Zeller’s congruence is an algorithm developed by Christian Zeller to calculate the day of the week. The formula is h = (q + 26(m+1)//10 + k + k//4 +j//4 +5j) % 7 where - h is the day of the week (0: Saturday, 1: Sunday, 2: Monday, 3: Tuesday, 4: Wednesday, 5: Thursday, 6: Friday). - q is the day of the month. - m is the month (3: March, 4: April, ..., 12: December). January and February are counted as months 13 and 14 of the previous year. - j is year//100. - k is the year of the century (i. e., year % 100). Write a program that prompts the user to enter a year, month, and day of the month, and then it displays the name of the day of the week.

Here is the program:

import java.util.Scanner;   // to accept input from user

public class Main {  //class definition

public static void main(String[] args) {  //start of main function

 Scanner input = new Scanner(System.in);  //creates Scanner class object

 System.out.print("Enter year: ");  //prompts user to enter Year

 int year = input.nextInt();  // reads input year from user

 System.out.print("Enter month: ");  //prompts user to enter month

 int month = input.nextInt();  // reads input month from user

 System.out.print("Enter the day of the month: ");  //prompts user to enter day of month

 int dayM = input.nextInt();  // reads input day of month from user

 if (month == 1 || month == 2){  //if month is January or February

 month = (month == 1) ? 13 : 14;  //if month is January set month to 13 and 14 otherwise

 year--; }  //decrements value of year

int dayW = (dayM + (26 * (month + 1)) / 10 + (year % 100)  

   + (year % 100) / 4 + (year / 100) / 4 + 5 * (year / 100)) % 7;   //computes day of the week

     System.out.print("Day of the week is ");  //prints day of week

 switch(dayW)  {  //used to print day of the week

 case 0: System.out.println("Saturday"); break;  //if 0 then displays Saturday

 case 1: System.out.println("Sunday"); break; //1 then displays Sunday

 case 2: System.out.println("Monday"); break;  //2 then displays Monday

 case 3: System.out.println("Tuesday"); break;  //3 then displays Tuesday

 case 4: System.out.println("Wednesday"); break;  //4 then displays Wednesday

 case 5: System.out.println("Thursday"); break;  //5 then displays Thursday

 case 6: System.out.println("Friday");  }  }       } //6 then displays Friday

Explanation:

The program first prompts the user to enter the values of year, month and day of month. Then uses the following formula to compute day of the week in that particular year, month and day of week:

Suppose

year = 2020

month = 9

day of month = dayM = 6

Then dayM is calculated as

(dayM + (26 * (month + 1)) / 10 + (year % 100)  

   + (year % 100) / 4 + (year / 100) / 4 + 5 * (year / 100)) % 7

(6+ (26 * (9+ 1)) / 10 + (2020% 100)  

   + (2020% 100) / 4 + (2020/ 100) / 4 + 5 * (2020/ 100)) % 7;

This gives answer as 1.

Now if we see the switch statement the day corresponding to 1 is Sunday

So the day on year 2020, month 9 and day of the month 6 is Sunday.

The screenshot of program along with its output is attached.