Section2.26FRQ APCalendar for Loops and Control Structures
The AP exam’s first free response question (FRQ) is on Methods and Control Structures using expressions, loops, and if statements. Students will write two methods or one constructor and one method of a given class based on provided specifications and examples. In Part A (4 points),the method or constructor will require students to write iterative or conditional statements, or both, as well as statements that call methods in the specified class. In Part B (3 points), the method or constructor will require calling String methods. The AP exam provides the method header with some parameter variables and other methods that you will need to call in the solution. This question does not involve more complex topics such as arrays.
public class APCalendar
{
/** Returns true if year is a leap year and false otherwise. */
private static boolean isLeapYear(int year)
{
/* implementation not shown */
}
/**
* Returns the number of leap years between year1 and year2, inclusive.
* Precondition: 0 <= year1 <= year2
*/
public static int numberOfLeapYears(int year1, int year2)
{
/* to be implemented in part (a) */
}
/**
* Returns the value representing the day of the week for the first day of
* year, where 0 denotes Sunday, 1 denotes Monday, ..., and 6 denotes Saturday.
*/
private static int firstDayOfYear(int year)
{
/* implementation not shown */
}
/**
* Returns n, where month, day, and year specify the nth day of the year.
* Returns 1 for January 1 (month = 1, day = 1) of any year. Precondition: The
* date represented by month, day, year is a valid date.
*/
private static int dayOfYear(int month, int day, int year)
{
/* implementation not shown */
}
/**
* Returns the value representing the day of the week for the given date
* (month, day, year), where 0 denotes Sunday, 1 denotes Monday, ..., and 6
* denotes Saturday. Precondition: The date represented by month, day, year is
* a valid date.
*/
public static int dayOfWeek(int month, int day, int year)
{
/* to be implemented in part (b) */
}
// There may be instance variables, constructors, and other methods not shown.
}
Write the static method numberOfLeapYears, which returns the number of leap years between year1 and year2, inclusive. In order to calculate this value, a helper method is provided for you.
/** Returns the number of leap years between year1 and year2, inclusive.
* Precondition: 0 <= year1 <= year2
*/
public static int numberOfLeapYears(int year1, int year2)
Also, circle what the return type of what you need to return. In this case, the return type of numberOfLeapYears is int and you need to calculate the number of leap years between year1 and year2 and return it. Declare a variable for this return value and return it at the end of the method to get 1 point.
/** Returns the number of leap years between year1 and year2, inclusive.
* Precondition: 0 <= year1 <= year2
*/
public static int numberOfLeapYears(int year1, int year2)
{
int numLeapYears = 0;
// Your loop will go in here
return numLeapYears;
}
Next, plan your loop. The following exercises will help you to plan your loop.
Although you could use a while loop. It is easier to use a for loop in this case. Use a while loop when you don’t know how many times a loop needs to execute.
It is usually easiest to use a for loop if you know how many times the loop should execute using the given information. Figure out what the initial and ending values of the loop variable should be. Some of the method parameters will usually be used for these. In this case, we need to loop from year1 to year2. The preconditions stated for the method tells us that we don’t have to worry about year1 and year2 being out of order or below 0. So don’t waste time on error-checking these values. Here’s a possible loop:
Note that you are given a method to use called isLeapYear(). The method header for it says that it returns a boolean. Any method that starts with the word “is” usually returns a boolean. If it returns a boolean, that is a signal to you that you should use it in an if statement. The method will usually take an argument. If it is used inside the loop, this could be the loop variable. For example,
In the 2019 AP exam, part A numberOfLeapYears method was worth 5 points using the rubric below. Did you receive all 5 points? In class, your teacher may have you grade each others’ code.
In part B of the AP Calendar FRQ, you need to write the code inside a static method dayOfWeek, which returns the integer value representing the day of the week for the given date (month, day, year), where 0 denotes Sunday, 1 denotes Monday, …, and 6 denotes Saturday. This seems difficult at first, but helper methods are given to you to do most of the work. You just need to put them together to calculate the value. The helper methods given to you are:
firstDayOfYear(year) returns the integer value representing the day of the week for the first day of year, where 0 denotes Sunday, 1 denotes Monday, …, and 6 denotes Saturday. For example, since 2019 began on a Tuesday, firstDayOfYear(2019) returns 2.
dayOfYear(month, day, year) returns n, where month, day, and year specify the nth day of the year. For the first day of the year, January 1 (month = 1, day = 1), the value 1 is returned. This method accounts for whether year is a leap year. For example, dayOfYear(3, 1, 2017) returns 60, since 2017 is not a leap year, while dayOfYear(3, 1, 2016) returns 61, since 2016 is a leap year.
If you know that 1/1/2019 was a Tuesday (2) using the firstDayYear method, and you know that today is the nth day of the year using the dayOfYear method, you can figure out what day of the week today is by adding those together. Try some examples below.
Which of the following expressions return the right value for the day of the week (5) for Jan. 4th 2019 given that firstDayOfYear(2019) returns 2 and dayOfYear(1,4,2019) returns 4?
Since 1/1/19 is a Tuesday (2), Jan. 8th 2019, the 8th day of the year, is 7 days later, but since there are only 7 days of the week, so we need to start over at 0 on each Sunday.
Since 1/1/19 is a Tuesday (2), Jan. 8th 2019, the 8th day of the year, is 7 days later, but since there are only 7 days of the week, so we need to start over at 0 on each Sunday.
But there is no 9th day of week. There are only 7 days of the week. So when we reach a Sunday, we must start back at 0. This is a place where the remainder operator % is useful. Note that 9 % 7 = 2 which means that 1/8/2019 is the 2nd day of the week starting at 0.
Use remainder whenever you need to wrap around to the front if the value goes over the limit (num % limit). For example here for weekdays or for hours and minutes.
Use remainder to check for odd or even numbers (num % 2 != 0) is odd and (num % 2 == 0) is even. Actually, you can use it to check if any number is evenly divisible by another (num1 %
num2 == 0).
Complete the program below to figure out a day of the week from 0-6 where 0 is Sunday and 6 is Saturday for 7 days of the week. What value would you use for the divisor?
Which of the following expressions return the right value for the day of the week (2) for Jan. 8th 2019 given that firstDayOfYear(2019) returns 2 and dayOfYear(1,8,2019) returns 8?
In the 2019 AP exam, part B dayOfWeek method was worth 4 points using the rubric below. Did you receive all 4 points? In class, your teacher may have you grade each others’ code.
