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https://github.com/willybrauner/dijkstra-algorithm
Dijkstra's algorithm implementation for any data structure
https://github.com/willybrauner/dijkstra-algorithm
algorithm dijkstra dijkstra-algorithm
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Dijkstra's algorithm implementation for any data structure
- Host: GitHub
- URL: https://github.com/willybrauner/dijkstra-algorithm
- Owner: willybrauner
- License: mit
- Created: 2022-06-25T13:40:38.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2022-06-29T20:46:22.000Z (over 2 years ago)
- Last Synced: 2023-03-10T21:57:56.704Z (over 1 year ago)
- Topics: algorithm, dijkstra, dijkstra-algorithm
- Language: TypeScript
- Homepage:
- Size: 5.92 MB
- Stars: 6
- Watchers: 2
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# Dijkstra's algorithm
This repos contains an implementation of [dijkstra's algorithm](https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm) that can be used with any data structure.
> Dijkstra's algorithm is a variant of the [BFS algorithm](https://en.wikipedia.org/wiki/Breadth-first_search) that finds the shortest path between two nodes in a graph.
## Motivation
I discovered the Dijkstra's algorithm when I was working on [advent-of-code 2021 day 15](https://adventofcode.com/2021/day/15).
Each example of the algorithm implementation was very specific to the data structure of the current use case, so I tried to write a generic and flexible implementation with the help of [Paul Brauner](https://github.com/polux).
[Dijkstra's function](./src/dijkstra.ts) can accept different data structure as input:
(example of inputs used in [unit tests](./src/dijkstra.test.ts))
1. On this 2D matrix (from advent-of-code example), each vertex is a vec2 coordinate `(y, x)` when the cost of the path is number of the cooridnate.
```ts
const matrix = [
[1, 1, 6, 3, 7, 5, 1, 7, 4, 2],
[1, 3, 8, 1, 3, 7, 3, 6, 7, 2],
[2, 1, 3, 6, 5, 1, 1, 3, 2, 8],
[3, 6, 9, 4, 9, 3, 1, 5, 6, 9],
[7, 4, 6, 3, 4, 1, 7, 1, 1, 1],
[1, 3, 1, 9, 1, 2, 8, 1, 3, 7],
[1, 3, 5, 9, 9, 1, 2, 4, 2, 1],
[3, 1, 2, 5, 4, 2, 1, 6, 3, 9],
[1, 2, 9, 3, 1, 3, 8, 5, 2, 1],
[2, 3, 1, 1, 9, 4, 4, 5, 8, 1],
]
```
2. This graph can be used too when object keys are verticies and values are neighbors associated to there own cost.
```ts
const graph = {
start: { A: 5, B: 2 },
A: { start: 1, C: 4, D: 2 },
B: { A: 8, D: 7 },
C: { D: 6, finish: 3 },
D: { finish: 1 },
finish: {},
}
```
## Usage
In order to accept different data structures, `dijkstra` recieves some functions as params:
- `getNeighbors: (v: GVertex) => GVertex[]` returns array of vertices that are neighbors of `v`
- `getCostBetweenVertices: (a: GVertex, b: GVertex) => number` returns cost of edge between thwo vertices
- `source: GVertex` vertex from which algorithm starts
- `isTarget: (vertex: GVertex) => boolean` returns `true` if vertex is the target
- `queue = priorityQueueMinHeap()` queue that is used to store vertices in order of their distance from source
exemple of usage:
```ts
const getNeighbors = (vertex) => Object.keys(graph[vertex])
const distanceBetweenTwoVertices = (v1, v2) => graph[v1][v2]
const isTarget = (vertex) => vertex === "finish"
const shortestPathCost: number = dijkstra(
getNeighbors,
distanceBetweenTwoVertices,
"start",
isTarget
)
```
`dijkstra` returns the shortest path cost from source to target
## Priority Queue
This algorithm is using a [priority queue](https://en.wikipedia.org/wiki/Priority_queue) to store vertices in order of their distance from source. The last one is a big part of Dijkstra implementation if we want to use it with big data structures.
Two types of priority queue have been tested in this algorithm:
- [priority Queue min](./src/priorityQueueMin.ts) (`O(n)`complexity)
- [priority Queue min with binary heap](./src/priorityQueueMinHeap.ts) (`O(log n)`complexity)
The second one will be more efficient because binary heap doesn't require us to iterate over the list.
## Requirement
- node js `>= 16`
- npm `>= 8`
## test it
- Clone the repos
```shell
$ git clone [email protected]:willybrauner/dijkstra-algorithm.git
```
- Install dépendencies
```shell
$ npm i
```
- Start tests once
```shell
$ npm run test
```
- Start tests in watch mode
```shell
$ npm run test:watch
```
## Credits
© Willy Brauner & Paul Brauner