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[FEATURE]: Add Kahn's Algorithm in Graphs #1795#1796
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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 +1,29 @@ | ||
| 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 | ||
| } |
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 +1,62 @@ | ||
| 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([]) | ||
| }) | ||
| }) |
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