Graph Algorithm
A graph algorithm is a set of computational steps and processes designed to perform specific tasks on graph data structures, which are mathematical representations of a collection of objects and the relationships between them. Graphs consist of vertices (also called nodes) and edges (also called links), with the vertices representing the objects and the edges representing the relationships between those objects. Graph algorithms play a crucial role in various fields such as social network analysis, transportation and logistics, computer networks, and biology, among others. Some well-known graph algorithms include Dijkstra's shortest path algorithm, Prim's minimum spanning tree algorithm, and the Ford-Fulkerson maximum flow algorithm.
Graph algorithms can be broadly classified into two categories: traversal and pathfinding algorithms, and optimization algorithms. Traversal and pathfinding algorithms involve exploring the vertices and edges of a graph, typically to find a specific vertex or a path between two vertices. These algorithms include depth-first search (DFS), breadth-first search (BFS), and Dijkstra's shortest path algorithm. Optimization algorithms, on the other hand, focus on finding an optimal solution to a problem defined on the graph. Examples of optimization algorithms are Prim's and Kruskal's minimum spanning tree algorithms, and the Ford-Fulkerson maximum flow algorithm. These algorithms have diverse applications, such as routing in transportation networks, analyzing social networks, optimizing network flows, and solving various combinatorial problems.
class Graph {
constructor () {
this.adjacencyMap = {}
}
addVertex (v) {
this.adjacencyMap[v] = []
}
containsVertex (vertex) {
return typeof (this.adjacencyMap[vertex]) !== 'undefined'
}
addEdge (v, w) {
let result = false
if (this.containsVertex(v) && this.containsVertex(w)) {
this.adjacencyMap[v].push(w)
this.adjacencyMap[w].push(v)
result = true
}
return result
}
printGraph () {
const keys = Object.keys(this.adjacencyMap)
for (const i of keys) {
const values = this.adjacencyMap[i]
let vertex = ''
for (const j of values) { vertex += j + ' ' }
console.log(i + ' -> ' + vertex)
}
}
/**
* Prints the Breadth first traversal of the graph from source.
*
* @param {number} source The source vertex to start BFS.
*/
bfs (source) {
const queue = []
const visited = new Set()
queue.unshift([source, 0]) // level of source is 0
visited.add(source)
while (queue.length) {
const front = queue[0]
const node = front[0]
const level = front[1]
queue.shift() // remove the front of the queue
console.log(`Visited node ${node} at level ${level}.`)
for (const next of this.adjacencyMap[node]) {
if (!visited.has(next)) { // not visited
queue.unshift([next, level + 1]) // level 1 more than current
visited.add(next)
}
}
}
}
}
const example = () => {
const g = new Graph()
g.addVertex(1)
g.addVertex(2)
g.addVertex(3)
g.addVertex(4)
g.addVertex(5)
g.addEdge(1, 2)
g.addEdge(1, 3)
g.addEdge(2, 4)
g.addEdge(2, 5)
console.log('Printing the adjacency list:\n')
g.printGraph()
// perform a breadth first search
console.log('\nBreadth first search at node 1:\n')
g.bfs(1)
}
example()
