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https://github.com/TheAlgorithms/C-Plus-Plus.git
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Merge pull request #1 from aneee004/hld
Added heavy_light_decomposition.cpp
This commit is contained in:
Aniruthan R
446
range_queries/heavy_light_decomposition.cpp
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446
range_queries/heavy_light_decomposition.cpp
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/*
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* @file
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* @Simple Heavy-Light Decomposition implementation
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* Author: Aniruthan R
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* @email: aniruth11052000@gmail.com
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* @CodeChef: aneee004
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* @CodeForces: aneee
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*
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* TODO: Support edge weight quereis, by storing the edge weight value in it's child
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*
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* algorithm verified by testing in CSES path queries: https://cses.fi/problemset/task/1138
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*/
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#include<iostream>
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#include<vector>
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#include<cstring>
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#include<string>
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#include<list>
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#include<cmath>
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#include<cassert>
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#include<algorithm>
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#include<numeric>
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/**
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* Function Documentation:
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* Heavy-Light Decomposition is a technique on trees, that supports the following:
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* 1: Update node s, with a value v
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* 2: Return the (sum) of all node values on the simple path from a to b
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* (sum) can also be replced with XOR, OR, AND, min, or max
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*
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* The update is done in O(log n) time, and
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* the query is done in O(log^2 n) time with HLD
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* where, n is the number of nodes
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*
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* The template type is the data type of the value stored in the nodes.
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* If a non-primitive data-type is used as a template,
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* the coressponding operators must be overloaded.
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*
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* An HLD object can only be created with a constant number of nodes, and
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* it cannot be changed later. Creaty an empty instance is not supported.
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*
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* To start answering updates and queries,
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* 1. Create an instance of HLD<X> object (obj), with the required data type.
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* 2. Read in the edge/parent information and update it with obj.add_edge().
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* Note: The edges addes must be 0 indexed.
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* 3. Create a vector with initial node values, and call set_node_val() with it.
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* 4. Call obj.init() to populate the required information for supporting operations.
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* 5. Call obj.update(node, new_val), to update the value at index 'node' to the new value.
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* Note: node must be 0 indexed
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* 6. Call obj.query(a, b) to get the (sum) of node values in the simple path from a to b.
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* Note: a and b, must be 0 indexed.
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*
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* Sample I/O at the bottom.
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*/
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/* A Basic Tree, which supports binary lifting */
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template<typename X>
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class Tree {
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/*
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* Deleting the default constructor
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* An instance can only be created with the number of nodes
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*/
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private:
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std::vector<std::list<int>> t_adj;
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const int t_nodes, t_maxlift;
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std::vector<std::vector<int>> t_par;
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std::vector<int> t_depth, t_size;
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int t_root;
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std::vector<X> t_val;
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template<typename T> friend class HLD;
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/* Defaults:
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* t_node indexing are zero based
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* t_root is 0
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* depth of root_node is 0
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*/
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void dfs_size(int u, int p = -1) {
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for(const int& v : t_adj[u]) {
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if(v^p) {
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dfs_size(v, u);
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t_size[u] += t_size[v];
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}
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}
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}
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void dfs_lca(int u, int p = -1) {
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t_par[u][0] = p;
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if(p != -1) t_depth[u] = 1 + t_depth[p];
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for(int k = 1; k < t_maxlift; k++) {
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if(t_par[u][k-1] != -1) {
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t_par[u][k] = t_par[t_par[u][k-1]][k-1];
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}
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}
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for(const int& v: t_adj[u]) {
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if(v^p) {
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dfs_lca(v, u);
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}
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}
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}
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public:
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explicit Tree(int nodes)
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: t_nodes(nodes), t_maxlift(static_cast<int>(floor(log2(nodes))) + 1) {
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/* Initialize and resize all the vectors */
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t_root = 0; /* Default */
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t_adj.resize(t_nodes);
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t_par.assign(t_nodes, std::vector<int>(t_maxlift, -1));
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t_depth.assign(t_nodes, 0);
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t_size.assign(t_nodes, 1);
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t_val.resize(t_nodes);
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}
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void add_edge(const int u, const int v) {
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t_adj[u].push_back(v);
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t_adj[v].push_back(u);
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}
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void change_root(int new_root) {
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t_root = new_root;
