Bytes

A bit is a 0 or a 1. Bits can be combined to represent numbers in binary representation. For example, the numbers $0$ through 7 can be represented in binary by

Decimal Binary
$0$ 000
$1$ 001
$2$ 010
$3$ 011
$4$ 100
$5$ 101
$6$ 110
$7$ 111

In general, if you want to represent the numbers $0$ through $2^n-1$ (or $-2^{n-1}-1$ to $2^{n-1}-1$ if you care about negative numbers too), you need at least $n$ bits. One byte is 8 bits. Therefore, using $z$ bytes of data, we can represent the numbers from $0$ to \(2^{8z}-1\) (or $-2^{8z-1}-1$ to $2^{8z-1}-1$ if, again, you care about negative numbers). The range of numbers we can represent depends on the number of bytes we use: more bytes equals more numbers!

Variable Types

There are 8 fundamental variable types (and a bonus important variable type):

  1. byte. This is an integer between $-128$ and $127$ represented by 1 byte.
  2. short. This is an integer between $-32768$ and $32767$ represented by 2 bytes.
  3. int. This is an integer between $-2^{31}$ and $2^{31}-1$ represented by 4 bytes.
  4. long. This is an integer between $-2^{63}$ and $2^{63}-1$ represented by 8 bytes.
  5. float. This is a decimal with precision up to $6$ or $7$ decimal digits. It has a smaller range than double and is represented by 4 bytes. Use this if you want to minimize how large your program is and don’t care about precision.
  6. double. This is a decimal with precision up to $15$ or $16$ decimal digits. It has a larger range than float and is represented by 8 bytes. Use this if you care about precision and don’t care about how large your program is.
  7. char. Basically a letter in the alphabet. We denote a char by encasing it around 2 ' single quotes. char’s also have numerical values assigned by ASCII convention. You can get the numerical value by casting to an integer: int castedCharacter = (int)c;, where $c$ was of type char.
  8. boolean. You have only two options: true or false. 1 byte.
  9. String. Technically, string’s are not a fundamental variable type, but they’re worth talking about. A string is treated as an array of char’s. We denote a String by encasing it around 2 "double quotes. To get the char array of the string, use java.lang.String.toCharArray(String s).

Note that all number variable types are signed in Java! When declaring the existence of a variable, we do variableType variableName;. If we also want to set it equal to something at the same time, we do variableType variableName = initialValue;.

Conditional Statements

Sometimes, I only want to do something with my code when some other thing is true. To check for equality, use the == operation (use the s1.equals(s2) method for String’s s1 and s2). To check for inequality, use the != operation. $<, \leq, >, \geq$ are represented by <, <=, >, >=, respectively. Here is an example of using conditional statements:

public class Example {
    // Our class doesn't have any fields.

    public Example() {
        // Nothing to construct either.
    }
    
    public void doStuff(int n) {
        if (n == 6) {
            System.out.println("Equals 6.");
        }
        else if (n > 6) {
            System.out.println("Greater than 6.");
        else {
            System.out.println("Less than 6.");
        }
        
        if (n != 6) {
            System.out.println("Also not equal to 6.");
        }
    }
    
    public static void main(String[] args) {
        Example example = new Example();
        example.doStuff(6);
        example.doStuff(7);
        example.doStuff(3);
    }
}

We introduced the idea of if, else if, and else statements. To only do something when multiple conditions are true, use the && ‘and’ operator. To only do something when at least one of a number of conditions are true, use the || ‘or’ operator.

Repetitions and Loops

Sometimes, we want to keep doing something a repeated number of times. If we know how many times we want to do something, use a for loop. If we don’t know yet how many times we want to do something use a while loop. Both types of loops check for equality every iteration. Here is an example of both a for loop and while loop that will print the first $n$ positive even numbers:

public class Example {
    // Our class doesn't have any fields.

    public Example() {
        // Nothing to construct either.
    }
    
    public void useForLoop(int n) {
        /*
         * int i = 1 declares the existence of a variable i and sets it 
         * initially equal to 1. The for loop continues to iterate until 
         * i < n + 1 is no longer true. i++ means that we increment i by 1 
         * after every iteration.
         */
        for (int i = 1; i < n + 1; i = i + 1) {
            System.out.println(2 * i);
        }
    }
    
    public void useWhileLoop(int n) {
        /*
         * As long as n > 0 is true,
         * continue looping.
         */
        while (n > 0) {
             System.out.println(2 * n);
             n = n - 1;
         }
    }
    
    public static void main(String[] args) {
        Example example = new Example();
        // What will this for loop print out?
        example.useForLoop(5);
        // What will this while loop print out? How is it different from 
        // what the for loop prints out?
        example.useWhileLoop(5);
    }
}

Exercises

Problem 1

In the comments of the main section in the code snippet in the Repetitions and Loops section above, we asked the following three questions:

  1. What will the for loop print out?
  2. What will the while loop print out?
  3. How are the outputs of the for and while loops different?

