Merge branch 'master' into kosaraju_improve

Author: siriak

DIRECTORY.md

@@ -810,6 +810,7 @@
               * [FordFulkersonTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/FordFulkersonTest.java)
               * [HamiltonianCycleTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/HamiltonianCycleTest.java)
               * [JohnsonsAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithmTest.java)
+              * [KahnsAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KahnsAlgorithmTest.java)
               * [KosarajuTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KosarajuTest.java)
               * [TarjansAlgorithmTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/TarjansAlgorithmTest.java)
               * [WelshPowellTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/WelshPowellTest.java)

src/main/java/com/thealgorithms/datastructures/graphs/HamiltonianCycle.java

@@ -1,8 +1,14 @@
 package com.thealgorithms.datastructures.graphs;
 
+import java.util.Arrays;
+
 /**
- * Java program for Hamiltonian Cycle
- * <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">wikipedia</a>
+ * Java program to find a Hamiltonian Cycle in a graph.
+ * A Hamiltonian Cycle is a cycle that visits every vertex exactly once
+ * and returns to the starting vertex.
+ *
+ * <p>For more details, see the
+ * <a href="https://en.wikipedia.org/wiki/Hamiltonian_path">Wikipedia article</a>.
  *
  * @author  <a href="https://github.com/itsAkshayDubey">Akshay Dubey</a>
  */
@@ -14,30 +20,30 @@ public class HamiltonianCycle {
     private int[][] graph;
 
     /**
-     * Find hamiltonian cycle for given graph G(V,E)
+     * Finds a Hamiltonian Cycle for the given graph.
      *
-     * @param graph Adjacency matrix of a graph G(V, E)
-     *              for which hamiltonian path is to be found
-     * @return Array containing hamiltonian cycle
-     *         else returns 1D array with value -1.
+     * @param graph Adjacency matrix representing the graph G(V, E), where V is
+     *              the set of vertices and E is the set of edges.
+     * @return An array representing the Hamiltonian cycle if found, otherwise an
+     *         array filled with -1 indicating no Hamiltonian cycle exists.
      */
     public int[] findHamiltonianCycle(int[][] graph) {
+        // Single vertex graph
+        if (graph.length == 1) {
+            return new int[] {0, 0};
+        }
+
         this.vertex = graph.length;
         this.cycle = new int[this.vertex + 1];
 
-        // Initialize path array with -1 value
-        for (int i = 0; i < this.cycle.length; i++) {
-            this.cycle[i] = -1;
-        }
+        // Initialize the cycle array with -1 to represent unvisited vertices
+        Arrays.fill(this.cycle, -1);
 
         this.graph = graph;
-
         this.cycle[0] = 0;
         this.pathCount = 1;
         if (!isPathFound(0)) {
-            for (int i = 0; i < this.cycle.length; i++) {
-                this.cycle[i] = -1;
-            }
+            Arrays.fill(this.cycle, -1);
         } else {
             this.cycle[this.cycle.length - 1] = this.cycle[0];
         }
@@ -46,62 +52,55 @@ public int[] findHamiltonianCycle(int[][] graph) {
     }
 
     /**
-     * function to find paths recursively
-     * Find paths recursively from given vertex
+     * Recursively searches for a Hamiltonian cycle from the given vertex.
      *
-     * @param vertex Vertex from which path is to be found
-     * @returns true if path is found false otherwise
+     * @param vertex The current vertex from which to explore paths.
+     * @return {@code true} if a Hamiltonian cycle is found, otherwise {@code false}.
      */
     public boolean isPathFound(int vertex) {
         boolean isLastVertexConnectedToStart = this.graph[vertex][0] == 1 && this.pathCount == this.vertex;
         if (isLastVertexConnectedToStart) {
             return true;
         }
 
-        /* all vertices selected but last vertex not linked to 0 **/
+        // If all vertices are visited but the last vertex is not connected to the start
         if (this.pathCount == this.vertex) {
             return false;
         }
 
         for (int v = 0; v < this.vertex; v++) {
-            /* if connected **/
-            if (this.graph[vertex][v] == 1) {
-                /* add to path **/
-                this.cycle[this.pathCount++] = v;
-
-                /* remove connection **/
+            if (this.graph[vertex][v] == 1) { // Check if there is an edge
+                this.cycle[this.pathCount++] = v; // Add the vertex to the cycle
                 this.graph[vertex][v] = 0;
                 this.graph[v][vertex] = 0;
 
