Add Topological Sorting Algorithm (#3060)
Co-authored-by: thanhtri122002 <thanhnt122002@122002> Co-authored-by: Andrii Siriak <siryaka@gmail.com> Co-authored-by: Anh Pham <62592224+anhpham197@users.noreply.github.com> Co-authored-by: SanOtaku <SanOtaku098@gmail.com> Co-authored-by: Raghav Taneja <97575679+RaghavTaneja@users.noreply.github.com> Co-authored-by: Andrii Siriak <siryaka@gmail.com> Co-authored-by: Hai Nguyen <88832724+ntquanghai@users.noreply.github.com> Co-authored-by: Utkarsh Yadav <Utkarshrock1510@gmail.com> Co-authored-by: Phạm Minh Hiếu <84634830+Ph1eu@users.noreply.github.com> Co-authored-by: nguyenviettrung-bi11276 <101244039+nguyenviettrung-bi11276@users.noreply.github.com> Co-authored-by: TaiNguyen2001 <102779475+TaiNguyen2001@users.noreply.github.com> Co-authored-by: de <88503943+HuyQHoang@users.noreply.github.com> Co-authored-by: thanhtri122002 <93241140+thanhtri122002@users.noreply.github.com> Co-authored-by: thanhtri122002 <thanhnt122002@122002>
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Jonathan Taylor
GitHub
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src/main/java/com/thealgorithms/sorts/TopologicalSort.java
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src/main/java/com/thealgorithms/sorts/TopologicalSort.java
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package com.thealgorithms.sorts;
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import java.util.*;
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/**
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* The Topological Sorting algorithm linearly orders a DAG or Directed Acyclic Graph into
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* a linked list. A Directed Graph is proven to be acyclic when a DFS or Depth First Search is
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* performed, yielding no back-edges.
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*
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* https://en.wikipedia.org/wiki/Topological_sorting
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*
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* @author Jonathan Taylor (https://github.com/Jtmonument)
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* Based on Introduction to Algorithms 3rd Edition
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*/
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public class TopologicalSort {
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/*
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* Enum to represent the colors for the depth first search
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* */
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private enum Color {
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WHITE, GRAY, BLACK
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}
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/*
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* Class to represent vertices
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* */
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private static class Vertex {
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/*
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* Name of vertex
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* */
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public final String label;
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/*
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* Weight of vertex
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* (more accurately defined as the time that a vertex has begun a visit in DFS)
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* */
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public int weight;
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/*
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* The time that the vertex has finished a visit in DFS
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* */
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public int finished;
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/*
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* π parent of the vertex
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* */
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public Vertex predecessor;
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/*
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* Represents the category of visit in DFS
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* */
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public Color color = Color.WHITE;
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/*
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* The array of names of descendant vertices
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* */
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public final ArrayList<String> next = new ArrayList<>();
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public Vertex(String label) {
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this.label = label;
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}
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}
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/*
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* Graph class uses the adjacency list representation
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* */
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static class Graph {
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/*
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* Adjacency list representation
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* */
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private final HashMap<String, Vertex> adj = new LinkedHashMap<>();
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/*
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* Function to add an edge to the graph
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* */
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public void addEdge(String label, String... next) {
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adj.put(label, new Vertex(label));
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if (!next[0].isEmpty())
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Collections.addAll(adj.get(label).next, next);
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}
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}
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static class BackEdgeException extends RuntimeException {
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public BackEdgeException(String backEdge) {
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super("This graph contains a cycle. No linear ordering is possible. " + backEdge);
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}
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}
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/*
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* Time variable in DFS
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* */
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private static int time;
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/*
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* Depth First Search
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*
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* DFS(G)
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* for each vertex u ∈ G.V
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* u.color = WHITE
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* u.π = NIL
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* time = 0
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* for each vertex u ∈ G.V
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* if u.color == WHITE
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* DFS-VISIT(G, u)
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*
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* Performed in Θ(V + E) time
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* */
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public static LinkedList<String> sort(Graph graph) {
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LinkedList<String> list = new LinkedList<>();
