From 0feb41618872014f0809942ca1def0978eac1225 Mon Sep 17 00:00:00 2001 From: Hardik Pawar <97388607+Hardvan@users.noreply.github.com> Date: Thu, 24 Oct 2024 11:11:55 +0530 Subject: [PATCH] Enhance docs, add tests in `Kruskal` (#5967) --- DIRECTORY.md | 1 + .../datastructures/graphs/Kruskal.java | 107 ++++++++--------- .../datastructures/graphs/KruskalTest.java | 112 ++++++++++++++++++ 3 files changed, 161 insertions(+), 59 deletions(-) create mode 100644 src/test/java/com/thealgorithms/datastructures/graphs/KruskalTest.java diff --git a/DIRECTORY.md b/DIRECTORY.md index 0539f0df1..1def3e25c 100644 --- a/DIRECTORY.md +++ b/DIRECTORY.md @@ -812,6 +812,7 @@ * [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) + * [KruskalTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/datastructures/graphs/KruskalTest.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) * hashmap diff --git a/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java b/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java index eb5b65d5c..25c4548da 100644 --- a/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java +++ b/src/main/java/com/thealgorithms/datastructures/graphs/Kruskal.java @@ -1,27 +1,34 @@ package com.thealgorithms.datastructures.graphs; -// Problem -> Connect all the edges with the minimum cost. -// Possible Solution -> Kruskal Algorithm (KA), KA finds the minimum-spanning-tree, which means, the -// group of edges with the minimum sum of their weights that connect the whole graph. -// The graph needs to be connected, because if there are nodes impossible to reach, there are no -// edges that could connect every node in the graph. -// KA is a Greedy Algorithm, because edges are analysed based on their weights, that is why a -// Priority Queue is used, to take first those less weighted. -// This implementations below has some changes compared to conventional ones, but they are explained -// all along the code. import java.util.Comparator; import java.util.HashSet; import java.util.PriorityQueue; +/** + * The Kruskal class implements Kruskal's Algorithm to find the Minimum Spanning Tree (MST) + * of a connected, undirected graph. The algorithm constructs the MST by selecting edges + * with the least weight, ensuring no cycles are formed, and using union-find to track the + * connected components. + * + *

Key Features:

+ * + * + *

Time Complexity: O(E log V), where E is the number of edges and V is the number of vertices.

