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feat: Add Hierholzer's Algorithm for Eulerian Circuits (#6726)
* feat: Add Hierholzer's Algorithm for Eulerian Circuits * fix: Add more test cases to improve code coverage * feat: Add Hierholzer's Algorithm for Eulerian Circuits * fix: Apply clang-format after merge * fix: Apply all formatting, style, and efficiency fixes * docs: Apply feedback and improve Javadoc * docs: Add Hierholzer's Algorithm to DIRECTORY.md
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‎DIRECTORY.md‎

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- 📄 [FordFulkerson](src/main/java/com/thealgorithms/datastructures/graphs/FordFulkerson.java)
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- 📄 [Graphs](src/main/java/com/thealgorithms/datastructures/graphs/Graphs.java)
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- 📄 [HamiltonianCycle](src/main/java/com/thealgorithms/datastructures/graphs/HamiltonianCycle.java)
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- 📄 [HierholzerAlgorithm](src/main/java/com/thealgorithms/graph/HierholzerAlgorithm.java)
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- 📄 [JohnsonsAlgorithm](src/main/java/com/thealgorithms/datastructures/graphs/JohnsonsAlgorithm.java)
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- 📄 [KahnsAlgorithm](src/main/java/com/thealgorithms/datastructures/graphs/KahnsAlgorithm.java)
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- 📄 [Kosaraju](src/main/java/com/thealgorithms/datastructures/graphs/Kosaraju.java)

‎src/main/java/com/thealgorithms/graph/HierholzerAlgorithm.java‎

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package com.thealgorithms.graph;
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import java.util.Collections;
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import java.util.HashMap;
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import java.util.HashSet;
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import java.util.LinkedList;
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import java.util.List;
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import java.util.Map;
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import java.util.Set;
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import java.util.Stack;
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/**
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* Implementation of Hierholzer's algorithm to find an Eulerian Circuit in an undirected graph.
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* <p>
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* An Eulerian circuit is a trail in a graph that visits every edge exactly once,
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* starting and ending at the same vertex. This algorithm finds such a circuit if one exists.
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* </p>
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* <p>
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* This implementation is designed for an <strong>undirected graph</strong>. For a valid Eulerian
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* circuit to exist, the graph must satisfy two conditions:
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* <ol>
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* <li>All vertices with a non-zero degree must be part of a single connected component.</li>
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* <li>Every vertex must have an even degree (an even number of edges connected to it).</li>
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* </ol>
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* </p>
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* <p>
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* The algorithm runs in O(E + V) time, where E is the number of edges and V is the number of vertices.
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* The graph is represented by a Map where keys are vertices and values are a LinkedList of adjacent vertices.
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* </p>
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*
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* @see <a href="https://en.wikipedia.org/wiki/Eulerian_path#Hierholzer's_algorithm">Wikipedia: Hierholzer's algorithm</a>
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*/
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public final class HierholzerAlgorithm {
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private final Map<Integer, LinkedList<Integer>> graph;
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public HierholzerAlgorithm(Map<Integer, LinkedList<Integer>> graph) {
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this.graph = (graph == null) ? new HashMap<>() : graph;
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}
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public boolean hasEulerianCircuit() {
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if (graph.isEmpty()) {
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return true;
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}
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for (List<Integer> neighbors : graph.values()) {
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if (neighbors.size() % 2 != 0) {
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return false;
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}
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}
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return isCoherentlyConnected();
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}
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public List<Integer> findEulerianCircuit() {
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if (!hasEulerianCircuit()) {
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return Collections.emptyList();
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}
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Map<Integer, LinkedList<Integer>> tempGraph = new HashMap<>();
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for (Map.Entry<Integer, LinkedList<Integer>> entry : graph.entrySet()) {
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tempGraph.put(entry.getKey(), new LinkedList<>(entry.getValue()));
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}
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Stack<Integer> currentPath = new Stack<>();
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LinkedList<Integer> circuit = new LinkedList<>();
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int startVertex = -1;
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for (Map.Entry<Integer, LinkedList<Integer>> entry : tempGraph.entrySet()) {
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if (!entry.getValue().isEmpty()) {
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startVertex = entry.getKey();
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break;
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}
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}
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if (startVertex == -1) {
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if (graph.isEmpty()) {
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return Collections.emptyList();
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}
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return Collections.singletonList(graph.keySet().iterator().next());
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}
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currentPath.push(startVertex);
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while (!currentPath.isEmpty()) {
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int currentVertex = currentPath.peek();
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if (tempGraph.containsKey(currentVertex) && !tempGraph.get(currentVertex).isEmpty()) {
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int nextVertex = tempGraph.get(currentVertex).pollFirst();
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tempGraph.get(nextVertex).remove(Integer.valueOf(currentVertex));
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currentPath.push(nextVertex);
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} else {
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circuit.addFirst(currentVertex);
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currentPath.pop();
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}
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}
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return circuit;
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}
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private boolean isCoherentlyConnected() {
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if (graph.isEmpty()) {
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return true;
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}
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Set<Integer> visited = new HashSet<>();
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int startNode = -1;
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for (Map.Entry<Integer, LinkedList<Integer>> entry : graph.entrySet()) {
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if (!entry.getValue().isEmpty()) {
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startNode = entry.getKey();
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break;
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}
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}
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if (startNode == -1) {
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return true;
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}
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dfs(startNode, visited);
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for (Map.Entry<Integer, LinkedList<Integer>> entry : graph.entrySet()) {
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if (!entry.getValue().isEmpty() && !visited.contains(entry.getKey())) {
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return false;
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}
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}
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return true;
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}
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private void dfs(int u, Set<Integer> visited) {
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visited.add(u);
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if (graph.containsKey(u)) {
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for (int v : graph.get(u)) {
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if (!visited.contains(v)) {
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dfs(v, visited);
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}
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}
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}
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}
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}

