CPSC 110-08: Computing on Mobile Phones Spring 2012 Homework: Leap Year Due: Wednesday 2/29 (before class)

CS Principles

• 15: The student can develop an algorithm.
• 20: The student can use functional abstraction to manage complexity in programs.

Introduction

2012 is a Leap Year. But what exactly is a leap year and what years are leap years?

In this homework (and follow-up in class assignment) we will look at the definition of a leap year and turn it into an algorithm to test whether any given year is a leap year or not.

About Leap Years

A leap year consists of 366 (rather than 365) days, with the extra day coming on February 29. The purpose of the extra day is to bring the calendar more in line with the time it takes the earth to make a full orbit around the sun, which takes 365.242199 days. The leap year adjustment occurs approximately (although not exactly) every 4th year.

A closer approximation is provided by the following rule, which was adopted as part of the Gregorian Calendar:

Leap Year Definition. A year is a leap year if it is evenly divisible by 4 but not evenly divisible by 100 unless it is also evenly divisible by 400. So 1996 was a leap year. But 1900 was not a leap year because, although it is divisible by 4, it is also divisible by 100 and not by 400. 2000 is a leap year because it is divisible by 400.

Here are some interesting facts about leap years from timeanddate.com:

• Without leap years you would lose around 6 hours off the calendar per year. In 100 years, the calendar would off by 24 days.

• Leap years were introduced by Julius Caesar over 2000 years ago, but the rule then was simply divisible by 4. That led to too many leap years in the Julian Calendar, causing it to be off by 1 day every 128 years.

• When the conversion to the Gregorian Calendar was made in February 1582 by Pope Gregory, 10 days were dropped in October 1582 to bring the calendar in alignment with the equinox -- i.e., that moment when the Earth's tilt on its axis is in alignment with the sun's axis.

• Great Britain and its colonies (the U.S.) didn't adopt the Gregorian Calendar until 1752, when 11 days were dropped (September 3 - 13). Try to look up the calenar for 1752.

• The year 2000 was the first time the 3rd clause of the definition came into play -- i.e., "also divisible by 400" -- in most parts of the world.

• Legend has it that leap years confer on women the privilege of proposing marriage to men. For example, here's a quote from The American Farmer, published in 1827:

  [During a Leap Year] the Ladyes have the sole privilege, during the time it continueth, of making love unto the men, which they may doe either by wordes or lookes, as unto them it seemeth proper; and moreover, no man will be entitled to the benefit of Clergy who dothe refuse to accept the offers of a ladye, or who dothe in any wise treate her proposal withe slight or contumely.

  There was even a 2010 movie with this theme. Was 2010 a leap year?

Homework

Let's build an app to figure out if a a year entered by the user is a Leap Year.

• User Interface: Create a new app named LeapYear with the following user interface (Click to enlarge.)

  The app contains a Label with the text "Leap Year?", a TextBox where the user will enter a year, a Button that the user will click to test whether the year is a leap year, and a Notifier that will display the answer.

• Blocks Editor: Create the following blocks for your app (click to enlarge):

  

  As you can see, when Button1 is clicked, the app takes the text from TextBox1 and tests whether it isLeapYear or not. It then uses a Notifier component to report the result.

  The isLeapYear block here is only partially defined. We'll complete it in class. It is an example of a procedureWithResult block -- also known as a programmer-defined function. You can find it in the Built-in > Definition drawer.

  

  Functions: You've been using lots of built-in functions in your apps -- e.g., Math functions like random integer and Text functions like join and make text. In this app we'll be writing our own functions to simplify our algorithm. The isLeapYear function is an example of a boolean function -- i.e., one that returns either true or false. This lets us use it in the Test slot of an if/else block.

• Use the emulator to test the app. Can you see that the isLeapYear block will always return false. So, no matter what year the user enters, the app will always report that it is NOT a leap year. We'll fix this in class.

• Algorithm: To test whether a year is a leap year or not we need an if/then algorithm that expresses the logic contained in the above definition. Here's a pseudocode algorithm for the definition of a leap year (the # lines are comments meant to explain the logic):

  # Definition of leap year.
  if year is divisible by 4:
     then if year is divisible by 100:
        then if year is divisible by 400:
           set isALeapYear to true          # Divisible by 4 and 100 and 400
        else
           set isALeapYear to false         # Divisible by 4 and 100 but not 400
     else
        set isALeapYear to true             # Divisible by 4 but not by 100
  else 
     set isALeapYear to false               # Not divisible by 4
  

  Notice in this algorithm that one if/else statement (block) is contained (nested) inside another. How many if/else blocks are involved?

• Challenges: (Give these your best shot. We'll complete them in class.)
  1. Translate the if/else pseudocode into a nested App Inventor if/else block.

  2. How do you define is divisible by in App Inventor? HINT: Look in the Math drawer.

  3. Where should you put the nested if/else algorithm?

• Create a Portfolio page for this app with a screen shot of your blocks editor.

Getting Help

The TAs are available on Sunday, Tuesday, and Thursday evenings in MCEC 136. See the syllabus for their hours.

In Class

We'll finish the LeapYear app.