A Problem Solved: Leap Years

Problem statement

Is this year a leap year? Will the year 3000 be a leap year? Let’s write a program to find out.

Pseudocode

The overall logic of the program is not complicated, as you can see from the following pseudocode:

Describe the program’s purpose
Ask the user to type a year
Read the year
Test whether the year is a leap year
Display the results

Let’s tackle the hardest part—testing whether a year is a leap year. A year is a leap year if it is:

• Divisible by 4 but not divisible by 100
  or
• Divisible by 400

For example, the years 2000 and 2008 were leap years, but 2099 and 3000 will not be.

We need to translate the criteria for a leap year into Java. If year is an int variable containing the year, we can list each of the necessary tests in English and its Java equivalent, as follows:

• Divisible by 4     year % 4 == 0
• Not divisible by 100 year % 100 != 0
• Divisible by 400   year % 400 == 0

For the year to be divisible by 4, the remainder after dividing the year by 4 must be 0. This will be the case if the expression year % 4 is 0, that is, if the expression year % 4 == 0 is true. Similarly, a year is not divisible by 100 if the remainder after dividing the year by 100 is not 0. In that case, the expression year % 100 != 0 is true. Both of these criteria must be true simultaneously to satisfy the requirement “Divisible by 4 but not divisible by 100.” That is, a year is a leap year if the expression, (year % 4 == 0) && (year % 100 != 0) is true.

If this expression is false, the year can still be a leap year if it is divisible by 400—that is, if year % 400 == 0 is true. By combining these observations, we see that a year is a leap year if the expression,
( (year % 4 == 0) && (year % 100 != 0) ) || (year % 400 == 0)
is true.

Program

You can see this expression used in the following leap-year program.