Question 4: 2D Array

Finding a block of empty seats

Unit 4
6 points
About 22 minutes

You write one method that traverses, analyzes or changes data in a 2D array, often of objects, using the classes described in the question. New since the course was revised for 2025–26 (first tested in May 2026): it's worth 6 points instead of 9, and points are no longer taken off as penalties. On the exam: Question 4 of 4, 6 points. Section II has 4 free-response questions in 90 minutes (45% of the score), all assessing Practice 2 (Develop Code). The exam is fully digital in Bluebook: you type your Java, and the Java Quick Reference is provided. No calculator. Suggested time is our split of the 90 minutes by points; College Board gives no per-question timing.

The question and its sources

A theater's booking system stores its seats in a two-dimensional array of Seat objects. Each row of the array is one row of seats, from left to right. When an element of a two-dimensional array is accessed, the first index is the row and the second index is the column.

The Seat class

Java

public class Seat
{
    /** Returns true if someone has booked this seat; false otherwise */
    public boolean isTaken()
    { /* implementation not shown */ }
 
    // There may be instance variables, constructors, and methods that are not shown.
}

The SeatingChart class

Java

public class SeatingChart
{
    /**
     * The seats in the theater. seats has at least one row and at least
     * one column, and contains no null elements.
     */
    private Seat[][] seats;
 
    /**
     * Returns the index of the first row that has at least k empty seats
     * next to each other, or -1 if no row does, as described in the
     * question.
     * Precondition: k > 0
     */
    public int firstRowWithBlock(int k)
    { /* to be implemented */ }
 
    // There may be instance variables, constructors, and methods that are not shown.
}

Example: seats ("taken" means isTaken() returns true)

Row	Column 0	Column 1	Column 2	Column 3	Column 4	Column 5
0	taken	taken	empty	taken	empty	empty
1	empty	taken	empty	empty	empty	taken
2	empty	empty	empty	empty	taken	taken
3	taken	taken	taken	taken	taken	taken

Source: Hypothetical example

Example calls on the seats above

Call	Value returned	Why
`firstRowWithBlock(2)`	0	Row 0 has 2 empty seats next to each other (columns 4 and 5).
`firstRowWithBlock(3)`	1	Row 1 has 3 (columns 2–4). Row 0 has at most 2.
`firstRowWithBlock(4)`	2	Row 2 has 4 (columns 0–3).
`firstRowWithBlock(5)`	-1	No row has 5 empty seats next to each other.

Source: Hypothetical example

Suggested time: 22 minutes

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Part (a)

6 points

Write the SeatingChart method firstRowWithBlock. Seats next to each other must be in the same row: empty seats at the end of one row and the start of the next row do not form a block. Complete method firstRowWithBlock.public int firstRowWithBlock(int k)

Your answer to part (a)

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