You Need Power, Wisdom, and Courage When Using Recursion

🔖 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

📋 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 lab is recursion 🙂

🖥️ Example Output

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

C++

TriangleNumberCalculator calculator;
 
cout << calculator.value(1); // This should print out 1
cout << calculator.value(2); // This should print out 3
cout << calculator.value(4); // This should print out 10
 
cout << calculator.add(1, 1); // This should print out 2
cout << calculator.add(2, 3); // This should print out 9
cout << calculator.add(4, 2); // This should print out 13
 
cout << calculator.subtract(1, 1); // This should print out 0
cout << calculator.subtract(2, 3); // This should print out -3
cout << calculator.subtract(4, 2); // This should print out 7

Java

 
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

What is the biggest argument you can enter into TriangleNumberCalculator#value(int n) before you get a stack overflow error?
What is the biggest argument you can enter into TriangleNumberCalculator#add(int n) before you get a stack overflow error?
What is the biggest argument you can enter into TriangleNumberCalculator#subtract(int n) before you get a stack overflow error?
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!

(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!

(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!

🔗 Useful Links

Java Project Template

📘 Works Cited

N/A

More Than Equations

Explorer