Question

(Huge Integer Class) Create a class HugeInteger which uses a 40 -element array of digits to store integers as large as 40 digits each. Provide methods input, output, add and subtract. For comparing HugeInteger objects, provide the following methods: isEqualTo, isNotEqualTo, isGreaterThan, isLessThan, isGreaterThan0rEqualTo and isLessThanOrEqualTo. Each of these is a predicate method that returns true if the relationship holds between the two HugeInteger objects and returns false if the relationship does not hold. Provide a predicate method iszero. If you feel ambitious, also provide methods multiply, divide and remainder. [Note: Primitive boolean values can be output as the word "true" or the word "false" with format specifier \(\$ b\).

Short answer

A class HugeInteger can store up to 40-digit numbers, perform basic arithmetic, and compare two objects using array-based methods.

Step-by-step solution

Define the Class Structure

First, define a class named `HugeInteger`. Inside this class, include a private member variable `digits` to store a 40-element array of integers. This array will represent the huge integer, with each element holding a single digit from 0 to 9.

Implement Input Method

Create a method called `input` which initializes the `digits` array based on a string input representing a huge integer. The method should parse the input string and populate the array starting from the end, handling leading zeros appropriately.

Implement Output Method

Develop a method named `output` to print the `HugeInteger`. This method iterates through the `digits` array and formats the output by ignoring leading zeros until it finds the most significant digit.

Implement Addition Method

Write a method `add`, which takes another `HugeInteger` object as a parameter. Perform addition using typical digit-by-digit addition, ensuring to manage carries between digits if the sum exceeds a single digit.

Implement Subtraction Method

Create a `subtract` method for subtracting one `HugeInteger` from another, taking into account borrowing when the digit of the minuend is smaller than the subtrahend.

Implement Predicate Methods

Add methods `isEqualTo`, `isNotEqualTo`, `isGreaterThan`, `isLessThan`, `isGreaterThanOrEqualTo`, and `isLessThanOrEqualTo`. Each method compares two `HugeInteger` objects by iterating over their digits to check the specified condition and return a boolean result.

Implement isZero Method

Implement `isZero`, which checks if the `HugeInteger` is zero by iterating over the `digits` array; if all elements are zero, return true, otherwise false.

Extend with Ambitious Methods

For multiplication, division, and finding the remainder, implement `multiply`, `divide`, and `remainder` methods. These should follow basic arithmetic rules, scaling the typical operations of smaller numbers to arrays of digits, respecting carries, and borrows appropriately.

Key concepts

Class Design

When designing a class, especially in Object-Oriented Programming (OOP), you need to organize and set up a blueprint that represents the real-world entity you're modeling. The `HugeInteger` class is an example of this, where the objective is to handle large integers using OOP principles.

In the case of `HugeInteger`, the class design involves defining the data and behavior that this integer will have. The class should encapsulate:

• Attributes: These are represented by a private array `digits` of size 40, which stores individual digits of a large number, maintaining encapsulation and restricting direct access from outside the class.
• Methods: Functions like `input`, `output`, and those for arithmetic operations (`add`, `subtract`) and comparisons function as the class's interface. They enable interaction with `HugeInteger` objects.

This design allows for the handling of big numbers efficiently and ensures methods handle operations internally. Each method respects object encapsulation and allows only appropriate exposures, ensuring that the implementation details remain hidden and easily manageable.

Data Structures

Data structures help in organizing and storing data efficiently. For the `HugeInteger` class, the primary data structure involves using an array of integers. Arrays are simple data structures that allow access to elements using an index. In this context, a 40-element array is utilized to store each digit of a potentially huge integer separately.

By doing so, you can perform arithmetic and comparison operations on a per-digit basis, similar to how calculators handle multi-digit calculations. This way, the indexing aligns each digit in its place value, simplifying the periodical operations such as carrying over in addition and borrowing in subtraction:

• Efficient representation of large numbers where each position in the array corresponds to a digit.
• Facilitates operations over entities that do not fit into standard data types (like `int` or `long`).
• Allows easy iteration for comparisons and logical evaluations of numbers.

This structure supports direct interaction with segments of the stored integer, making individual digits accessible for manipulation while maintaining the whole integer's value.

Algorithm Development

Algorithm development is a critical step in solving specific problems using programming. In the `HugeInteger` class, several algorithms are employed to effectively manage operations like addition and subtraction of large numbers. For instance, let's consider the `add` method:

• Begin from the least significant digit (rightmost) of both `HugeInteger` objects.
• Add corresponding digits from both numbers, including any carry from previous additions.
• If a sum exceeds 9, set that digit’s place in the result to the individual sum mod 10, and carry over the 1 to the next digit.
• Continue until reaching the most significant digit (leftmost).

Similarly, subtraction involves borrowing, where necessary, ensuring all operations respect the constraints of digit manipulation within the array:

• Handle potential negative results appropriately and accurately.

Developing efficient algorithms like these ensures that operations perform correctly under a wide range of scenarios, providing reliable results while handling edge cases like carries and borrows automatically.

Boolean Logic

Boolean logic forms the foundation of decision-making in programming. It uses true or false values derived from logical statements and comparisons. With the `HugeInteger` class, boolean logic is crucial in evaluating the relationships between objects. The predicate methods within this class (e.g., `isEqualTo`, `isNotEqualTo`) implement boolean logic by returning true or false based on specific conditions. Here's how they work:

• Iterate through the digits of both numbers, comparing corresponding elements for equality.
• If any pair of digits fails to satisfy the comparison, return straight false indicating inequality or unmatched condition.
• If loops complete without finding discrepancies, consider the numbers matching and return true.

This logic applies to other comparisons like `isGreaterThan` or `isLessThan`, helping to drive conditional operations within the program.
All operations ensure bulletproof handling of conditions, leveraging cascaded logical checks to affirm the correct state of the large integers, supporting comprehensive and error-free execution of relational operations.