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Add Heavy-Light Decomposition (HLD) (#6169)
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Nithin U
@ -723,6 +723,8 @@
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* [WordLadder](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/WordLadder.java)
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* zigZagPattern
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* [ZigZagPattern](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/strings/zigZagPattern/ZigZagPattern.java)
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* tree
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* [HeavyLightDecomposition](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/tree/HeavyLightDecomposition.java)
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* test
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* java
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* com
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@ -1367,3 +1369,5 @@
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* [WordLadderTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/WordLadderTest.java)
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* zigZagPattern
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* [ZigZagPatternTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/strings/zigZagPattern/ZigZagPatternTest.java)
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* tree
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* [HeavyLightDecompositionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/tree/HeavyLightDecompositionTest.java)
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@ -0,0 +1,157 @@
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package com.thealgorithms.tree;
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import java.util.ArrayList;
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import java.util.List;
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/**
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* Heavy-Light Decomposition (HLD) implementation in Java.
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* HLD is used to efficiently handle path queries on trees, such as maximum,
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* sum, or updates. It decomposes the tree into heavy and light chains,
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* enabling queries in O(log N) time.
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* Wikipedia Reference: https://en.wikipedia.org/wiki/Heavy-light_decomposition
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* Author: Nithin U.
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* Github: https://github.com/NithinU2802
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*/
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public class HeavyLightDecomposition {
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private List<List<Integer>> tree;
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private int[] parent;
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private int[] depth;
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private int[] subtreeSize;
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private int[] chainHead;
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private int[] position;
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private int[] nodeValue;
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private int[] segmentTree;
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private int positionIndex;
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public HeavyLightDecomposition(int n) {
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tree = new ArrayList<>();
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for (int i = 0; i <= n; i++) {
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tree.add(new ArrayList<>());
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}
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parent = new int[n + 1];
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depth = new int[n + 1];
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subtreeSize = new int[n + 1];
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chainHead = new int[n + 1];
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position = new int[n + 1];
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nodeValue = new int[n + 1];
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segmentTree = new int[4 * (n + 1)];
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for (int i = 0; i <= n; i++) {
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chainHead[i] = -1;
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}
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positionIndex = 0;
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}
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public int getPosition(int index) {
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return position[index];
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}
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public int getPositionIndex() {
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return positionIndex;
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}
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public void addEdge(int u, int v) {
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tree.get(u).add(v);
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tree.get(v).add(u);
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}
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private void dfsSize(int node, int parentNode) {
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parent[node] = parentNode;
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subtreeSize[node] = 1;
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for (int child : tree.get(node)) {
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if (child != parentNode) {
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depth[child] = depth[node] + 1;
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dfsSize(child, node);
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subtreeSize[node] += subtreeSize[child];
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}
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}
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}
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private void decompose(int node, int head) {
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chainHead[node] = head;
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position[node] = positionIndex++;
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int heavyChild = -1;
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int maxSubtreeSize = -1;
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for (int child : tree.get(node)) {
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if (child != parent[node] && subtreeSize[child] > maxSubtreeSize) {
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heavyChild = child;
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maxSubtreeSize = subtreeSize[child];
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}
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}
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if (heavyChild != -1) {
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decompose(heavyChild, head);
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}
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for (int child : tree.get(node)) {
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if (child != parent[node] && child != heavyChild) {
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decompose(child, child);
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}
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}
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}
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private void buildSegmentTree(int node, int start, int end) {
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if (start == end) {
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segmentTree[node] = nodeValue[start];
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return;
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}
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int mid = (start + end) / 2;
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buildSegmentTree(2 * node, start, mid);
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buildSegmentTree(2 * node + 1, mid + 1, end);
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segmentTree[node] = Math.max(segmentTree[2 * node], segmentTree[2 * node + 1]);
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}
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public void updateSegmentTree(int node, int start, int end, int index, int value) {
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if (start == end) {
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segmentTree[node] = value;
