feat: added topological sorting algorithm

Author: RaviSadam

Graphs/TopoSortIterative.js

@@ -0,0 +1,47 @@
+import Queue from '../Data-Structures/Queue/Queue'
+/**
+ * @author {RaviSadam}
+ * @name TopoSortIterative
+ * @description -
+ * Topological sorting algorithm implementation in JavaScript(Khan's Algorithm)
+ * @summary
+ * Topological sorting for Directed Acyclic Graph is a linear ordering of vertices
+ * such that for every directed edge u-v, vertex u comes before v in the ordering.
+ *
+ * @param graph - Graph (adjacency list)
+ * @returns {Array} - Gives null if graph has cycle otherwise result array
+ *
+ */
+
+export function TopoSortIterative(graph) {
+  const n = graph.length
+  const inDegree = Array(n).fill(0)
+  const queue = new Queue()
+  const result = Array(n).fill(0)
+  let index = 0
+
+  for (const neighbors of graph) {
+    for (const neighbor of neighbors) {
+      inDegree[neighbor] += 1
+    }
+  }
+
+  for (let i = 0; i < n; i++) {
+    if (inDegree[i] === 0) {
+      queue.enqueue(i)
+    }
+  }
+  while (queue.length !== 0) {
+    const node = queue.dequeue()
+    result[index] = node
+    index += 1
+    for (let neighbor of graph[node]) {
+      inDegree[neighbor] -= 1
+      if (inDegree[neighbor] === 0) {
+        queue.enqueue(neighbor)
+      }
+    }
+  }
+  if (index !== n) return null
+  return result
+}

Graphs/TopoSortRecursive.js

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+function TopoSortRecursiveFunction(graph, visited, stack, path, vertex) {
+  //marking current vertex as visited
+  visited.add(vertex)
+
+  //marking current vertex as being part of current path
+  path[vertex] = 1
+  if (graph[vertex] && graph[vertex].length !== 0) {
+    for (const neighbor of graph[vertex]) {
+      //if neighbor is not visited then visit else continue
+      if (!visited.has(neighbor)) {
+        TopoSortRecursiveFunction(graph, visited, stack, path, neighbor)
+      } else if (path[neighbor] == 1) return
+    }
+  }
+
+  //unmarking vertex
+  path[vertex] = 0
+
+  //visited all vertex coming after the current vertex
+  //so added to stack
+  stack.push(vertex)
+}
+
+/**
+ *
+ * @author {RaviSadam}
+ * @name TopoSortRecursive
+ * @description -
+ * Topological sorting algorithm implementation in JavaScript
+ * @summary
+ * Topological sorting for Directed Acyclic Graph is a linear ordering of vertices
+ * such that for every directed edge u-v, vertex u comes before v in the ordering.
+ *
+ * @param graph - Graph (adjacency list)
+ * @returns {Array} - Gives null if graph has cycle otherwise result array
+ *
+ */
+export function TopoSortRecursive(graph) {
+  const n = graph.length
+  const stack = []
+  //visited set for keep tracking of visited vertises
+  const visited = new Set()
+
+  //path array for keep tacking of vertices
+  //visited in current path
+
+  const path = Array(n).fill(0)
+  for (let i = 0; i < n; i++) {
+    if (!visited.has(i)) {
+      TopoSortRecursiveFunction(graph, visited, stack, path, i)
+    }
+  }
+  for (const value of path) {
+    if (value === 1) return null
+  }
+  //reverse the stack for getting exact topological order
+  stack.reverse()
+  return stack
+}

Graphs/test/TopoSortIterative.test.js

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+import { TopoSortIterative } from '../TopoSortIterative'
+
+describe('Iterative Topological Sorting', () => {
+  test('Graph without cycle', () => {
+    const graph = [[], [], [3], [1], [0, 1], [0, 2]]
+
+    expect(TopoSortIterative(graph, 6)).toEqual([4, 5, 0, 2, 3, 1])
+  })
+  test('Graph with cycle', () => {
+    const graph = [[2], [], [3, 5], [0, 1], [0, 2]]
+
+    expect(TopoSortIterative(graph, 6)).toBe(null)
+  })
+})

Graphs/test/TopoSortRecursive.test.js

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+import { TopoSortRecursive } from '../TopoSortRecursive'
+
+describe('Recursive Topological Sorting', () => {
+  test('Graph without cycle', () => {
+    const graph = [[], [], [3], [1], [0, 1], [0, 2]]
+
+    expect(TopoSortRecursive(graph, 6)).toEqual([5, 4, 2, 3, 1, 0])
+  })
+  test('Graph with cycle', () => {
+    const graph = [[2], [], [3, 5], [0, 1], [0, 2]]
+
+    expect(TopoSortRecursive(graph, 6)).toBe(null)
+  })
+  test('Graph with disconnected components', () => {
+    const graph = [[1, 2], [3], [3], [], [5], []]
+    expect(TopoSortRecursive(graph, 6)).toEqual([4, 5, 0, 2, 1, 3])
+  })
+})