LAB 3.1 EASTER
Background
A convenient algorithm for determining the date of Easter in a given year was devised in 1876 and first appeared in Butcher’s Ecclesiastical Handbook. This algorithm holds for any year in the Gregorian calendar, which means years including and after 1583. Subject to minor adaptations, the algorithm is as follows:
- Let y be the year (such as 1583 or 2003).
- Divide y by 19 and call the remainder a. Ignore the quotient.
- Divide y by 100 and get a quotient b and a remainder c.
- Divide b by 4 and get a quotient d and a remainder e.
- Divide b + 8 by 25 and get a quotient f. Ignore the remainder.
- Divide b - f + 1 by 3 and get a quotient g. Ignore the remainder.
- Divide 19 * a + b - d - g + 15 by 30 and get a remainder h. Ignore the quotient.
- Divide c by 4 and get a quotient i and a remainder k.
- Divide 32 + 2 * e + 2 * i - h - k by 7 and get a remainder r. Ignore the quotient.
- Divide a + 11 * h + 22 * r by 451 and get a quotient m. Ignore the remainder.
- Divide h + r - 7 * m + 114 by 31 and get a quotient n and a remainder p.
The value of n gives the month (3 for March and 4 for April) and the value of p + 1 gives the day of the month. For example, if y is 2003:
a = 8
b = 20
c = 3
d = 5
e = 0
f = 1
g = 6
h = 26
i = 0
k = 3
r = 3
m = 0
n = 4
p = 19
Therefore, in 2003, Easter fell on April 20 (month = n = 4 and day = p + 1 = 20).
Basic Assignment:
Write a program that calculates the day that Easter falls on for a given year.
The program should display the values for all of the variables and the date for Easter. A Sample run output for the year 2003 would be:
a = 3
b = 20
c = 17
d = 5
e = 0
f = 1
g = 6
h = 21
i = 4
k = 1
r = 4
m = 0
n = 4
p = 15
Easter in 2017 falls on 4/16
Verify that your program gives all the output shown above for the year 2017.
Verify that your program gives the correct date for these years:
Easter in 2000 falls on 4/23
Easter in 2001 falls on 4/15
Easter in 2002 falls on 3/31
Challenge Assignments:
- In addition to the Basic Lab, find the day of the week that Independence Day, July 4th, falls on for a given date. This is a good learning lab if you understand how to read APIs but have never worked with dates and times in Java before. Try using the Calendar API. The point is to do the work yourself by reading and understanding the API rather than copy and paste an online solution.
A Sample run output for the year 2003 would be:
a = 8
b = 20
c = 3
d = 5
e = 0
f = 1
g = 6
h = 26
i = 0
k = 3
r = 3
m = 0
n = 4
p = 19
Easter in 2003 falls on 4/20
Independence Day in 2003 falls on a Friday
If everything above was too easy for you, try coding the Easter lab in a language you've never used before. How about Python, C++, Javascript, PHP, Perl, or Ruby? Or perhaps something really obscure like Brain**k? Pick a language from the IDE list online at Tutorials Point
If you write your code in a language in addition to Java, upload your additional file by dragging multiple files onto the submission form's Upload button. And be sure to name your file using our standard convention. For example, P3_Wang_Michael_Easter.cpp would be for a C++ file.
Instructions:
- This program has been started for you:
public class PX_LastName_FirstName_Easter {
public static void main(String[] args) {
// Year to calculate Easter
int y = 2017;
// Perform Easter calculations
int a = y % 19;
System.out.println("a = " + a);
int b = y / 100;
System.out.println("b = " + b);
...
// Print out final result
...
Important!! From now on you must name your files and classes following this naming convention:
P#_LastName_FirstName_Assignment.java
Example: P2_Wang_Michael_Easter.java.
- Capitalize the start of each section
- Follow the convention exactly
- If you misname your file you will lose points because it puts your assignment out of order when graded.
After completing the program, upload it by 11:59 pm on the due date using the form below.
Upload your .java file only. (No .class files or .bluej project files!)
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