-                /* if vertex not already selected solve recursively **/
+                // Recursively attempt to complete the cycle
                 if (!isPresent(v)) {
                     return isPathFound(v);
                 }
 
-                /* restore connection **/
+                // Restore the edge if the path does not work
                 this.graph[vertex][v] = 1;
                 this.graph[v][vertex] = 1;
 
-                /* remove path **/
                 this.cycle[--this.pathCount] = -1;
             }
         }
         return false;
     }
 
     /**
-     * function to check if path is already selected
-     * Check if path is already selected
+     * Checks if a vertex is already part of the current Hamiltonian path.
      *
-     * @param vertex Starting vertex
+     * @param vertex The vertex to check.
+     * @return {@code true} if the vertex is already in the path, otherwise {@code false}.
      */
     public boolean isPresent(int vertex) {
         for (int i = 0; i < pathCount - 1; i++) {
             if (cycle[i] == vertex) {
                 return true;
             }
         }
-
         return false;
     }
 }

src/main/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithm.java

@@ -21,17 +21,18 @@
  */
 public final class JohnsonsAlgorithm {
 
-    // Constant representing infinity
     private static final double INF = Double.POSITIVE_INFINITY;
 
-    /**
-     * A private constructor to hide the implicit public one.
-     */
     private JohnsonsAlgorithm() {
     }
 
     /**
      * Executes Johnson's algorithm on the given graph.
+     * Steps:
+     * 1. Add a new vertex to the graph and run Bellman-Ford to compute modified weights
+     * 2. t the graph using the modified weights
+     * 3. Run Dijkstra's algorithm for each vertex to compute the shortest paths
+     * The final result is a 2D array of shortest distances between all pairs of vertices.
      *
      * @param graph The input graph represented as an adjacency matrix.
      * @return A 2D array representing the shortest distances between all pairs of vertices.
@@ -40,13 +41,10 @@ public static double[][] johnsonAlgorithm(double[][] graph) {
         int numVertices = graph.length;
         double[][] edges = convertToEdgeList(graph);
 
-        // Step 1: Add a new vertex and run Bellman-Ford
         double[] modifiedWeights = bellmanFord(edges, numVertices);
 
-        // Step 2: Reweight the graph
         double[][] reweightedGraph = reweightGraph(graph, modifiedWeights);
 
-        // Step 3: Run Dijkstra's algorithm for each vertex
         double[][] shortestDistances = new double[numVertices][numVertices];
         for (int source = 0; source < numVertices; source++) {
             shortestDistances[source] = dijkstra(reweightedGraph, source, modifiedWeights);
@@ -74,7 +72,6 @@ public static double[][] convertToEdgeList(double[][] graph) {
             }
         }
 
-        // Convert the List to a 2D array
         return edgeList.toArray(new double[0][]);
     }
 
@@ -89,7 +86,7 @@ public static double[][] convertToEdgeList(double[][] graph) {
     private static double[] bellmanFord(double[][] edges, int numVertices) {
         double[] dist = new double[numVertices + 1];
         Arrays.fill(dist, INF);
-        dist[numVertices] = 0; // Distance to the new source vertex is 0
+        dist[numVertices] = 0;
 
         // Add edges from the new vertex to all original vertices
         double[][] allEdges = Arrays.copyOf(edges, edges.length + numVertices);

src/main/java/com/thealgorithms/datastructures/graphs/KahnsAlgorithm.java

@@ -9,96 +9,120 @@
 import java.util.Set;
 
 /**
- * A class that represents the adjaceny list of a graph
+ * A class representing the adjacency list of a directed graph. The adjacency list
+ * maintains a mapping of vertices to their adjacent vertices.
+ *
+ * @param <E> the type of vertices, extending Comparable to ensure that vertices
+ * can be compared
  */
 class AdjacencyList<E extends Comparable<E>> {
 
     Map<E, ArrayList<E>> adj;
 
+    /**
+     * Constructor to initialize the adjacency list.
+     */
     AdjacencyList() {
-        adj = new LinkedHashMap<E, ArrayList<E>>();
+        adj = new LinkedHashMap<>();
     }
 
     /**
-     * This function adds an Edge to the adjaceny list
+     * Adds a directed edge from one vertex to another in the adjacency list.
+     * If the vertex does not exist, it will be added to the list.
      *
-     * @param from , the vertex the edge is from
-     * @param to, the vertex the edge is going to
+     * @param from the starting vertex of the directed edge
+     * @param to   the destination vertex of the directed edge
      */
     void addEdge(E from, E to) {
-        try {
-            adj.get(from).add(to);
-        } catch (Exception E) {
-            adj.put(from, new ArrayList<E>());
-            adj.get(from).add(to);
+        if (!adj.containsKey(from)) {
+            adj.put(from, new ArrayList<>());
         }
+        adj.get(from).add(to);
         if (!adj.containsKey(to)) {
-            adj.put(to, new ArrayList<E>());
+            adj.put(to, new ArrayList<>());
         }
     }
 
