Added: Tarjan's SCC algorithm and test cases

vedas-dixit · vedas-dixit · commit 258e2bcfb5a1 · 2025-04-15T17:10:13.000+05:30
diff --git a/Graphs/TarjanSCC.js b/Graphs/TarjanSCC.js
@@ -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 }
diff --git a/Graphs/test/TarjanSCC.test.js b/Graphs/test/TarjanSCC.test.js
@@ -0,0 +1,72 @@
+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))
+})