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return;
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}
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int mid = (start + end) / 2;
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if (index <= mid) {
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updateSegmentTree(2 * node, start, mid, index, value);
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} else {
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updateSegmentTree(2 * node + 1, mid + 1, end, index, value);
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}
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segmentTree[node] = Math.max(segmentTree[2 * node], segmentTree[2 * node + 1]);
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}
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public int querySegmentTree(int node, int start, int end, int left, int right) {
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if (left > end || right < start) {
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return Integer.MIN_VALUE;
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}
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if (left <= start && end <= right) {
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return segmentTree[node];
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}
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int mid = (start + end) / 2;
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int leftQuery = querySegmentTree(2 * node, start, mid, left, right);
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int rightQuery = querySegmentTree(2 * node + 1, mid + 1, end, left, right);
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return Math.max(leftQuery, rightQuery);
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}
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public int queryMaxInPath(int u, int v) {
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int result = Integer.MIN_VALUE;
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while (chainHead[u] != chainHead[v]) {
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if (depth[chainHead[u]] < depth[chainHead[v]]) {
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int temp = u;
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u = v;
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v = temp;
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}
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result = Math.max(result, querySegmentTree(1, 0, positionIndex - 1, position[chainHead[u]], position[u]));
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u = parent[chainHead[u]];
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}
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if (depth[u] > depth[v]) {
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int temp = u;
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u = v;
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v = temp;
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}
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result = Math.max(result, querySegmentTree(1, 0, positionIndex - 1, position[u], position[v]));
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return result;
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}
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public void initialize(int root, int[] values) {
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dfsSize(root, -1);
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decompose(root, root);
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for (int i = 0; i < values.length; i++) {
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nodeValue[position[i]] = values[i];
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}
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buildSegmentTree(1, 0, positionIndex - 1);
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}
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}
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@ -0,0 +1,69 @@
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package com.thealgorithms.tree;
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import static org.junit.jupiter.api.Assertions.assertEquals;
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import static org.junit.jupiter.api.Assertions.assertTrue;
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import org.junit.jupiter.api.BeforeEach;
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import org.junit.jupiter.api.Test;
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class HeavyLightDecompositionTest {
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private HeavyLightDecomposition hld;
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private final int[] values = {0, 10, 20, 30, 40, 50};
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/**
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* Initializes the test environment with a predefined tree structure and values.
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*/
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@BeforeEach
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void setUp() {
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hld = new HeavyLightDecomposition(5);
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hld.addEdge(1, 2);
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hld.addEdge(1, 3);
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hld.addEdge(2, 4);
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hld.addEdge(2, 5);
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hld.initialize(1, values);
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}
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/**
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* Verifies that the tree initializes successfully without errors.
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*/
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@Test
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void testBasicTreeInitialization() {
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assertTrue(true, "Basic tree structure initialized successfully");
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}
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/**
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* Tests the maximum value query in the path between nodes.
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*/
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@Test
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void testQueryMaxInPath() {
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assertEquals(50, hld.queryMaxInPath(4, 5), "Max value in path (4,5) should be 50");
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assertEquals(30, hld.queryMaxInPath(3, 2), "Max value in path (3,2) should be 30");
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}
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/**
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* Tests updating a node's value and ensuring it is reflected in queries.
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*/
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@Test
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void testUpdateNodeValue() {
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hld.updateSegmentTree(1, 0, hld.getPositionIndex() - 1, hld.getPosition(4), 100);
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assertEquals(100, hld.queryMaxInPath(4, 5), "Updated value should be reflected in query");
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}
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/**
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* Tests the maximum value query in a skewed tree structure.
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*/
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@Test
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void testSkewedTreeMaxQuery() {
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assertEquals(40, hld.queryMaxInPath(1, 4), "Max value in skewed tree (1,4) should be 40");
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}
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/**
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* Ensures query handles cases where u is a deeper node correctly.
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*/
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@Test
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void testDepthSwapInPathQuery() {
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assertEquals(50, hld.queryMaxInPath(5, 2), "Query should handle depth swap correctly");
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assertEquals(40, hld.queryMaxInPath(4, 1), "Query should handle swapped nodes correctly and return max value");
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}
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}
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