Question

(Separating Digits) Write methods that accomplish each of the following tasks: a) Calculate the integer part of the quotient when integer a is divided by integer b. b) Calculate the integer remainder when integer a is divided by integer b. c) Use the methods developed in parts (a) and (b) to write a method displayDigits that receives an integer between 1 and 99999 and displays it as a sequence of digits, separating each pair of digits by two spaces. For example, the integer 4562 should appear as \(4 \quad 5 \quad 6 \quad 2\) Incorporate the methods into an application that inputs an integer and calls displayDigits by passing the method the integer entered. Display the results.

Short answer

To display an integer as a sequence of digits, create methods to calculate the quotient and remainder, use these to split the number into digits, and then display them with spacing.

Step-by-step solution

- Define a method to calculate the quotient

Define a method named calculateQuotient that takes two integer arguments a and b. This method returns the integer part of the quotient when a is divided by b using the division operator (a/b). Ensure that a and b are integers to guarantee an integer result.

- Define a method to calculate the remainder

Define a method named calculateRemainder that takes two integer arguments a and b. This method returns the remainder of a divided by b using the modulus operator (a%b).

- Define the displayDigits method

Define a method named displayDigits that takes an integer named number between 1 and 99999. The method should repeatedly divide the number by 10 using calculateQuotient to obtain each digit starting from the highest place value, and use calculateRemainder to find the next number to process. The method should store the digits in an array or use another method to keep track of them in reverse order.

- Print the digits with spacing

Inside displayDigits method, iterate through the array with digits in reverse to print each digit separated by two spaces. Use a loop to print the elements of the array and ensure correct spacing.

- Incorporate methods into the application

Create a main application that prompts the user to input an integer. Use a scanner or equivalent input method to capture the user's input. Validate that the input is an integer between 1 and 99999. If valid, call displayDigits by passing the integer to it. Print the results accordingly.

- Execute and test the application

Execute the application. Test it with various integers to ensure that the methods are working correctly and that the program displays the sequence of digits with proper spacing between each pair of digits.

Key concepts

Understanding Integer Division in Java

When learning Java programming, understanding how integer division works is a fundamental concept. Integer division refers to dividing one integer by another and obtaining a result that is also an integer. In Java, when you divide two integers, the result is the whole number part of the quotient, and any fractional part is discarded.

For example, dividing 7 by 2 using integer division yields 3, not 3.5, because the fractional part (.5) is dropped. This is unlike the floating-point division, where the result includes the decimal part. The importance of integer division in programming can be seen in situations where you need to group items or calculate how many times a smaller integer fits into a larger one without considering the remainder.

Here's how you can perform integer division in Java:

• Ensure both operands are integers.
• Use the division operator (/).
• The result will automatically be the integer part of the quotient.

To get a better grasp of this, consider the method calculateQuotient in the exercise, which takes two integers and returns their division result as an integer.

Demystifying the Modulus Operator

Often students struggle with the modulus operator, but it's quite a simple yet powerful tool in Java. The modulus operator, denoted by %, calculates the remainder of the division of two numbers. For instance, if you divide 10 by 3, the quotient is 3 and the remainder is 1. The modulus operator would give you 1 when you calculate 10 % 3.

The modulus is essential in programming for tasks such as determining if a number is even or odd (a number is even if it's divisible by 2 with a remainder of 0), or when breaking down numbers into smaller components, like in our displayDigits method.

Using the modulus operator is straightforward:

• Take two integers.
• Apply the modulus operator (%) between them.
• The result is the remainder of the division.

As demonstrated in the calculateRemainder method from the exercise, this operation is fundamental for separating digits of a larger number.

Mastering Array Manipulation

Array manipulation is a core skill in Java programming as it involves working with collections of data. Java arrays are homogeneous data structures that store multiple values of the same type. In the context of the exercise provided, arrays can be used to store the individual digits of an integer for further manipulation.

Here are some key array manipulation techniques:

• Declaration: Specify the type of data your array will hold.
• Initialization: Allocate memory for the array, defining its size.
• Assignment: Add or change the values stored in the array at specific indices.
• Traversal: Loop through the array to access or modify elements.
• Utility functions: Use built-in Java functions like Arrays.toString() for printing or Arrays.sort() for ordering.

In our displayDigits method, we need to store the digits of the input number in reverse order, which requires initializing an array, populating it with the digits (using loops and array indices), and then traversing it to print out the numbers according to the specified format.