CSE1120 Discrete Structures - Computer Project

2022-2023 Spring Semester

Overview

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

• Assessment
• Solutions

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.