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https://github.com/christs8920/shortest-path-algorithms
An implementation and analysis of 3 shortest path algorithms with Python.
https://github.com/christs8920/shortest-path-algorithms
algorithms bellman-ford bellman-ford-algorithm dijkstra dijkstra-algorithm floyd-warshall floyd-warshall-algorithm python shortest-path-algorithm
Last synced: about 1 month ago
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An implementation and analysis of 3 shortest path algorithms with Python.
- Host: GitHub
- URL: https://github.com/christs8920/shortest-path-algorithms
- Owner: ChrisTs8920
- License: mit
- Created: 2024-08-01T09:03:44.000Z (5 months ago)
- Default Branch: main
- Last Pushed: 2024-08-03T09:58:43.000Z (5 months ago)
- Last Synced: 2024-08-03T10:56:16.811Z (5 months ago)
- Topics: algorithms, bellman-ford, bellman-ford-algorithm, dijkstra, dijkstra-algorithm, floyd-warshall, floyd-warshall-algorithm, python, shortest-path-algorithm
- Language: Python
- Homepage:
- Size: 56.6 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Implementation and analysis of shortest path algorithms using Python
## Description
This repository implements and analyzes 3 shortest path algorithms in Python:
- Dijkstra's
- Floyd-Warshall
- Bellman-Ford
>*This project was made during my Graph theory course in university.*
## Summary
These algorithms find the shortest path between 2 vertices in a **weighted** graph. A graph is a collection of **vertices** connected by **edges**, which can represent real networks. For **example** in a computer network, the computers are the vertices and the connections between them are the edges (i.e. cables). In a weighted graph, each edge has an associated value attached to it, which represents the cost, the distance or the time it takes to traverse them. A graph can be directed or undirected.
These algorithms have many different applications in the real world, including:
- **Network routing:** Determine the most efficient path for data packets in computer networks.
- **Geographic Information Systems (GIS):** Used in mapping and navigation services (Google maps) to find optimal routes and minimize distances.
- **Robotics:** Path planning for autonomous robots to navigate in environments.
- **VLSI design:** Find optimal routes for connecting various circuit components such as gates and transistors.
### Dijkstra's
- Invented by Edsger W. Dijkstra in 1956.
- Finds the shortest path from a given vertice to any other vertice. Can also find the shortest path between a given start vertice and a destination vertice.
- Used in graphs where the weights are **positive** numbers.
- Time complexity: $O(n^2)$, where $n$ the number of vertices.
### Floyd-Warshall
- Also known as Floyd or Roy-Warshall, published in it's current form by Robert Floyd in 1962.
- Finds shortest path between **all** pairs of vertices.
- Can be used in graphs where the weights are either **positive** or **negative**.
- Time complexity: $O(n^3)$, where $n$ the number of vertices.
### Bellman-Ford
- Proposed by Alfonso Shimbel in 1955 but got named after Richard Bellman and Lester Ford Jr.
- Finds the shortest path from a given vertice to any other vertice. Can also find the shortest path between a given start vertice and a destination vertice.
- Slower than Dijkstra's, but more flexible since it can be used in graphs with **positive** or **negative** weights.
- Time complexity: $O(n*m)$, where $n$ the number of vertices, $m$ the number of edges.
## Example graphs used
>A visualization of the graphs used in code
### Example 1
### Example 2