‎src/test/java/com/thealgorithms/graph/HierholzerAlgorithmTest.java‎

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package com.thealgorithms.graph;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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import static org.junit.jupiter.api.Assertions.assertFalse;
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import static org.junit.jupiter.api.Assertions.assertTrue;
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import java.util.Arrays;
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import java.util.Collections;
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import java.util.HashMap;
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import java.util.LinkedList;
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import java.util.List;
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import java.util.Map;
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import org.junit.jupiter.api.Test;
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public class HierholzerAlgorithmTest {
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@Test
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public void testFindsEulerianCircuitInSimpleTriangleGraph() {
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Map<Integer, LinkedList<Integer>> graph = new HashMap<>();
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graph.put(0, new LinkedList<>(Arrays.asList(1, 2)));
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graph.put(1, new LinkedList<>(Arrays.asList(0, 2)));
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graph.put(2, new LinkedList<>(Arrays.asList(0, 1)));
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HierholzerAlgorithm algorithm = new HierholzerAlgorithm(graph);
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assertTrue(algorithm.hasEulerianCircuit());
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List<Integer> circuit = algorithm.findEulerianCircuit();
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assertEquals(4, circuit.size());
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assertEquals(circuit.get(0), circuit.get(circuit.size() - 1));
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}
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@Test
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public void testFailsForGraphWithOddDegreeVertices() {
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Map<Integer, LinkedList<Integer>> graph = new HashMap<>();
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graph.put(0, new LinkedList<>(Collections.singletonList(1)));
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graph.put(1, new LinkedList<>(Collections.singletonList(0)));
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HierholzerAlgorithm algorithm = new HierholzerAlgorithm(graph);
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assertFalse(algorithm.hasEulerianCircuit());
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assertTrue(algorithm.findEulerianCircuit().isEmpty());
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}
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@Test
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public void testFailsForDisconnectedGraph() {
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Map<Integer, LinkedList<Integer>> graph = new HashMap<>();
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graph.put(0, new LinkedList<>(Arrays.asList(1, 2)));
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graph.put(1, new LinkedList<>(Arrays.asList(0, 2)));
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graph.put(2, new LinkedList<>(Arrays.asList(0, 1)));
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graph.put(3, new LinkedList<>(Arrays.asList(4, 5)));
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graph.put(4, new LinkedList<>(Arrays.asList(3, 5)));
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graph.put(5, new LinkedList<>(Arrays.asList(3, 4)));
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HierholzerAlgorithm algorithm = new HierholzerAlgorithm(graph);
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assertFalse(algorithm.hasEulerianCircuit());
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}
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@Test
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public void testHandlesEmptyGraph() {
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Map<Integer, LinkedList<Integer>> graph = new HashMap<>();
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HierholzerAlgorithm algorithm = new HierholzerAlgorithm(graph);
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assertTrue(algorithm.hasEulerianCircuit());
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assertTrue(algorithm.findEulerianCircuit().isEmpty());
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}
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}

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