     /**
-     * @param v, A vertex in a graph
-     * @return returns an ArrayList of all the adjacents of vertex v
+     * Retrieves the list of adjacent vertices for a given vertex.
+     *
+     * @param v the vertex whose adjacent vertices are to be fetched
+     * @return an ArrayList of adjacent vertices for vertex v
      */
     ArrayList<E> getAdjacents(E v) {
         return adj.get(v);
     }
 
     /**
-     * @return returns a set of all vertices in the graph
+     * Retrieves the set of all vertices present in the graph.
+     *
+     * @return a set containing all vertices in the graph
      */
     Set<E> getVertices() {
         return adj.keySet();
     }
 }
 
+/**
+ * A class that performs topological sorting on a directed graph using Kahn's algorithm.
+ *
+ * @param <E> the type of vertices, extending Comparable to ensure that vertices
+ * can be compared
+ */
 class TopologicalSort<E extends Comparable<E>> {
 
     AdjacencyList<E> graph;
     Map<E, Integer> inDegree;
 
+    /**
+     * Constructor to initialize the topological sorting class with a given graph.
+     *
+     * @param graph the directed graph represented as an adjacency list
+     */
     TopologicalSort(AdjacencyList<E> graph) {
         this.graph = graph;
     }
 
     /**
-     * Calculates the in degree of all vertices
+     * Calculates the in-degree of all vertices in the graph. The in-degree is
+     * the number of edges directed into a vertex.
      */
     void calculateInDegree() {
         inDegree = new HashMap<>();
         for (E vertex : graph.getVertices()) {
-            if (!inDegree.containsKey(vertex)) {
-                inDegree.put(vertex, 0);
-            }
+            inDegree.putIfAbsent(vertex, 0);
             for (E adjacent : graph.getAdjacents(vertex)) {
-                try {
-                    inDegree.put(adjacent, inDegree.get(adjacent) + 1);
-                } catch (Exception e) {
-                    inDegree.put(adjacent, 1);
-                }
+                inDegree.put(adjacent, inDegree.getOrDefault(adjacent, 0) + 1);
             }
         }
     }
 
     /**
-     * Returns an ArrayList with vertices arranged in topological order
+     * Returns an ArrayList containing the vertices of the graph arranged in
+     * topological order. Topological sorting ensures that for any directed edge
+     * (u, v), vertex u appears before vertex v in the ordering.
+     *
+     * @return an ArrayList of vertices in topological order
+     * @throws IllegalStateException if the graph contains a cycle
      */
     ArrayList<E> topSortOrder() {
         calculateInDegree();
-        Queue<E> q = new LinkedList<E>();
+        Queue<E> q = new LinkedList<>();
 
-        for (final var entry : inDegree.entrySet()) {
+        for (var entry : inDegree.entrySet()) {
             if (entry.getValue() == 0) {
                 q.add(entry.getKey());
             }
         }
 
         ArrayList<E> answer = new ArrayList<>();
+        int processedVertices = 0;
 
         while (!q.isEmpty()) {
             E current = q.poll();
             answer.add(current);
+            processedVertices++;
+
             for (E adjacent : graph.getAdjacents(current)) {
                 inDegree.put(adjacent, inDegree.get(adjacent) - 1);
                 if (inDegree.get(adjacent) == 0) {
@@ -107,12 +131,16 @@ ArrayList<E> topSortOrder() {
             }
         }
 
+        if (processedVertices != graph.getVertices().size()) {
+            throw new IllegalStateException("Graph contains a cycle, topological sort not possible");
+        }
+
         return answer;
     }
 }
 
 /**
- * A driver class that sorts a given graph in topological order.
+ * A driver class that sorts a given graph in topological order using Kahn's algorithm.
  */
 public final class KahnsAlgorithm {
     private KahnsAlgorithm() {
@@ -130,7 +158,7 @@ public static void main(String[] args) {
 
         TopologicalSort<String> topSort = new TopologicalSort<>(graph);
 
-        // Printing the order
+        // Printing the topological order
         for (String s : topSort.topSortOrder()) {
             System.out.print(s + " ");
         }