testing: improve DisjointSetUnionTest (#6440)

* testing: improve DisjointSetUnionTest

* testing: redundant variable for DisjointSetUnionTest

src/test/java/com/thealgorithms/datastructures/disjointsetunion/DisjointSetUnionTest.java

@@ -122,4 +122,109 @@ public class DisjointSetUnionTest {
         assertEquals(root, node1);
         assertEquals(node1, node3.parent);
     }
+
+    @Test
+    public void testUnionByRankSmallerToLarger() {
+        DisjointSetUnion<Integer> dsu = new DisjointSetUnion<>();
+        Node<Integer> node1 = dsu.makeSet(1);
+        Node<Integer> node2 = dsu.makeSet(2);
+        Node<Integer> node3 = dsu.makeSet(3);
+
+        // Create tree with node1 as root and rank 1
+        dsu.unionSets(node1, node2);
+        assertEquals(1, node1.rank);
+        assertEquals(0, node2.rank);
+
+        // Union single node (rank 0) with tree (rank 1)
+        // Smaller rank tree should attach to larger rank tree
+        dsu.unionSets(node3, node1);
+        assertEquals(node1, dsu.findSet(node3));
+        assertEquals(1, node1.rank); // Rank should not increase
+    }
+
+    @Test
+    public void testUnionByRankEqualRanks() {
+        DisjointSetUnion<Integer> dsu = new DisjointSetUnion<>();
+        Node<Integer> node1 = dsu.makeSet(1);
+        Node<Integer> node2 = dsu.makeSet(2);
+        Node<Integer> node3 = dsu.makeSet(3);
+        Node<Integer> node4 = dsu.makeSet(4);
+
+        // Create two trees of equal rank (1)
+        dsu.unionSets(node1, node2);
+        dsu.unionSets(node3, node4);
+        assertEquals(1, node1.rank);
+        assertEquals(1, node3.rank);
+
+        // Union two trees of equal rank
+        dsu.unionSets(node1, node3);
+        Node<Integer> root = dsu.findSet(node1);
+        assertEquals(2, root.rank); // Rank should increase by 1
+    }
+
+    @Test
+    public void testLargeChainPathCompression() {
+        DisjointSetUnion<Integer> dsu = new DisjointSetUnion<>();
+        Node<Integer> node1 = dsu.makeSet(1);
+        Node<Integer> node2 = dsu.makeSet(2);
+        Node<Integer> node3 = dsu.makeSet(3);
+        Node<Integer> node4 = dsu.makeSet(4);
+        Node<Integer> node5 = dsu.makeSet(5);
+
+        // Create a long chain: 1 -> 2 -> 3 -> 4 -> 5
+        dsu.unionSets(node1, node2);
+        dsu.unionSets(node2, node3);
+        dsu.unionSets(node3, node4);
+        dsu.unionSets(node4, node5);
+
+        // Find from the deepest node
+        Node<Integer> root = dsu.findSet(node5);
+
+        // Path compression should make all nodes point directly to root
+        assertEquals(root, node5.parent);
+        assertEquals(root, node4.parent);
+        assertEquals(root, node3.parent);
+        assertEquals(root, node2.parent);
+        assertEquals(root, node1.parent);
+    }
+
+    @Test
+    public void testMultipleDisjointSets() {
+        DisjointSetUnion<Integer> dsu = new DisjointSetUnion<>();
+        Node<Integer> node1 = dsu.makeSet(1);
+        Node<Integer> node2 = dsu.makeSet(2);
+        Node<Integer> node3 = dsu.makeSet(3);
+        Node<Integer> node4 = dsu.makeSet(4);
+        Node<Integer> node5 = dsu.makeSet(5);
+        Node<Integer> node6 = dsu.makeSet(6);
+
+        // Create two separate components
+        dsu.unionSets(node1, node2);
+        dsu.unionSets(node2, node3);
+
+        dsu.unionSets(node4, node5);
+        dsu.unionSets(node5, node6);
+
+        // Verify they are separate
+        assertEquals(dsu.findSet(node1), dsu.findSet(node2));
+        assertEquals(dsu.findSet(node2), dsu.findSet(node3));
+        assertEquals(dsu.findSet(node4), dsu.findSet(node5));
+        assertEquals(dsu.findSet(node5), dsu.findSet(node6));
+
+        assertNotEquals(dsu.findSet(node1), dsu.findSet(node4));
+        assertNotEquals(dsu.findSet(node3), dsu.findSet(node6));
+    }
+
+    @Test
+    public void testEmptyValues() {
+        DisjointSetUnion<String> dsu = new DisjointSetUnion<>();
+        Node<String> emptyNode = dsu.makeSet("");
+        Node<String> nullNode = dsu.makeSet(null);
+
+        assertEquals(emptyNode, dsu.findSet(emptyNode));
+        assertEquals(nullNode, dsu.findSet(nullNode));
+
+        dsu.unionSets(emptyNode, nullNode);
+        assertEquals(dsu.findSet(emptyNode), dsu.findSet(nullNode));
+    }
 }