Add Heavy-Light Decomposition (HLD) (#6169)

src/test/java/com/thealgorithms/tree/HeavyLightDecompositionTest.java

@@ -0,0 +1,69 @@
+package com.thealgorithms.tree;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+
+class HeavyLightDecompositionTest {
+
+    private HeavyLightDecomposition hld;
+    private final int[] values = {0, 10, 20, 30, 40, 50};
+
+    /**
+     * Initializes the test environment with a predefined tree structure and values.
+     */
+    @BeforeEach
+    void setUp() {
+        hld = new HeavyLightDecomposition(5);
+        hld.addEdge(1, 2);
+        hld.addEdge(1, 3);
+        hld.addEdge(2, 4);
+        hld.addEdge(2, 5);
+        hld.initialize(1, values);
+    }
+
+    /**
+     * Verifies that the tree initializes successfully without errors.
+     */
+    @Test
+    void testBasicTreeInitialization() {
+        assertTrue(true, "Basic tree structure initialized successfully");
+    }
+
+    /**
+     * Tests the maximum value query in the path between nodes.
+     */
+    @Test
+    void testQueryMaxInPath() {
+        assertEquals(50, hld.queryMaxInPath(4, 5), "Max value in path (4,5) should be 50");
+        assertEquals(30, hld.queryMaxInPath(3, 2), "Max value in path (3,2) should be 30");
+    }
+
+    /**
+     * Tests updating a node's value and ensuring it is reflected in queries.
+     */
+    @Test
+    void testUpdateNodeValue() {
+        hld.updateSegmentTree(1, 0, hld.getPositionIndex() - 1, hld.getPosition(4), 100);
+        assertEquals(100, hld.queryMaxInPath(4, 5), "Updated value should be reflected in query");
+    }
+
+    /**
+     * Tests the maximum value query in a skewed tree structure.
+     */
+    @Test
+    void testSkewedTreeMaxQuery() {
+        assertEquals(40, hld.queryMaxInPath(1, 4), "Max value in skewed tree (1,4) should be 40");
+    }
+
+    /**
+     * Ensures query handles cases where u is a deeper node correctly.
+     */
+    @Test
+    void testDepthSwapInPathQuery() {
+        assertEquals(50, hld.queryMaxInPath(5, 2), "Query should handle depth swap correctly");
+        assertEquals(40, hld.queryMaxInPath(4, 1), "Query should handle swapped nodes correctly and return max value");
+    }
+}