https://github.com/furk4nbulut/cse1120-discrete-structures-computer-project

olutions for the CSE1120 Discrete Structures course project (Spring 2022-2023). Includes Java implementations for mathematical proofs, Lucas numbers, and least airfare routes.
https://github.com/furk4nbulut/cse1120-discrete-structures-computer-project

discrete-structures java

Last synced: 5 days ago
JSON representation

olutions for the CSE1120 Discrete Structures course project (Spring 2022-2023). Includes Java implementations for mathematical proofs, Lucas numbers, and least airfare routes.

• Host: GitHub
• URL: https://github.com/furk4nbulut/cse1120-discrete-structures-computer-project
• Owner: Furk4nBulut
• Created: 2023-05-25T12:42:08.000Z (over 1 year ago)
• Default Branch: master
• Last Pushed: 2024-08-10T06:48:11.000Z (3 months ago)
• Last Synced: 2024-08-10T08:11:48.018Z (3 months ago)
• Topics: discrete-structures, java
• Language: Java
• Homepage:
• Size: 572 KB
• Stars: 1
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
# CSE1120 Discrete Structures - Computer Project

## 2022-2023 Spring Semester

### Overview

You can access the assessment and the solutions from the following links:

- [Assessment](CSE1120_ComputerProject.docx)

- [Solutions](Report.pdf)

### Problems and Solutions

1. **Mathematical Induction Proof**

   **Problem Statement:**

   Use mathematical induction to show that a given equation holds for all nonnegative integers \( n \). 

   **Solution:**

   The proof involves two main steps:

   - **Base Case:** Verify the equation for the initial value (usually \( n = 0 \) or \( n = 1 \)).

   - **Inductive Step:** Assume the equation is true for an arbitrary integer \( k \), and then show it holds for \( k + 1 \).

   The details of the proof can be found in the `Q1.java` file.

2. **Equation Validation Program**

   **Problem Statement:**

   Write a computer program to validate the given equation.

   **Solution:**

   A Java program is provided that takes an integer \( n \) as input and verifies whether the equation holds. The code can be found in `Q2.java`.

3. **Lucas Numbers Generator**

   **Problem Statement:**

   Write a recursive method to generate Lucas numbers.

   **Solution:**

   A recursive Java method is implemented to generate Lucas numbers. The Lucas numbers are similar to Fibonacci numbers but with different initial values. The implementation can be found in `Q3.java`.

4. **Least Airfare Route Finder**

   **Problem Statement:**

   Write a computer program to find a route with the least total airfare that visits each of the cities in a given graph, where the weight on an edge represents the least price available for a flight between the two cities.

   **Solution:**

   The solution involves implementing an algorithm to find the shortest path in a weighted graph. The code for finding the minimum airfare route can be found in `Q4.java`.

### Files

- `Q1.java` - Contains the detailed proof for the mathematical induction problem.

- `Q2.java` - Java program for validating the equation.

- `Q3.java` - Java program for generating Lucas numbers.

- `Q4.java` - Java program for finding the least total airfare route.