+ */ public class Kruskal { - // Complexity: O(E log V) time, where E is the number of edges in the graph and V is the number - // of vertices - private static class Edge { + /** + * Represents an edge in the graph with a source, destination, and weight. + */ + static class Edge { - private int from; - private int to; - private int weight; + int from; + int to; + int weight; Edge(int from, int to, int weight) { this.from = from; @@ -30,51 +37,30 @@ public class Kruskal { } } - private static void addEdge(HashSet[] graph, int from, int to, int weight) { + /** + * Adds an edge to the graph. + * + * @param graph the adjacency list representing the graph + * @param from the source vertex of the edge + * @param to the destination vertex of the edge + * @param weight the weight of the edge + */ + static void addEdge(HashSet[] graph, int from, int to, int weight) { graph[from].add(new Edge(from, to, weight)); } - public static void main(String[] args) { - HashSet[] graph = new HashSet[7]; - for (int i = 0; i < graph.length; i++) { - graph[i] = new HashSet<>(); - } - addEdge(graph, 0, 1, 2); - addEdge(graph, 0, 2, 3); - addEdge(graph, 0, 3, 3); - addEdge(graph, 1, 2, 4); - addEdge(graph, 2, 3, 5); - addEdge(graph, 1, 4, 3); - addEdge(graph, 2, 4, 1); - addEdge(graph, 3, 5, 7); - addEdge(graph, 4, 5, 8); - addEdge(graph, 5, 6, 9); - - System.out.println("Initial Graph: "); - for (int i = 0; i < graph.length; i++) { - for (Edge edge : graph[i]) { - System.out.println(i + " <-- weight " + edge.weight + " --> " + edge.to); - } - } - - Kruskal k = new Kruskal(); - HashSet[] solGraph = k.kruskal(graph); - - System.out.println("\nMinimal Graph: "); - for (int i = 0; i < solGraph.length; i++) { - for (Edge edge : solGraph[i]) { - System.out.println(i + " <-- weight " + edge.weight + " --> " + edge.to); - } - } - } - + /** + * Kruskal's algorithm to find the Minimum Spanning Tree (MST) of a graph. + * + * @param graph the adjacency list representing the input graph + * @return the adjacency list representing the MST + */ public HashSet[] kruskal(HashSet[] graph) { int nodes = graph.length; - int[] captain = new int[nodes]; - // captain of i, stores the set with all the connected nodes to i + int[] captain = new int[nodes]; // Stores the "leader" of each node's connected component HashSet[] connectedGroups = new HashSet[nodes]; HashSet[] minGraph = new HashSet[nodes]; - PriorityQueue edges = new PriorityQueue<>((Comparator.comparingInt(edge -> edge.weight))); + PriorityQueue edges = new PriorityQueue<>(Comparator.comparingInt(edge -> edge.weight)); for (int i = 0; i < nodes; i++) { minGraph[i] = new HashSet<>(); connectedGroups[i] = new HashSet<>(); @@ -83,18 +69,21 @@ public class Kruskal { edges.addAll(graph[i]); } int connectedElements = 0; - // as soon as two sets merge all the elements, the algorithm must stop while (connectedElements != nodes && !edges.isEmpty()) { Edge edge = edges.poll(); - // This if avoids cycles + + // Avoid forming cycles by checking if the nodes belong to different connected components if (!connectedGroups[captain[edge.from]].contains(edge.to) && !connectedGroups[captain[edge.to]].contains(edge.from)) { - // merge sets of the captains of each point connected by the edge + // Merge the two sets of nodes connected by the edge connectedGroups[captain[edge.from]].addAll(connectedGroups[captain[edge.to]]); - // update captains of the elements merged + + // Update the captain for each merged node connectedGroups[captain[edge.from]].forEach(i -> captain[i] = captain[edge.from]); - // add Edge to minimal graph + + // Add the edge to the resulting MST graph addEdge(minGraph, edge.from, edge.to, edge.weight); - // count how many elements have been merged + + // Update the count of connected nodes connectedElements = connectedGroups[captain[edge.from]].size(); } } diff --git a/src/test/java/com/thealgorithms/datastructures/graphs/KruskalTest.java b/src/test/java/com/thealgorithms/datastructures/graphs/KruskalTest.java new file mode 100644 index 000000000..b18f161ef --- /dev/null +++ b/src/test/java/com/thealgorithms/datastructures/graphs/KruskalTest.java @@ -0,0 +1,112 @@ +package com.thealgorithms.datastructures.graphs; + +import static org.junit.jupiter.api.Assertions.assertEquals; +import static org.junit.jupiter.api.Assertions.assertTrue; + +import java.util.ArrayList; +import java.util.Arrays; +import java.util.HashSet; +import java.util.List; +import org.junit.jupiter.api.BeforeEach; +import org.junit.jupiter.api.Test; + +public class KruskalTest { + + private Kruskal kruskal; + private HashSet[] graph; + + @BeforeEach + public void setUp() { + kruskal = new Kruskal(); + int n = 7; + graph = new HashSet[n]; + for (int i = 0; i < n; i++) { + graph[i] = new HashSet<>(); + } + + // Add edges to the graph + Kruskal.addEdge(graph, 0, 1, 2); + Kruskal.addEdge(graph, 0, 2, 3); + Kruskal.addEdge(graph, 0, 3, 3); + Kruskal.addEdge(graph, 1, 2, 4); + Kruskal.addEdge(graph, 2, 3, 5); + Kruskal.addEdge(graph, 1, 4, 3); + Kruskal.addEdge(graph, 2, 4, 1); + Kruskal.addEdge(graph, 3, 5, 7); + Kruskal.addEdge(graph, 4, 5, 8); + Kruskal.addEdge(graph, 5, 6, 9); + } + + @Test + public void testKruskal() { + int n = 6; + HashSet[] graph = new HashSet[n]; + + for (int i = 0; i < n; i++) { + graph[i] = new HashSet<>(); + } + + Kruskal.addEdge(graph, 0, 1, 4); + Kruskal.addEdge(graph, 0, 2, 2); + Kruskal.addEdge(graph, 1, 2, 1); + Kruskal.addEdge(graph, 1, 3, 5); + Kruskal.addEdge(graph, 2, 3, 8); + Kruskal.addEdge(graph, 2, 4, 10); + Kruskal.addEdge(graph, 3, 4, 2); + Kruskal.addEdge(graph, 3, 5, 6); + Kruskal.addEdge(graph, 4, 5, 3); + + HashSet[] result = kruskal.kruskal(graph); + + List> actualEdges = new ArrayList<>(); + for (HashSet edges : result) { + for (Kruskal.Edge edge : edges) { + actualEdges.add(Arrays.asList(edge.from, edge.to, edge.weight)); + } + } + + List> expectedEdges = Arrays.asList(Arrays.asList(1, 2, 1), Arrays.asList(0, 2, 2), Arrays.asList(3, 4, 2), Arrays.asList(4, 5, 3), Arrays.asList(1, 3, 5)); + + assertTrue(actualEdges.containsAll(expectedEdges) && expectedEdges.containsAll(actualEdges)); + } + + @Test + public void testEmptyGraph() { + HashSet[] emptyGraph = new HashSet[0]; + HashSet[] result = kruskal.kruskal(emptyGraph); + assertEquals(0, result.length); + } + + @Test + public void testSingleNodeGraph() { + HashSet[] singleNodeGraph = new HashSet[1]; + singleNodeGraph[0] = new HashSet<>(); + HashSet[] result = kruskal.kruskal(singleNodeGraph); + assertTrue(result[0].isEmpty()); + } + + @Test + public void testGraphWithDisconnectedNodes() { + int n = 5; + HashSet[] disconnectedGraph = new HashSet[n]; + for (int i = 0; i < n; i++) { + disconnectedGraph[i] = new HashSet<>(); + } + + Kruskal.addEdge(disconnectedGraph, 0, 1, 2); + Kruskal.addEdge(disconnectedGraph, 2, 3, 4); + + HashSet[] result = kruskal.kruskal(disconnectedGraph); + + List> actualEdges = new ArrayList<>(); + for (HashSet edges : result) { + for (Kruskal.Edge edge : edges) { + actualEdges.add(Arrays.asList(edge.from, edge.to, edge.weight)); + } + } + + List> expectedEdges = Arrays.asList(Arrays.asList(0, 1, 2), Arrays.asList(2, 3, 4)); + + assertTrue(actualEdges.containsAll(expectedEdges) && expectedEdges.containsAll(actualEdges)); + } +}