ApachUSA / Basic-algorithms-on-graphs

Realization of basic algorithms on an oriented graph (Dijkstra, Prim's, Ford–Fulkerson, DFS, BFS)

Graph algorithms

(Dijkstra, Prim's, Ford–Fulkerson, Depth-first search, Breadth-first search)

Introduction

During my university studies there were several lab works related to graph algorithms. I decided to combine them into one application, as they have the same foundation. This work is a little more than a year old, I would probably write a much better one now, but I'll leave it as it is. Maybe someone will find it useful as a good example of implementing graphs and algorithms.

Technologies

• The system is implemented using WPF and MVVM pattern.
• Moving vertices is implemented using Microsoft.Xaml.Behaviors.Wpf

Functions

General

• Only oriented graphs are used in the application
• The function of saving the graph and restoring works
• In the Saves folder there is a saved graph for each algorithm as an example
• ⚠️When saving, specify only the file name (.json will be set automatically)
• ⚠️ After using the algorithm, don't forget to clean the result with the eraser next to it

Dijkstra

Dijkstra's algorithm is an algorithm used to determine the shortest path from the initial node to all other nodes.

• The shortest path from node A to node B is marked in green.

Dijkstra

Depth-first search

Depth-first search (DFS) is one of the graph traversal methods. Depth-first search strategy, as the name suggests, is to go "deep" into the graph as far as possible. Visited but still unused vertices accumulate in the stack, so the later a vertex is visited, the sooner it will be used.

• Only graph traversal is implemented, not search
• In the field you need to enter the time in milliseconds for animation
• The result is displayed in colors and additionally the stack is displayed
• At the end, topological sorting is applied and displayed next to it (vertex numbers change too).

DFS

Breadth-first search

BFS (Breadth-First Search) is a graph search algorithm that explores all vertices in one level before moving to the next level. Breadth-first search, roughly speaking, is based on replacing the stack with a queue. After this modification, the earlier a vertex is visited (placed in the queue), the earlier it is used (removed from the queue).

• Only graph traversal is implemented, not search
• In the field you need to enter the time in milliseconds for animation
• The result is displayed in colors and additionally the queue is displayed

BFS

Prim's

Prima Algorithm is an algorithm for constructing the minimum spanning tree of a weighted connected undirected graph.

• As it was said before, the system uses oriented graphs, so the algorithm checks not only the edge you created (1 -> 2), but also the reverse edge (2 -> 1).
• The final minimum spanning tree is displayed in green color.

Prim's

Ford–Fulkerson

The Ford-Falkerson algorithm is a greedy approach to calculate the maximum possible flow in a network or graph.

• The upper value of the edge is responsible for the capacity and the lower value for the flow
• The maximum flow is displayed at the bottom of the algorithm window

Ford–Fulkerson