diff --git a/src/main/java/com/thealgorithms/datastructures/graphs/UndirectedAdjacencyListGraph.java b/src/main/java/com/thealgorithms/datastructures/graphs/UndirectedAdjacencyListGraph.java new file mode 100644 index 000000000..8aafc1ef3 --- /dev/null +++ b/src/main/java/com/thealgorithms/datastructures/graphs/UndirectedAdjacencyListGraph.java @@ -0,0 +1,69 @@ +package com.thealgorithms.datastructures.graphs; + +import java.util.ArrayList; +import java.util.HashMap; +import java.util.HashSet; + +public class UndirectedAdjacencyListGraph { + private ArrayList> adjacencyList = new ArrayList<>(); + + /** + * Adds a new node to the graph by adding an empty HashMap for its neighbors. + * @return the index of the newly added node in the adjacency list + */ + public int addNode() { + adjacencyList.add(new HashMap<>()); + return adjacencyList.size() - 1; + } + + /** + * Adds an undirected edge between the origin node (@orig) and the destination node (@dest) with the specified weight. + * If the edge already exists, no changes are made. + * @param orig the index of the origin node + * @param dest the index of the destination node + * @param weight the weight of the edge between @orig and @dest + * @return true if the edge was successfully added, false if the edge already exists or if any node index is invalid + */ + public boolean addEdge(int orig, int dest, int weight) { + int numNodes = adjacencyList.size(); + if (orig >= numNodes || dest >= numNodes || orig < 0 || dest < 0) { + return false; + } + + if (adjacencyList.get(orig).containsKey(dest)) { + return false; + } + + adjacencyList.get(orig).put(dest, weight); + adjacencyList.get(dest).put(orig, weight); + return true; + } + + /** + * Returns the set of all adjacent nodes (neighbors) for the given node. + * @param node the index of the node whose neighbors are to be retrieved + * @return a HashSet containing the indices of all neighboring nodes + */ + public HashSet getNeighbors(int node) { + return new HashSet<>(adjacencyList.get(node).keySet()); + } + + /** + * Returns the weight of the edge between the origin node (@orig) and the destination node (@dest). + * If no edge exists, returns null. + * @param orig the index of the origin node + * @param dest the index of the destination node + * @return the weight of the edge between @orig and @dest, or null if no edge exists + */ + public Integer getEdgeWeight(int orig, int dest) { + return adjacencyList.get(orig).getOrDefault(dest, null); + } + + /** + * Returns the number of nodes currently in the graph. + * @return the number of nodes in the graph + */ + public int size() { + return adjacencyList.size(); + } +} diff --git a/src/main/java/com/thealgorithms/dynamicprogramming/TreeMatching.java b/src/main/java/com/thealgorithms/dynamicprogramming/TreeMatching.java new file mode 100644 index 000000000..9fd82ccaf --- /dev/null +++ b/src/main/java/com/thealgorithms/dynamicprogramming/TreeMatching.java @@ -0,0 +1,78 @@ +package com.thealgorithms.dynamicprogramming; + +import com.thealgorithms.datastructures.graphs.UndirectedAdjacencyListGraph; + +/** + * This class implements the algorithm for calculating the maximum weighted matching in a tree. + * The tree is represented as an undirected graph with weighted edges. + * + * Problem Description: + * Given an undirected tree G = (V, E) with edge weights γ: E → N and a root r ∈ V, + * the goal is to find a maximum weight matching M ⊆ E such that no two edges in M + * share a common vertex. The sum of the weights of the edges in M, ∑ e∈M γ(e), should be maximized. + * For more Information: Matching (graph theory) + * + * @author Deniz Altunkapan + */ +public class TreeMatching { + + private UndirectedAdjacencyListGraph graph; + private int[][] dp; + + /** + * Constructor that initializes the graph and the DP table. + * + * @param graph The graph that represents the tree and is used for the matching algorithm. + */ + public TreeMatching(UndirectedAdjacencyListGraph graph) { + this.graph = graph; + this.dp = new int[graph.size()][2]; + } + + /** + * Calculates the maximum weighted matching for the tree, starting from the given root node. + * + * @param root The index of the root node of the tree. + * @param parent The index of the parent node (used for recursion). + * @return The maximum weighted matching for the tree, starting from the root node. + * + */ + public int getMaxMatching(int root, int parent) { + if (root < 0 || root >= graph.size()) { + throw new IllegalArgumentException("Invalid root: " + root); + } + maxMatching(root, parent); + return Math.max(dp[root][0], dp[root][1]); + } + + /** + * Recursively computes the maximum weighted matching for a node, assuming that the node + * can either be included or excluded from the matching. + * + * @param node The index of the current node for which the matching is calculated. + * @param parent The index of the parent node (to avoid revisiting the parent node during recursion). + */ + private void maxMatching(int node, int parent) { + dp[node][0] = 0; + dp[node][1] = 0; + + int sumWithoutEdge = 0; + for (int adjNode : graph.getNeighbors(node)) { + if (adjNode == parent) { + continue; + } + maxMatching(adjNode, node); + sumWithoutEdge += Math.max(dp[adjNode][0], dp[adjNode][1]); + } + + dp[node][0] = sumWithoutEdge; + + for (int adjNode : graph.getNeighbors(node)) { + if (adjNode == parent) { + continue; + } + int weight = graph.getEdgeWeight(node, adjNode); + dp[node][1] = Math.max(dp[node][1], sumWithoutEdge - Math.max(dp[adjNode][0], dp[adjNode][1]) + dp[adjNode][0] + weight); + } + } +} diff --git a/src/test/java/com/thealgorithms/dynamicprogramming/TreeMatchingTest.java b/src/test/java/com/thealgorithms/dynamicprogramming/TreeMatchingTest.java new file mode 100644 index 000000000..d5418770a --- /dev/null +++ b/src/test/java/com/thealgorithms/dynamicprogramming/TreeMatchingTest.java @@ -0,0 +1,120 @@ +package com.thealgorithms.dynamicprogramming; + +import static org.junit.jupiter.api.Assertions.assertEquals; + +import com.thealgorithms.datastructures.graphs.UndirectedAdjacencyListGraph; +import org.junit.jupiter.api.BeforeEach; +import org.junit.jupiter.api.Test; + +class TreeMatchingTest { + UndirectedAdjacencyListGraph graph; + + @BeforeEach + void setUp() { + graph = new UndirectedAdjacencyListGraph(); + for (int i = 0; i < 14; i++) { + graph.addNode(); + } + } + + @Test + void testMaxMatchingForGeneralTree() { + graph.addEdge(0, 1, 20); + graph.addEdge(0, 2, 30); + graph.addEdge(1, 3, 40); + graph.addEdge(1, 4, 10); + graph.addEdge(2, 5, 20); + graph.addEdge(3, 6, 30); + graph.addEdge(3, 7, 30); + graph.addEdge(5, 8, 40); + graph.addEdge(5, 9, 10); + + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(110, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testMaxMatchingForBalancedTree() { + graph.addEdge(0, 1, 20); + graph.addEdge(0, 2, 30); + graph.addEdge(0, 3, 40); + graph.addEdge(1, 4, 10); + graph.addEdge(1, 5, 20); + graph.addEdge(2, 6, 20); + graph.addEdge(3, 7, 30); + graph.addEdge(5, 8, 10); + graph.addEdge(5, 9, 20); + graph.addEdge(7, 10, 10); + graph.addEdge(7, 11, 10); + graph.addEdge(7, 12, 5); + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(100, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testMaxMatchingForTreeWithVariedEdgeWeights() { + graph.addEdge(0, 1, 20); + graph.addEdge(0, 2, 30); + graph.addEdge(0, 3, 40); + graph.addEdge(0, 4, 50); + graph.addEdge(1, 5, 20); + graph.addEdge(2, 6, 20); + graph.addEdge(3, 7, 30); + graph.addEdge(5, 8, 10); + graph.addEdge(5, 9, 20); + graph.addEdge(7, 10, 10); + graph.addEdge(4, 11, 50); + graph.addEdge(4, 12, 20); + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(140, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void emptyTree() { + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(0, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testSingleNodeTree() { + UndirectedAdjacencyListGraph singleNodeGraph = new UndirectedAdjacencyListGraph(); + singleNodeGraph.addNode(); + + TreeMatching treeMatching = new TreeMatching(singleNodeGraph); + assertEquals(0, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testLinearTree() { + graph.addEdge(0, 1, 10); + graph.addEdge(1, 2, 20); + graph.addEdge(2, 3, 30); + graph.addEdge(3, 4, 40); + + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(60, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testStarShapedTree() { + graph.addEdge(0, 1, 15); + graph.addEdge(0, 2, 25); + graph.addEdge(0, 3, 35); + graph.addEdge(0, 4, 45); + + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(45, treeMatching.getMaxMatching(0, -1)); + } + + @Test + void testUnbalancedTree() { + graph.addEdge(0, 1, 10); + graph.addEdge(0, 2, 20); + graph.addEdge(1, 3, 30); + graph.addEdge(2, 4, 40); + graph.addEdge(4, 5, 50); + + TreeMatching treeMatching = new TreeMatching(graph); + assertEquals(100, treeMatching.getMaxMatching(0, -1)); + } +}