[FEATURE]: Add Kahn's Algorithm in Graphs #1795

Author: Virus2hell

Graphs/KahnsAlgorithm.js

@@ -0,0 +1,29 @@
+export function kahnTopologicalSort(V, edges) {
+  const adj = Array.from({ length: V }, () => [])
+  const indegree = new Array(V).fill(0)
+
+  for (const [u, v] of edges) {
+    adj[u].push(v)
+    indegree[v]++
+  }
+
+  const queue = []
+  for (let i = 0; i < V; i++) {
+    if (indegree[i] === 0) queue.push(i)
+  }
+
+  const topoOrder = []
+  let idx = 0
+  while (idx < queue.length) {
+    const node = queue[idx++]
+    topoOrder.push(node)
+
+    for (const nei of adj[node]) {
+      indegree[nei]--
+      if (indegree[nei] === 0) queue.push(nei)
+    }
+  }
+
+  if (topoOrder.length !== V) return []
+  return topoOrder
+}

Graphs/__tests__/KahnsAlgorithm.test.js

@@ -0,0 +1,62 @@
+import { kahnTopologicalSort } from '../KahnsAlgorithm.js'
+
+describe("Kahn's Algorithm - Topological Sort", () => {
+  test('returns a valid topological order for a DAG', () => {
+    const V = 6
+    const edges = [
+      [5, 2],
+      [5, 0],
+      [4, 0],
+      [4, 1],
+      [2, 3],
+      [3, 1]
+    ]
+
+    const order = kahnTopologicalSort(V, edges)
+    expect(order.length).toBe(V)
+
+    // verify topological property
+    const pos = new Array(V)
+    for (let i = 0; i < order.length; i++) pos[order[i]] = i
+
+    for (const [u, v] of edges) {
+      expect(pos[u]).toBeLessThan(pos[v])
+    }
+  })
+
+  test('returns empty array when graph contains a cycle', () => {
+    const V = 3
+    const edges = [
+      [0, 1],
+      [1, 2],
+      [2, 0] // cycle
+    ]
+    const order = kahnTopologicalSort(V, edges)
+    expect(order).toEqual([])
+  })
+
+  test('includes isolated nodes', () => {
+    const V = 4
+    const edges = [
+      [0, 1],
+      [2, 3]
+    ]
+
+    const order = kahnTopologicalSort(V, edges)
+    expect(order.length).toBe(V)
+
+    const pos = new Array(V)
+    for (let i = 0; i < order.length; i++) pos[order[i]] = i
+
+    for (const [u, v] of edges) {
+      expect(pos[u]).toBeLessThan(pos[v])
+    }
+  })
+
+  test('works with empty graph', () => {
+    const V = 0
+    const edges = []
+    const order = kahnTopologicalSort(V, edges)
+    expect(order).toEqual([])
+  })
+})