Math Class

Intro

The Math class in Java is part of the java.lang package, which is automatically imported, hence you don’t need to manually import it. The Math class provides a collection of methods and constants for performing mathematical operations.

Key points about the Math class:

  • Static Methods: The methods of the Math class are static, meaning you can call them directly using the class name without needing to create an instance of the Math class. For example, Math.sqrt(25) will return 5.0. Commonly Used Methods:
  • Math.abs(double a): Returns the absolute value of a.
  • Math.sqrt(double a): Returns the square root of a.
  • Math.pow(double a, double b): Returns a raised to the power of b.
  • Math.max(double a, double b): Returns the greater of a and b.
  • Math.min(double a, double b): Returns the lesser of a and b.
  • Math.round(double a): Rounds a to the nearest integer.
  • Math.random(): Returns a double value greater than or equal to 0.0 and less than 1.0.

Evaluation of Expressions Using the Math Class

Let’s dive into evaluating expressions and demonstrating program statements using Math class methods. We will explore how to use these methods in Java code through examples.

Example 1: Calculating the Hypotenuse of a Right Triangle

public class Triangle {
    public static void main(String[] args){
        double a = 3;
        double b = 4;
        double c = Math.sqrt(Math.pow(a, 2) + Math.pow(b, 2));
        System.out.println("Hypotenuse: " + c);
    }
}
Triangle.main(null)

Hypotenuse: 5.0

Math.pow()
  • As stated previously, Math.pow() method is used to raise a number to a specified power. Here, it is used to calculate the squares of the sides a and b
Math.sqrt()
  • As Math.sqrt() method calculates the square root of a number. Here, it is used to find the square root of the sum of the squares of a and b, which gives the length of the hypotenuse

Example 2: Finding the Larger of Two Numbers

public class Larger{
    public static void main(String[] args){
        double num1 = 7.25;
        double num2 = 7.20;
        double larger = Math.max(num1, num2);
        System.out.println("The larger number is: " + larger);
    }
}
Larger.main(null)

The larger number is: 7.25

Math.max()
  • Used to find the maximum of two numbers. In this example, it is used to determine the larger number between num1 and num2

Using Math.random() and Setting Up a Range

Math.random() is a versatile method used to generate random numbers. However, it returns a double value that is greater than or equal to 0.0 and less than 1.0. Often, you’ll need a random integer within a specific range, say from min to max (inclusive). To achieve this, you can scale and shift the result of Math.random().

Example: Generating a Random Integer Between 1 and 10

public class Generate{
    public static void main(String[] args){
        int min = 1;
        int max = 10;
        int randomNum = (int)(Math.random() * ((max - min) + 1)) + min;
        System.out.println("Random Number: " + randomNum);
    }
}
Generate.main(null)

Random Number: 2

Example FRQ

2016 1a: RandomStringChooser Method

A RandomStringChooser object is constructed from an array of non-null String values. When the object is first constructed, all of the strings are considered available. The RandomStringChooser class has a getNext method, which has the following behavior. A call to getNext returns a randomly chosen string from the available strings in the object. Once a particular string has been returned from a call to getNext, it is no longer available to be returned from subsequent calls to getNext. If no strings are available to be returned, getNext returns “NONE”. The following code segment shows an example of the behavior of RandomStringChooser.

String[] wordArray = {"wheels", "on", "the", "bus"}; 
RandomStringChooser sChooser = new RandomStringChooser(wordArray); 
for (int k = 0; k < 6; k++) { 
    System.out.print(sChooser.getNext() + " "); 
}

One possible output is shown below. Because sChooser has only four strings, the string “NONE” is printed twice.

bus the wheels on NONE NONE

Write the entire RandomStringChooser class. Your implementation must include an appropriate constructor and any necessary methods. Any instance variables must be private. The code segment in the example above should have the indicated behavior (that is, it must compile and produce a result like the possible output shown). Neither the constructor nor any of the methods should alter the parameter passed to the constructor, but your implementation may copy the contents of the array.

