The document discusses the Floyd-Warshall algorithm for finding the shortest paths between all pairs of vertices in a weighted graph. It describes the components used including JavaFX, Jfoenix library, and CSS. It outlines the classes involved like FloydWarshall, MainWindow, MatrixInput, and challenges in graphical representation, positioning, and finding shortest paths. It explains how the algorithm works by initializing the graph and iterating steps to update shortest distances based on intermediate vertices. Advantages are finding all shortest paths with a single execution but it has a complexity of O(n3).

1. INTRODUCTION
The Floyd Warshall Algorithm is for solving the all
pairs shortest path problem. It helps to find shortest
distances between every pair of vertices in a given
edge weighted directed Graph.

2. COMPONENTS
1. Java FX
2. Additional Library – Jfoenix
3. CSS – Cascading Style Sheet

3. COMPONENTS
1. Floyd Warshall
2. FXML Document
3. Category Chooser
4. Vertex and Edges
5. Manual Input
6. Table Viewer
7. Graph Viewer

4. CLASS DIAGRAM
Floyd Warshall
Main Window Matrix InputManual Input
Category Chooser Table RepresentationGraph Representation
Start Over
Close

5. CHALLENGES
1. Graphical Representation of Graph
2. Vertex and Edge Positioning
3. Finding Shortest Path
4. Automated Simulation
5. Table Coloring

6. HOW IT WORKS?
A B C
A
B
C
Path
Sequence
Initial Step
Graph
A B C
A
B
C

7. A B C
A B C
A
B
C
A
B
C
Path
Step 1
Step 2
Path Sequence
Sequence
A B C
A
B
C
A
B
C
A B C
D(ij)> D(ik)+D(kj)

8. A
B
C
A B C
Path Sequence
A B C
A
B
C
Step 3

9. ADVANTAGES & DISADVANTAGES
Advantages:
1. Shortest Path
2. Easy to Modify
3. Single execution to find out length
Disadvantages:
1. O(n^3)