🔖 Background Information

In mathematics, the triangular numbers are a sequence of numbers where the nth number is given by the sum from 1 to N.

\[T_N = 1 + 2 + 3 + ... + N-1 + N\]

For example, the first few triangular numbers are:

\[T_1 = 1\] \[T_2 = 1 + 2 = 3\] \[T_3 = 1 + 2 + 3 = 6\]

And so on…

🎯 Problem Statement

Create a class called TriangleNumberCalculator that performs calculations with triangular numbers (outlined in the Acceptance Criteria below).

✅ Acceptance Criteria

Create a class called TriangleNumberCalculator with the following methods:

  • int value(int n) which returns the nth triangular number
  • int add(int n, int m) which adds the nth and mth triangular numbers
  • int subtract(int n, int m) which subtracts the nth and mth triangular numbers

Be sure to test all of your methods using JUnit!

📋 Dev Notes

  • You must use recursion to calculate the triangular numbers. Yes, you could use a for loop to solve these problems, but the theme of this week is recursion 🙂

🖥️ Example Output

Here is an example of how you might use the TriangleNumberCalculator class.

TriangleNumberCalculator calculator = new TriangleNumberCalculator();

System.out.println(calculator.value(1)); // This should print out 1
System.out.println(calculator.value(2)); // This should print out 3
System.out.println(calculator.value(4)); // This should print out 10

System.out.println(calculator.add(1, 1)); // This should print out 2
System.out.println(calculator.add(2, 3)); // This should print out 9
System.out.println(calculator.add(4, 2)); // This should print out 13

System.out.println(calculator.subtract(1, 1)); // This should print out 0
System.out.println(calculator.subtract(2, 3)); // This should print out -3
System.out.println(calculator.subtract(4, 2)); // This should print out 7

📝 Thought Provoking Questions

  1. What is the biggest argument you can enter into TriangleNumberCalculator#value(int n) before you get a stack overflow error?
  2. What is the biggest argument you can enter into TriangleNumberCalculator#add(int n) before you get a stack overflow error?
  3. What is the biggest argument you can enter into TriangleNumberCalculator#subtract(int n) before you get a stack overflow error?
  4. How do your results for questions 1 - 3 relate to each other? Is this what you expected?

💼 Add-Ons For the Portfolio

(One Credit) Multiplication

Implement a method called int multiply(int n, int m) which multiplies the nth and mth triangular numbers. Be sure to test your method using JUnit!

(One Credit) Division

Implement a method called double divide(int n, int m) which divides the nth and mth triangular numbers. Be sure to test your method using JUnit!

(Two Credits) Sequence

Implement a method called sequence(int n) which returns a list of triangle numbers up to the Nth number: $T_1, T_2, T_3, …, T_N$. Be sure to test your method using JUnit!

📘 Works Cited

There are no works cited for this lab.