diff --git a/Graphs/Kosaraju.js b/Graphs/Kosaraju.js new file mode 100644 index 0000000000..a0b4266b0c --- /dev/null +++ b/Graphs/Kosaraju.js @@ -0,0 +1,100 @@ +/** + * Author: Adrito Mukherjee + * Kosaraju's Algorithm implementation in Javascript + * Kosaraju's Algorithm finds all the connected components in a Directed Acyclic Graph (DAG) + * It uses Stack data structure to store the Topological Sorted Order of vertices and also Graph data structure + * + * Wikipedia: https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm + * + */ + +class Kosaraju { + constructor (graph) { + this.connections = {} + this.reverseConnections = {} + this.stronglyConnectedComponents = [] + for (const [i, j] of graph) { + this.addEdge(i, j) + } + this.topoSort() + return this.kosaraju() + } + + addNode (node) { + // Function to add a node to the graph (connection represented by set) + this.connections[node] = new Set() + this.reverseConnections[node] = new Set() + this.topoSorted = [] + } + + addEdge (node1, node2) { + // Function to add an edge (adds the node too if they are not present in the graph) + if (!(node1 in this.connections) || !(node1 in this.reverseConnections)) { + this.addNode(node1) + } + if (!(node2 in this.connections) || !(node2 in this.reverseConnections)) { + this.addNode(node2) + } + this.connections[node1].add(node2) + this.reverseConnections[node2].add(node1) + } + + dfsTopoSort (node, visited) { + visited.add(node) + for (const child of this.connections[node]) { + if (!visited.has(child)) this.dfsTopoSort(child, visited) + } + this.topoSorted.push(node) + } + + topoSort () { + // Function to perform topological sorting + const visited = new Set() + const nodes = Object.keys(this.connections).map((key) => Number(key)) + for (const node of nodes) { + if (!visited.has(node)) this.dfsTopoSort(node, visited) + } + } + + dfsKosaraju (node, visited) { + visited.add(node) + this.stronglyConnectedComponents[ + this.stronglyConnectedComponents.length - 1 + ].push(node) + for (const child of this.reverseConnections[node]) { + if (!visited.has(child)) this.dfsKosaraju(child, visited) + } + } + + kosaraju () { + // Function to perform Kosaraju Algorithm + const visited = new Set() + while (this.topoSorted.length > 0) { + const node = this.topoSorted.pop() + if (!visited.has(node)) { + this.stronglyConnectedComponents.push([]) + this.dfsKosaraju(node, visited) + } + } + return this.stronglyConnectedComponents + } +} + +function kosaraju (graph) { + const stronglyConnectedComponents = new Kosaraju(graph) + return stronglyConnectedComponents +} + +export { kosaraju } + +// kosaraju([ +// [1, 2], +// [2, 3], +// [3, 1], +// [2, 4], +// [4, 5], +// [5, 6], +// [6, 4], +// ]) + +// [ [ 1, 3, 2 ], [ 4, 6, 5 ] ] diff --git a/Graphs/test/Kosaraju.test.js b/Graphs/test/Kosaraju.test.js new file mode 100644 index 0000000000..a2da394db7 --- /dev/null +++ b/Graphs/test/Kosaraju.test.js @@ -0,0 +1,30 @@ +import { kosaraju } from '../Kosaraju.js' + +test('Test Case 1', () => { + const graph = [ + [1, 2], + [2, 3], + [3, 1], + [2, 4], + [4, 5], + [5, 6], + [6, 4] + ] + const stronglyConnectedComponents = kosaraju(graph) + expect(stronglyConnectedComponents).toStrictEqual([ + [1, 3, 2], + [4, 6, 5] + ]) +}) + +test('Test Case 2', () => { + const graph = [ + [1, 2], + [2, 3], + [3, 1], + [2, 4], + [4, 5] + ] + const stronglyConnectedComponents = kosaraju(graph) + expect(stronglyConnectedComponents).toStrictEqual([[1, 3, 2], [4], [5]]) +})