Solution + Common Mistakes

public class RandomStringChooser {
    private List<String> words;
    public RandomStringChooser(String[] wordArray){

    words = new ArrayList<String>();

    for (String singleWord : wordArray){
    words.add(singleWord);
}}

public String getNext() {
    if (words.size() > 0){
        return words.remove((int)(Math.random() * words.size()));
}

    return "NONE";
}

}

Things to Look Out For

  • Making sure that when you initialize an instance variable to use the parameter in initialization
  • Properly casting with an integer when working with the random class
  • Don’t alter the constructor parameter!

Hacks

FRQ

In this assignment, you will work with a collection of randomly generated data represented by an ArrayList of ArrayLists of integers. You will design a class, named DataList, from scratch and implement methods within this class to manipulate the data according to specified criteria.

Requirements

  1. Class Declaration: Create a DataList class that encapsulates a collection of data.

    • The data collection should be an ArrayList of ArrayList of integers (ArrayList<ArrayList<Integer>>).
    • Include any necessary instance variables and a constructor to initialize the data structure.

  2. repopulate Method:

    • Write a method named repopulate in the DataList class. This method should fill each element of the collection with randomly generated values according to the following criteria:
      • Each value must be between 1 and MAX (inclusive), where MAX is a predefined constant in your class with a value that is not shown.
      • Each value must be divisible by 10.
      • Each value must not be divisible by 100.
    • Ensure that all valid values have an equal chance of being generated.
    • Precondition: The collection is not null and has at least one element.

Instructions

  • Design: Consider how you will structure your DataList class, including the choice of instance variables and the design of your constructor to properly initialize the data collection.
  • Implementation: Implement the repopulate method to meet the specified criteria. Think about how you can efficiently generate values that meet the requirements and how you’ll iterate through the ArrayList of ArrayLists to assign these values.
  • Testing: After implementing the repopulate method, consider writing a simple main method or unit tests to verify that your method works as expected. Generate a small collection and print the results to ensure values are correctly assigned according to the criteria.

Scientific Calculator

Situation: You are developing a scientific calculator application where users need to perform various mathematical operations.

(a) Discuss the purpose and utility of the Math class in Java programming. Provide examples of at least three methods provided by the Math class and explain their usage.

(b) Code: You need to implement a method calculateSquareRoot that takes a double number as input and returns its square root using the Math class. Write the method signature and the method implementation. Include comments to explain your code.

Scientific Calculator

(a) Purpose and Utility of the Math Class in Java Programming

The Math class in Java provides a set of methods for performing common mathematical operations. It serves as a utility class for mathematical computations, offering functions for basic arithmetic, trigonometry, exponential, logarithmic, and rounding operations. Here are examples of three methods provided by the Math class:

  1. Math.abs(double a): This method returns the absolute value of a given number. It disregards the sign of the number and returns its positive equivalent. For example: 
    double number = -10.5;
double absValue = Math.abs(number); // absValue will be 10.5
  2. Math.pow(double base, double exponent): This method returns the value of the first argument raised to the power of the second argument. It’s used for exponentiation. For example: 
    double base = 2.0;
double exponent = 3.0;
double result = Math.pow(base, exponent); // result will be 8.0 (2^3)
  3. Math.sin(double a): This method returns the sine of a given angle in radians. It’s useful for trigonometric calculations. For example: 
    double angleInRadians = Math.PI / 6; // 30 degrees in radians
double sinValue = Math.sin(angleInRadians); // sinValue will be 0.5

(b) Method Implementation: calculateSquareRoot

/**
 * Calculates the square root of a given double number using the Math class.
 *
 * @param number The input number whose square root needs to be calculated.
 * @return The square root of the input number.
 */
public static double calculateSquareRoot(double number) {
    // Using Math.sqrt() to calculate the square root
    double squareRoot = Math.sqrt(number);
    return squareRoot;
}

Explanation:

  • The method calculateSquareRoot takes a double parameter number for which the square root needs to be calculated.
  • Inside the method, Math.sqrt() is used to compute the square root of the input number.
  • The calculated square root is returned as the result of the method.