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Added: Tarjan's SCC algorithm and test cases#1774
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,109 @@ | ||
| /* | ||
| Tarjan's Algorithm to find all Strongly Connected Components (SCCs) in a directed graph. | ||
| It performs a DFS traversal while keeping track of the discovery and low-link values | ||
| to identify root nodes of SCCs. | ||
| Complexity: | ||
| Time: O(V + E), where V: vertices and E: edges. | ||
| Space: O(V), for stack | discovery arrays | result. | ||
| Reference: | ||
| https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm | ||
| https://cp-algorithms.com/graph/strongly-connected-components.html | ||
| */ | ||
| /** | ||
| * Finds all strongly connected components in a directed graph using Tarjan's algorithm. | ||
| * | ||
| * @param {Object} graph - Directed graph represented as an adjacency list. | ||
| * @returns {Array<Array<string|number>>} - List of strongly connected components (each SCC is a list of nodes). | ||
| * @throws {Error} If the input graph is invalid or empty | ||
| */ | ||
| function TarjanSCC(graph) { | ||
| // Input validation | ||
| if (!graph || typeof graph !== 'object' || Array.isArray(graph)) { | ||
| throw new Error( | ||
| 'Graph must be a non-null object representing an adjacency list' | ||
| ) | ||
| } | ||
| if (Object.keys(graph).length === 0) { | ||
| return [] | ||
| } | ||
| const ids = {} // Discovery time of each node | ||
| const low = {} // Lowest discovery time reachable from the node | ||
| const onStack = {} // To track if a node is on the recursion stack | ||
| const stack = [] // Stack to hold the current path | ||
| const result = [] // Array to store SCCs | ||
| let time = 0 // Global timer for discovery time | ||
| /** | ||
| * Convert node to its proper type (number if numeric string, otherwise string) | ||
| * @param {string|number} node | ||
| * @returns {string|number} | ||
| */ | ||
| function convertNode(node) { | ||
| return !isNaN(node) && String(Number(node)) === String(node) | ||
| ? Number(node) | ||
| : node | ||
| } | ||
| /** | ||
| * Recursive DFS function to explore the graph and find SCCs | ||
| * @param {string|number} node | ||
| */ | ||
| function dfs(node) { | ||
| if (!(node in graph)) { | ||
| throw new Error(`Node ${node} not found in graph`) | ||
| } | ||
| ids[node] = low[node] = time++ | ||
| stack.push(node) | ||
| onStack[node] = true | ||
| // Explore all neighbours | ||
| const neighbors = graph[node] | ||
| if (!Array.isArray(neighbors)) { | ||
| throw new Error(`Neighbors of node ${node} must be an array`) | ||
| } | ||
| for (const neighbor of neighbors) { | ||
| const convertedNeighbor = convertNode(neighbor) | ||
| if (!(convertedNeighbor in ids)) { | ||
| dfs(convertedNeighbor) | ||
| low[node] = Math.min(low[node], low[convertedNeighbor]) | ||
| } else if (onStack[convertedNeighbor]) { | ||
| low[node] = Math.min(low[node], ids[convertedNeighbor]) | ||
| } | ||
| } | ||
| // If the current node is the root of an SCC | ||
| if (ids[node] === low[node]) { | ||
| const scc = [] | ||
| let current | ||
| do { | ||
| current = stack.pop() | ||
| onStack[current] = false | ||
| scc.push(convertNode(current)) | ||
| } while (current !== node) | ||
| result.push(scc) | ||
| } | ||
| } | ||
| // Run DFS for all unvisited nodes | ||
| try { | ||
| for (const node in graph) { | ||
| const convertedNode = convertNode(node) | ||
| if (!(convertedNode in ids)) { | ||
| dfs(convertedNode) | ||
| } | ||
| } | ||
| } catch (error) { | ||
| throw new Error(`Error during graph traversal: ${error.message}`) | ||
| } | ||
| return result | ||
| } | ||
| export { TarjanSCC } |
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,92 @@ | ||
| import { TarjanSCC } from '../TarjanSCC.js' | ||
| test('Test Case 1 - Simple graph with two SCCs', () => { | ||
| const graph = { | ||
| 0: [1], | ||
| 1: [2], | ||
| 2: [0, 3], | ||
| 3: [4], | ||
| 4: [] | ||
| } | ||
| const result = TarjanSCC(graph) | ||
| // Sort the components before comparison since order doesn't matter | ||
| const expected = [[4], [3], [0, 2, 1]].map((comp) => comp.sort()) | ||
| const actual = result.map((comp) => comp.sort()) | ||
| expect(actual).toEqual(expect.arrayContaining(expected)) | ||
| }) | ||
| test('Test Case 2 - All nodes in one SCC', () => { | ||
| const graph = { | ||
| A: ['B'], | ||
| B: ['C'], | ||
| C: ['A'] | ||
| } | ||
| const result = TarjanSCC(graph) | ||
| // Sort the components before comparison since order doesn't matter | ||
| const expected = [['A', 'B', 'C']].map((comp) => comp.sort()) | ||
| const actual = result.map((comp) => comp.sort()) | ||
| expect(actual).toEqual(expect.arrayContaining(expected)) | ||
| }) | ||
| test('Test Case 3 - Disconnected nodes', () => { | ||
| const graph = { | ||
| 1: [], | ||
| 2: [], | ||
| 3: [] | ||
| } | ||
| const result = TarjanSCC(graph) | ||
| // Sort the components before comparison since order doesn't matter | ||
| const expected = [[1], [2], [3]].map((comp) => comp.sort()) | ||
| const actual = result.map((comp) => comp.sort()) | ||
| expect(actual).toEqual(expect.arrayContaining(expected)) | ||
| }) | ||
| test('Test Case 4 - Complex Graph', () => { | ||
| const graph = { | ||
| 0: [1], | ||
| 1: [2, 3], | ||
| 2: [0], | ||
| 3: [4], | ||
| 4: [5], | ||
| 5: [3] | ||
| } | ||
| const result = TarjanSCC(graph) | ||
| // Sort the components before comparison since order doesn't matter | ||
| const expected = [ | ||
| [0, 2, 1], | ||
| [3, 5, 4] | ||
| ].map((comp) => comp.sort()) | ||
| const actual = result.map((comp) => comp.sort()) | ||
| expect(actual).toEqual(expect.arrayContaining(expected)) | ||
| }) | ||
| test('Edge Case - Null input should throw error', () => { | ||
| expect(() => TarjanSCC(null)).toThrow( | ||
| 'Graph must be a non-null object representing an adjacency list' | ||
| ) | ||
| }) | ||
| test('Edge Case - Node with non-array neighbors should throw error', () => { | ||
| const graph = { | ||
| A: 'not-an-array' | ||
| } | ||
| expect(() => TarjanSCC(graph)).toThrow('Neighbors of node A must be an array') | ||
| }) | ||
| test('Edge Case - Neighbor not in graph should throw error', () => { | ||
| const graph = { | ||
| A: ['B'] | ||
| } | ||
| expect(() => TarjanSCC(graph)).toThrow('Node B not found in graph') | ||
| }) |
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