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‎src/main/java/com/thealgorithms/tree/HeavyLightDecomposition.java

+140-178
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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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*
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* HLD is used to efficiently handle path queries on trees, such as maximum, sum, or updates.
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* It decomposes the tree into heavy and light chains, enabling queries in O(log N) time.
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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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*
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* Wikipedia Reference: https://en.wikipedia.org/wiki/Heavy-light_decomposition
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*
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* Author: Nithin U.
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* Github: https://github.com/NithinU2802
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*
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*/
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import java.util.ArrayList;
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import java.util.List;
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public class HeavyLightDecomposition {
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private List<Integer>[] tree;
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private int[] parent, depth, subtreeSize, chainHead, position, nodeValue;
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private int[] segmentTree;
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private int positionIndex;
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public class HeavyLightDecomposition {
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private List<Integer>[] tree;
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private int[] parent, depth, subtreeSize, chainHead, position, nodeValue;
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private int[] segmentTree;
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private int positionIndex;
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@SuppressWarnings("unchecked")
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public HeavyLightDecomposition(int n) {
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tree = new ArrayList[n + 1];
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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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tree[i] = new ArrayList<>();
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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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public int getPosition(int index) {
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return position[index];
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}
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}
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public int getPositionIndex(){
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public int getPositionIndex() {
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return positionIndex;
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}
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@SuppressWarnings("unchecked")
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public HeavyLightDecomposition(int n) {
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tree = new ArrayList[n + 1]; // Causes "unchecked or unsafe operations" warning
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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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}
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public void addEdge(int u, int v) {
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tree[u].add(v);
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tree[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[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, maxSubtreeSize = -1;
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for (int child : tree[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[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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44-
for (int i = 0; i <= n; i++) {
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tree[i] = new ArrayList<>();
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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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/**
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* Adds an edge to the tree.
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*/
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public void addEdge(int u, int v) {
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tree[u].add(v);
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tree[v].add(u);
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}
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/**
60-
* First DFS to calculate subtree sizes and determine heavy children.
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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[node]) {
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if (child != parentNode) {
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depth[child] = depth[node] + 1;
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dfsSize(child, node);
70-
subtreeSize[node] += subtreeSize[child];
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}
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}
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}
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/**
76-
* Second DFS to perform Heavy-Light Decomposition.
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*/
78-
private void decompose(int node, int head) {
79-
chainHead[node] = head;
80-
position[node] = positionIndex++;
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82-
int heavyChild = -1, maxSubtreeSize = -1;
83-
84-
for (int child : tree[node]) {
85-
if (child != parent[node] && subtreeSize[child] > maxSubtreeSize) {
86-
heavyChild = child;
87-
maxSubtreeSize = subtreeSize[child];
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}
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}
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91-
if (heavyChild != -1) {
92-
decompose(heavyChild, head);
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}
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for (int child : tree[node]) {
96-
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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/**
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* Builds a Segment Tree to handle path queries efficiently.
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*/
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private void buildSegmentTree(int node, int start, int end) {
106-
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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/**
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* Updates a node's value in the Segment Tree.
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*/
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public void updateSegmentTree(int node, int start, int end, int index, int value) {
122-
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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/**
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* Queries the Segment Tree for the maximum value in a given range.
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*/
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public int querySegmentTree(int node, int start, int end, int left, int right) {
141-
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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/**
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* Queries the maximum value in the path from node u to node v.
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*/
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public int queryMaxInPath(int u, int v) {
160-
int result = Integer.MIN_VALUE;
161-
162-
while (chainHead[u] != chainHead[v]) {
163-
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]) {
174-
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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/**
184-
* Initializes the HLD structure and Segment Tree.
185-
*/
186-
public void initialize(int root, int[] values) {
187-
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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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++) {
154+
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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