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}
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void set_node_val(std::vector<X> node_val) {
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t_val = node_val;
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}
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/* Initialization, sizes and parents */
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void init() {
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assert(t_nodes > 0);
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dfs_size(t_root);
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dfs_lca(t_root);
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}
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/* Supports:
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* lift :- lift a node k units up the tree
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* kth_ancestor :- returns the kth ancestor
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* lca :- returns the least common ancestor
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*/
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/* in place lift */
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void lift(int* const p, int dist) {
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for(int k = 0; k < t_maxlift; k++) {
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if(*p == -1) return;
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if(dist & 1) {
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*p = t_par[*p][k];
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}
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dist >>= 1;
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}
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}
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/* returns the kth ancestor */
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int kth_ancestor(int p, const int& dist) {
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lift(&p, dist);
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return p;
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}
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/* returns the least common ancestor */
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int lca(int a, int b) {
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assert(a >= 0 and b >= 0 and a < t_nodes and b < t_nodes);
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if(t_depth[a] > t_depth[b]) {
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lift(&a, t_depth[a] - t_depth[b]);
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}
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if(t_depth[b] > t_depth[a]) {
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lift(&b, t_depth[b] - t_depth[a]);
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}
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if(a == b) return a;
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for(int k = 0; k < t_maxlift; k++) {
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if(t_par[a][k] != t_par[b][k]) {
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a = t_par[a][k];
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b = t_par[b][k];
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}
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}
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return t_par[a][0];
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}
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};
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/* Segment Tree, to store heavy chains */
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template<typename X>
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class SG {
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private:
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/* Change the sret_init, based on requirement:
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* Sum Query: 0 (Default)
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* XOR Query: 0 (Default)
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* Min Query: Infinity
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* Max Query: -Infinity
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*/
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/* Everything here is private,
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* and can only be acced thought the methods,
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* in the derived class (HLD).
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*/
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std::vector<X> s_tree;
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int s_size;
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template<typename T> friend class HLD;
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X sret_init = 0;
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X combine(X lhs, X rhs) {
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return lhs + rhs;
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}
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/* Construction requires a size */
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explicit SG(int size) {
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s_size = size;
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s_tree.assign(2*s_size, 0ll);
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}
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/* update a segment tree node value */
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void update(int p, X v) {
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for(p += s_size; p > 0; p >>= 1) s_tree[p] += v;
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}
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/* make a segment tree range query */
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X query(int l, int r) {
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X lhs = sret_init, rhs = sret_init;
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for(l += s_size, r += s_size + 1; l < r; l >>= 1, r >>= 1) {
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if(l & 1) lhs = combine(lhs, s_tree[l++]);
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if(r & 1) rhs = combine(s_tree[--r], rhs);
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}
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return combine(lhs, rhs);
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}
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void set_sret_init(int new_sret_init) {
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sret_init = new_sret_init;
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}
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};
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/* The Heavy-Light Decomposition class */
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template<typename X>
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class HLD : public Tree<X>, public SG<X> {
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private:
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int label;
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std::vector<int> h_label, h_heavychlid, h_parent;
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/* Utility functions */
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void dfs_hc(int u, int p = -1) {
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int hc_size = -1, hc_id = -1;
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for(const int& v : Tree<X>::t_adj[u]) {
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if(v^p) {
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dfs_hc(v, u);
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if(Tree<X>::t_size[v] > hc_size) {
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hc_size = Tree<X>::t_size[v];
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hc_id = v;
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}
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}
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}
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h_heavychlid[u] = hc_id;
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}
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void dfs_par(int u, int p = -1) {
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if(h_heavychlid[u] != -1) {
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h_parent[h_heavychlid[u]] = h_parent[u];
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dfs_par(h_heavychlid[u], u);
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}
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for(const int& v : Tree<X>::t_adj[u]) {
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if(v^p and v^h_heavychlid[u]) {
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dfs_par(v, u);
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}
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}
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}
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void dfs_labels(int u, int p = -1) {
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h_label[u] = label++;
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if(h_heavychlid[u] != -1) dfs_labels(h_heavychlid[u], u);
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for(const int& v : Tree<X>::t_adj[u]) {
