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Zeller’s Congruence | Find the Day for a Date
• Difficulty Level : Easy
• Last Updated : 16 May, 2018

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 day and the calendar date.
It is an algorithm to find the day of the week for any date.
For the Gregorian calender it is: For the julian calender it is: where,

1. h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, …, 6 = Friday)
2. q is the day of the month
3. m is the month (3 = March, 4 = April, 5 = May, …, 14 = February)
4. K the year of the century ( year % 100).
5. 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++

 // C++ program to find Find the Day  // for a Date  # include  # include  # include  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;  }     // Driver code  int main()  {  Zellercongruence(22, 10, 2017); //date (dd/mm/yyyy)  return 0;  }

## Java

 // Java program to find Find the Day  // for a Date  import java.util.*;     class GFG  {      // Print Day for a Date      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;          }      }             // Driver code      public static void main(String[] args)      {          Zellercongruence(22, 10, 2017); //date (dd/mm/yyyy)      }  }     /* This code is contributed by Mr. Somesh Awasthi */

## Python3

 # Python3 program to find Find the Day  # for a Date     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))                       # Driver code  Zellercongruence(22, 10, 2017) #date (dd/mm/yyyy)     # This code is contributed by Nikita Tiwari

## C#

 // C# program to find Find the Day  // for a Date  using System;     class GFG {             // Print Day for a Date      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;          }      }             // Driver code      public static void Main()      {                     //date (dd/mm/yyyy)          Zellercongruence(22, 10, 2017);       }  }     /* This code is contributed by vt_m */

## PHP

 

Output:

Sunday


Reference:

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