
}
}
|
Python3
def switch(h) :
return {
0 : "Saturday",
1 : "Sunday",
2 : "Monday",
3 : "Tuesday",
4 : "Wednesday",
5 : "Thursday",
6 : "Friday",
}[h]
def Zellercongruence(day, month, year) :
if (month == 1) :
month = 13
year = year - 1
if (month == 2) :
month = 14
year = year - 1
q = day
m = month
k = year % 100;
j = year // 100;
h = q + 13 * (m + 1) // 5 + k + k // 4 + j // 4 + 5 * j
h = h % 7
print(switch (h))
Zellercongruence(22, 10, 2017)
|
C#
using System;
class GFG {
static void Zellercongruence(int day,
int month, int year)
{
if (month == 1)
{
month = 13;
year--;
}
if (month == 2)
{
month = 14;
year--;
}
int q = day;
int m = month;
int k = year % 100;
int j = year / 100;
int h = q + 13 * (m + 1) / 5 + k + k / 4
+ j / 4 + 5 * j;
h = h % 7;
switch (h)
{
case 0 : Console.WriteLine("Saturday");
break;
case 1 : Console.WriteLine("Sunday");
break;
case 2 : Console.WriteLine("Monday");
break;
case 3 : Console.WriteLine("Tuesday");
break;
case 4 : Console.WriteLine("Wednesday");
break;
case 5 : Console.WriteLine("Thursday");
break;
case 6 : Console.WriteLine("Friday");
break;
}
}
public static void Main()
{
Zellercongruence(22, 10, 2017);
}
}
|
PHP
<?php
function Zellercongruence($day, $month, $year)
{
if ($month == 1)
{
$month = 13;
$year--;
}
if ($month == 2)
{
$month = 14;
$year--;
}
$q = $day;
$m = $month;
$k = $year % 100;
$j = $year / 100;
$h = $q + 13*($m + 1) / 5 + $k +
$k / 4 + $j / 4 + 5 * $j;
$h = $h % 7;
switch ($h)
{
case 1 : echo "Saturday \n";
break;
case 2 : echo "Sunday \n";
break;
case 3 : echo "Monday \n";
break;
case 4 : echo "Tuesday \n";
break;
case 5 : echo "Wednesday \n";
break;
case 6 : echo "Thursday \n";
break;
case 7 : echo "Friday \n";
break;
}
}
Zellercongruence(22, 10, 2017);
?>
|
Javascript
<script>
function Zellercongruence(day, month, year)
{
if (month == 1)
{
month = 13;
year--;
}
if (month == 2)
{
month = 14;
year--;
}
let q = day;
let m = month;
let k = year % 100;
let j = parseInt(year / 100, 10);
let h = q + parseInt(13 * (m + 1) / 5, 10) + k + parseInt(k / 4, 10) + parseInt(j / 4, 10) + 5 * j;
h = h % 7;
switch (h)
{
case 0 :
document.write("Saturday");
break;
case 1 :
document.write("Sunday");
break;
case 2 :
document.write("Monday");
break;
case 3 :
document.write("Tuesday");
break;
case 4 :
document.write("Wednesday");
break;
case 5 :
document.write("Thursday");
break;
case 6 :
document.write("Friday");
break;
}
}
Zellercongruence(22, 10, 2017);
</script>
|
Time Complexity: O(1)
Auxiliary Space: O(1)
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