Add Topological Sorting Algorithm (TheAlgorithms#3060)

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src/main/java/com/thealgorithms/sorts/TopologicalSort.java

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+package com.thealgorithms.sorts;
+
+import java.util.*;
+
+/**
+ * The Topological Sorting algorithm linearly orders a DAG or Directed Acyclic Graph into
+ * a linked list. A Directed Graph is proven to be acyclic when a DFS or Depth First Search is
+ * performed, yielding no back-edges.
+ *
+ * https://en.wikipedia.org/wiki/Topological_sorting
+ *
+ * @author Jonathan Taylor (https://github.com/Jtmonument)
+ * Based on Introduction to Algorithms 3rd Edition
+ */
+public class TopologicalSort {
+
+     /*
+     * Enum to represent the colors for the depth first search
+     * */
+    private enum Color {
+        WHITE, GRAY, BLACK
+    }
+
+     /*
+     * Class to represent vertices
+     * */
+    private static class Vertex {
+        /*
+        * Name of vertex
+        * */
+        public final String label;
+
+        /*
+        * Weight of vertex
+        * (more accurately defined as the time that a vertex has begun a visit in DFS)
+        * */
+        public int weight;
+
+        /*
+        * The time that the vertex has finished a visit in DFS
+        * */
+        public int finished;
+
+        /*
+        * π parent of the vertex
+        * */
+        public Vertex predecessor;
+
+        /*
+        * Represents the category of visit in DFS
+        * */
+        public Color color = Color.WHITE;
+
+        /*
+        * The array of names of descendant vertices
+        * */
+        public final ArrayList<String> next = new ArrayList<>();
+
+        public Vertex(String label) {
+            this.label = label;
+        }
+     }
+
+     /*
+     * Graph class uses the adjacency list representation
+     * */
+    static class Graph {
+
+        /*
+         * Adjacency list representation
+         * */
+        private final HashMap<String, Vertex> adj = new LinkedHashMap<>();
+
+        /*
+         * Function to add an edge to the graph
+         * */
+        public void addEdge(String label, String... next) {
+            adj.put(label, new Vertex(label));
+            if (!next[0].isEmpty())
+                Collections.addAll(adj.get(label).next, next);
+        }
+    }
+
+    static class BackEdgeException extends RuntimeException {
+
+        public BackEdgeException(String backEdge) {
+            super("This graph contains a cycle. No linear ordering is possible. " + backEdge);
+        }
+
+    }
+
+    /*
+     * Time variable in DFS
+     * */
+    private static int time;
+
+    /*
+     * Depth First Search
+     *
+     * DFS(G)
+     *   for each vertex u ∈ G.V
+     *       u.color = WHITE
+     *       u.π = NIL
+     *   time = 0
+     *   for each vertex u ∈ G.V
+     *   if u.color == WHITE
+     *       DFS-VISIT(G, u)
+     *
+     * Performed in Θ(V + E) time
+     * */
+    public static LinkedList<String> sort(Graph graph) {
+        LinkedList<String> list = new LinkedList<>();
+        graph.adj.forEach((name, vertex) -> {
+            if (vertex.color == Color.WHITE) {
+                list.addFirst(sort(graph, vertex, list));
+            }
+        });
+        return list;
+    }
+
+    /*
+     * Depth First Search Visit
+     *
+     * DFS-Visit(G, u)
+     *   time = time + 1
+     *   u.d = time
+     *   u.color = GRAY
+     *   for each v ∈ G.Adj[u]
+     *       if v.color == WHITE
+     *           v.π = u
+     *           DFS-Visit(G, u)
+     *   u.color = BLACK
+     *   time = time + 1
+     *   u.f = time
+     * */
+    private static String sort(Graph graph, Vertex u, LinkedList<String> list) {
+        time++;
+        u.weight = time;
+        u.color = Color.GRAY;
+        graph.adj.get(u.label).next.forEach(label -> {
+            if (graph.adj.get(label).color == Color.WHITE) {
+                graph.adj.get(label).predecessor = u;
+                list.addFirst(sort(graph, graph.adj.get(label), list));
+            } else if (graph.adj.get(label).color == Color.GRAY) {
+                /*
+                 * A back edge exists if an edge (u, v) connects a vertex u to its ancestor vertex v
+                 * in a depth first tree. If v.d ≤ u.d < u.f ≤ v.f
+                 *
+                 * In many cases, we will not know u.f, but v.color denotes the type of edge
+                 * */
+                throw new BackEdgeException("Back edge: " + u.label + " -> " + label);
+            }
+        });
+        u.color = Color.BLACK;
+        time++;
+        u.finished = time;
+        return u.label;
+    }
+}
+

src/test/java/com/thealgorithms/sorts/TopologicalSortTest.java

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+package com.thealgorithms.sorts;
+
+import org.junit.jupiter.api.Test;
+import static org.junit.jupiter.api.Assertions.*;
+import com.thealgorithms.sorts.TopologicalSort.Graph;
+import com.thealgorithms.sorts.TopologicalSort.BackEdgeException;
+
+import java.util.LinkedList;
+
+class TopologicalSortTest {
+    @Test
+    void successTest() {
+        /*
+         * Professor Bumstead example DAG. Each directed edge means that garment u must be put on
+         * before garment v.
+         * */
+        Graph graph = new Graph();
+        graph.addEdge("shirt", "tie", "belt");
+        graph.addEdge("tie", "jacket");
+        graph.addEdge("belt", "jacket");
+        graph.addEdge("watch", "");
+        graph.addEdge("undershorts", "pants", "shoes");
+        graph.addEdge("shoes", "");
+        graph.addEdge("socks", "shoes");
+        graph.addEdge("jacket","");
+        graph.addEdge("pants", "belt", "shoes");
+        LinkedList<String> expected = new LinkedList<>();
+        expected.add("socks");
+        expected.add("undershorts");
+        expected.add("pants");
+        expected.add("shoes");
+        expected.add("watch");
+        expected.add("shirt");
+        expected.add("belt");
+        expected.add("tie");
+        expected.add("jacket");
+        assertIterableEquals(expected, TopologicalSort.sort(graph));
+    }
+
+    @Test
+    public void failureTest() {
+
+        /*
+        * Graph example from Geeks For Geeks
+        * https://www.geeksforgeeks.org/tree-back-edge-and-cross-edges-in-dfs-of-graph/
+        * */
+        Graph graph = new Graph();
+        graph.addEdge("1", "2", "3", "8");
+        graph.addEdge("2", "4");
+        graph.addEdge("3", "5");
+        graph.addEdge("4", "6");
+        graph.addEdge("5", "4", "7", "8");
+        graph.addEdge("6", "2");
+        graph.addEdge("7", "");
+        graph.addEdge("8", "");
+        Exception exception = assertThrows(BackEdgeException.class, () -> TopologicalSort.sort(graph));
+        String expected = "This graph contains a cycle. No linear ordering is possible. " +
+                "Back edge: 6 -> 2";
+        assertEquals(exception.getMessage(), expected);
+    }
+}