Add Edmonds Blossom Algorithm (#5471)

2025-07-27 06:23:08 +08:00 · 2024-10-02 23:34:01 +05:30
parent 842ff5294f
commit e493eb2958
3 changed files with 372 additions and 0 deletions
--- a/src/test/java/com/thealgorithms/datastructures/graphs/EdmondsBlossomAlgorithmTest.java
+++ b/src/test/java/com/thealgorithms/datastructures/graphs/EdmondsBlossomAlgorithmTest.java
@ -0,0 +1,119 @@
+package com.thealgorithms.datastructures.graphs;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import java.util.Arrays;
+import java.util.Collections;
+import java.util.List;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Unit tests for the EdmondsBlossomAlgorithm class.
+ *
+ * These tests ensure that the Edmonds' Blossom Algorithm implementation
+ * works as expected for various graph structures, returning the correct
+ * maximum matching.
+ */
+public class EdmondsBlossomAlgorithmTest {
+
+    /**
+     * Helper method to convert a list of matching pairs into a sorted 2D array.
+     * Sorting ensures consistent ordering of pairs and vertices for easier comparison in tests.
+     *
+     * @param matching List of matched pairs returned by the algorithm.
+     * @return A sorted 2D array of matching pairs.
+     */
+    private int[][] convertMatchingToArray(List<int[]> matching) {
+        // Convert the list of pairs into an array
+        int[][] result = matching.toArray(new int[0][]);
+
+        // Sort each individual pair for consistency
+        for (int[] pair : result) {
+            Arrays.sort(pair);
+        }
+
+        // Sort the array of pairs to ensure consistent order
+        Arrays.sort(result, (a, b) -> Integer.compare(a[0], b[0]));
+        return result;
+    }
+
+    /**
+     * Test Case 1: A triangle graph where vertices 0, 1, and 2 form a cycle.
+     * The expected maximum matching is a single pair (0, 1) or any equivalent pair from the cycle.
+     */
+    @Test
+    public void testCase1() {
+        List<int[]> edges = Arrays.asList(new int[] {0, 1}, new int[] {1, 2}, new int[] {2, 0});
+        List<int[]> matching = EdmondsBlossomAlgorithm.maximumMatching(edges, 3);
+
+        int[][] expected = new int[][] {{0, 1}};
+        assertArrayEquals(expected, convertMatchingToArray(matching));
+    }
+
+    /**
+     * Test Case 2: A disconnected graph where vertices 0, 1, 2 form one component,
+     * and vertices 3, 4 form another. The expected maximum matching is two pairs:
+     * (0, 1) and (3, 4).
+     */
+    @Test
+    public void testCase2() {
+        List<int[]> edges = Arrays.asList(new int[] {0, 1}, new int[] {1, 2}, new int[] {3, 4});
+        List<int[]> matching = EdmondsBlossomAlgorithm.maximumMatching(edges, 5);
+
+        int[][] expected = new int[][] {{0, 1}, {3, 4}};
+        assertArrayEquals(expected, convertMatchingToArray(matching));
+    }
+
+    /**
+     * Test Case 3: A cycle graph involving vertices 0, 1, 2, 3 forming a cycle,
+     * with an additional edge (4, 5) outside the cycle.
+     * The expected maximum matching is (0, 1) and (4, 5).
+     */
+    @Test
+    public void testCase3() {
+        List<int[]> edges = Arrays.asList(new int[] {0, 1}, new int[] {1, 2}, new int[] {2, 3}, new int[] {3, 0}, new int[] {4, 5});
+        List<int[]> matching = EdmondsBlossomAlgorithm.maximumMatching(edges, 6);
+
+        // Updated expected output to include the maximum matching pairs
+        int[][] expected = new int[][] {{0, 1}, {2, 3}, {4, 5}};
+        assertArrayEquals(expected, convertMatchingToArray(matching));
+    }
+
+    /**
+     * Test Case 4: A graph with no edges.
+     * Since there are no edges, the expected matching is an empty set.
+     */
+    @Test
+    public void testCaseNoMatching() {
+        List<int[]> edges = Collections.emptyList(); // No edges
+        List<int[]> matching = EdmondsBlossomAlgorithm.maximumMatching(edges, 3);
+
+        int[][] expected = new int[][] {}; // No pairs expected
+        assertArrayEquals(expected, convertMatchingToArray(matching));
+    }
+
+    /**
+     * Test Case 5: A more complex graph with multiple cycles and extra edges.
+     * This tests the algorithm's ability to handle larger, more intricate graphs.
+     * The expected matching is {{0, 1}, {2, 5}, {3, 4}}.
+     */
+    @Test
+    public void testCaseLargeGraph() {
+        List<int[]> edges = Arrays.asList(new int[] {0, 1}, new int[] {1, 2}, new int[] {2, 3}, new int[] {3, 4}, new int[] {4, 5}, new int[] {5, 0}, new int[] {1, 4}, new int[] {2, 5});
+        List<int[]> matching = EdmondsBlossomAlgorithm.maximumMatching(edges, 6);
+
+        // Check if the size of the matching is correct (i.e., 3 pairs)
+        assertEquals(3, matching.size());
+
+        // Check that the result contains valid pairs (any order is fine)
+        // Valid maximum matchings could be {{0, 1}, {2, 5}, {3, 4}} or {{0, 1}, {2, 3}, {4, 5}}, etc.
+        int[][] possibleMatching1 = new int[][] {{0, 1}, {2, 5}, {3, 4}};
+        int[][] possibleMatching2 = new int[][] {{0, 1}, {2, 3}, {4, 5}};
+        int[][] result = convertMatchingToArray(matching);
+
+        // Assert that the result is one of the valid maximum matchings
+        assertTrue(Arrays.deepEquals(result, possibleMatching1) || Arrays.deepEquals(result, possibleMatching2));
+    }
+}