Please answer these three questions.

Problem 2

This problem is adapted from Codeforces.

Sometimes some words like "localization" or "internationalization" are so long that writing them many times in one text is quite tiresome. Let’s consider a word too long, if its length is strictly more than 10 characters. All too long words should be replaced with a special abbreviation. This abbreviation is made like this: we write down the first and the last letter of a word and between them we write the number of letters between the first and the last letters. For example, "localization" will be spelt as "l10n", and "internationalization" will be spelt as "i18n". Fill in the following code segments. Before starting, I’d recommend checking out this link.

public class Problem2 {
    // Our class doesn't have any fields.

    public Problem2() {
        // Nothing to construct either.
    }
    
    public static int numChar(String s) {
        // TODO: Return how many characters are in the input String s. Do
        // not use the .length() method. Try writing this using a for loop.
        return 0;
    }
    
    public static int numInternalChar(String s) {
        // TODO: Return how many characters are in the input String s, aside
        // from the first and the last character. This should be one line
        // of code using the result of numChar(String s) method above.
        return 0;
    }
    
    public static String abbreviate(String s) {
        // TODO: Using the above two methods, rewrite the FILL IN HERE's to 
        // give the requested abbreviation.
        
        // What do we want to do when the number of letters in the string
        // is more than 10?
        if (s.length() > 10) {
            return (Character.toString(s.charAt(0)) + 
                    Integer.toString(FILL IN HERE) + 
                    Character.toString(s.charAt(
                                    s.length() - 1)));
        }
        // What do we want to do if the word is short instead?
        else {
            return FILL IN HERE;
        }
    }
    
    public static void main(String[] args) {
        // Feel free to change THIS IS OUR STRING to whatever string 
        // you like!
        String ourString = "THIS IS OUR STRING";
        System.out.println(abbreviate(ourString));
    }
}

Try out your code on your computer and see if it works!

Problem 3

This problem is adapted from Caltech’s CS11 course.

Let’s write a program to represent an $(x, y)$ pair on the Cartesian plane as a Java class. Our goal is to be able to calculate the distance between any two points. For this problem, fill in the following code segments. Before starting, I’d recommend checking out this link.

import java.util.*;
import java.io.*;
import java.lang.Math;

/**
 * A two-dimensional point class.
 **/
public class Point2d {
    /** x coordinate of the point **/
    private double x;

    /** y coordinate of the point **/
    private double y;

    /** Constructor to initialize point to (x, y, z) value **/
    public Point2d(double x, double y) {
        this.x = x;
        this.y = y;
    }

    /** No-argument constructor: defaults to a point at the origin **/
    public Point2d() {
        this(0, 0);
    }

    /** Return the x coordinate of the point **/
    public double getX() {
        // TODO: Fill in what to return here.
    }

    /** Return the y coordinate of the point **/
    public double getY() {
        // TODO: Fill in what to return here.
    }

    /** Set the x coordinate of the point to val**/
    public void setX(double val) {
        // TODO: Fill in what to do here.
    }

    /** Set the y coordinate of the point to val **/
    public void setY(double val) {
        // TODO: Fill in what to do here.
    }

    /** Return if two points are equal. **/
    @Override
    public boolean equals(Point2d otherPoint) {
        // TODO: Check if two points are equal. Remember that two points 
        // are equal if their x coordinates are equal and their y 
        // coordinates are equal.
    }

    /** 
     * Return Euclidean distance between two points with 
     * double-precision
     **/
    public double distanceTo(Point2d otherPoint) {
        // TODO: You need to use the distance formula here. To find the 
        // square root of a number, you might need to look it up online. 
        // A simple Google search
        // "square root number Java" should suffice.

        // Remember to only calculate the distance to another point if
        // the two points are not equal! A good way of checking point
        // equality is using the equals() method you defined above.
    }

    public static void main(String[] args) {
        // Create a point (0, 3) on the xy plane.
        Point2d p1 = new Point2d(0, 3);
        // Create a point (4, 0) on the xy plane.
        Point2d p2 = new Point2d(4, 0);
        // Calculate the distance between the two points. You should expect 
        // to see 5 from the Pythagorean theorem.
        // TODO: Write and print the calculation here.
    }
}