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graph.adj.forEach((name, vertex) -> {
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if (vertex.color == Color.WHITE) {
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list.addFirst(sort(graph, vertex, list));
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}
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});
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return list;
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}
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/*
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* Depth First Search Visit
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*
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* DFS-Visit(G, u)
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* time = time + 1
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* u.d = time
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* u.color = GRAY
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* for each v ∈ G.Adj[u]
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* if v.color == WHITE
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* v.π = u
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* DFS-Visit(G, u)
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* u.color = BLACK
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* time = time + 1
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* u.f = time
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* */
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private static String sort(Graph graph, Vertex u, LinkedList<String> list) {
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time++;
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u.weight = time;
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u.color = Color.GRAY;
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graph.adj.get(u.label).next.forEach(label -> {
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if (graph.adj.get(label).color == Color.WHITE) {
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graph.adj.get(label).predecessor = u;
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list.addFirst(sort(graph, graph.adj.get(label), list));
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} else if (graph.adj.get(label).color == Color.GRAY) {
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/*
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* A back edge exists if an edge (u, v) connects a vertex u to its ancestor vertex v
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* in a depth first tree. If v.d ≤ u.d < u.f ≤ v.f
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*
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* In many cases, we will not know u.f, but v.color denotes the type of edge
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* */
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throw new BackEdgeException("Back edge: " + u.label + " -> " + label);
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}
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});
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u.color = Color.BLACK;
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time++;
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u.finished = time;
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return u.label;
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}
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}
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@ -0,0 +1,61 @@
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package com.thealgorithms.sorts;
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import org.junit.jupiter.api.Test;
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import static org.junit.jupiter.api.Assertions.*;
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import com.thealgorithms.sorts.TopologicalSort.Graph;
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import com.thealgorithms.sorts.TopologicalSort.BackEdgeException;
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import java.util.LinkedList;
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class TopologicalSortTest {
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@Test
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void successTest() {
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/*
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* Professor Bumstead example DAG. Each directed edge means that garment u must be put on
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* before garment v.
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* */
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Graph graph = new Graph();
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graph.addEdge("shirt", "tie", "belt");
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graph.addEdge("tie", "jacket");
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graph.addEdge("belt", "jacket");
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graph.addEdge("watch", "");
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graph.addEdge("undershorts", "pants", "shoes");
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graph.addEdge("shoes", "");
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graph.addEdge("socks", "shoes");
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graph.addEdge("jacket","");
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graph.addEdge("pants", "belt", "shoes");
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LinkedList<String> expected = new LinkedList<>();
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expected.add("socks");
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expected.add("undershorts");
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expected.add("pants");
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expected.add("shoes");
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expected.add("watch");
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expected.add("shirt");
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expected.add("belt");
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expected.add("tie");
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expected.add("jacket");
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assertIterableEquals(expected, TopologicalSort.sort(graph));
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}
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@Test
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public void failureTest() {
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/*
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* Graph example from Geeks For Geeks
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* https://www.geeksforgeeks.org/tree-back-edge-and-cross-edges-in-dfs-of-graph/
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* */
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Graph graph = new Graph();
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graph.addEdge("1", "2", "3", "8");
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graph.addEdge("2", "4");
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graph.addEdge("3", "5");
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graph.addEdge("4", "6");
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graph.addEdge("5", "4", "7", "8");
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graph.addEdge("6", "2");
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graph.addEdge("7", "");
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graph.addEdge("8", "");
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Exception exception = assertThrows(BackEdgeException.class, () -> TopologicalSort.sort(graph));
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String expected = "This graph contains a cycle. No linear ordering is possible. " +
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"Back edge: 6 -> 2";
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assertEquals(exception.getMessage(), expected);
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}
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}
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