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if(v^p and v^h_heavychlid[u]) {
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dfs_labels(v, u);
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}
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}
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}
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X chain_query(int a, int b) {
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X ret = SG<X>::sret_init;
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if(Tree<X>::t_depth[a] < Tree<X>::t_depth[b]) std::swap(a, b);
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while(Tree<X>::t_depth[a] >= Tree<X>::t_depth[b]) {
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int l = h_label[h_parent[a]];
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int r = h_label[a];
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if(Tree<X>::t_depth[h_parent[a]] < Tree<X>::t_depth[b]) {
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l += Tree<X>::t_depth[b] - Tree<X>::t_depth[h_parent[a]];
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}
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ret = SG<X>::combine(ret, SG<X>::query(l, r));
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a = Tree<X>::t_par[h_parent[a]][0];
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if(a == -1) break;
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}
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return ret;
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}
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public:
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explicit HLD<X>(int nodes) : Tree<X>(nodes), SG<X>(nodes) {
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/* Initialization and resize vectors */
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label = 0;
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h_label.assign(Tree<X>::t_nodes, -1);
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h_heavychlid.assign(Tree<X>::t_nodes, -1);
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h_parent.resize(Tree<X>::t_nodes);
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iota(h_parent.begin(), h_parent.end(), 0);
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}
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/* Initialization */
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void init() {
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Tree<X>::init();
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/* Fill the heavy child, greatest parent, and labels */
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label = 0;
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dfs_hc(Tree<X>::t_root);
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dfs_par(Tree<X>::t_root);
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dfs_labels(Tree<X>::t_root);
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/* Segment Tree Initialization */
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for(int i = 0; i < Tree<X>::t_nodes; i++) {
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SG<X>::s_tree[h_label[i] + Tree<X>::t_nodes] = Tree<X>::t_val[i];
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}
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for(int i = Tree<X>::t_nodes - 1; i > 0; i--) {
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SG<X>::s_tree[i] = SG<X>::combine(SG<X>::s_tree[i<<1], SG<X>::s_tree[i<<1|1]);
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}
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}
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/* Changes the value at node, to val */
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void update(int node, X val) {
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X diff = val - Tree<X>::t_val[node];
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SG<X>::update(h_label[node], diff);
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Tree<X>::t_val[node] = val;
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}
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/*
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* return the (sum) of node values in,
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* the simple path from a, to b
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*/
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X query(int a, int b) {
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int lc = Tree<X>::lca(a, b);
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X ret = SG<X>::sret_init;
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assert(lc != -1);
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ret += chain_query(a, lc);
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ret += chain_query(b, lc);
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return ret - Tree<X>::t_val[lc];
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}
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};
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void test_1() {
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std::cout << "Test 1:\n";
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/* Test details */
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int n = 5;
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std::vector<int64_t> node_values = {4, 2, 5, 2, 1};
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std::vector<std::vector<int>> edges = {
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{1, 2},
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{1, 3},
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{3, 4},
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{3, 5}
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};
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std::vector<std::vector<int>> queries = {
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{2, 4},
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{1, 3, 2},
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{2, 4},
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};
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/* ------------ */
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HLD<int64_t> hld(n);
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hld.set_node_val(node_values);
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for(int i = 0; i < n - 1; i++) {
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int u = edges[i][0], v = edges[i][1];
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hld.add_edge(u-1, v-1);
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}
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hld.init();
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for(const auto& q : queries) {
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int type = q[0];
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if(type == 1) {
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int p = q[1], x = q[2];
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hld.update(p - 1, x);
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}
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else if(type == 2) {
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int p = q[1];
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std::cout << hld.query(0, p - 1) << std::endl;
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}
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else {
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continue;
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}
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}
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}
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void test_2() {
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std::cout << "Test 2:\n";
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/* Test details (Bamboo) */
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int n = 10;
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std::vector<int64_t> node_values = {1, 8, 6, 8, 6, 2, 9, 2, 3, 2};
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std::vector<std::vector<int>> edges = {
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{10, 5},
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{6, 2},
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{10, 7},
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{5, 2},
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{3, 9},
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{8, 3},
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{1, 4},
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{6, 4},
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{8, 7}
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};
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std::vector<std::vector<int>> queries = {
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{2, 10},
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{2, 6},
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{1, 3, 4},
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{2, 9},
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{1, 5, 3},
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{1, 7, 8},
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{2, 4},
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{2, 8},
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{1, 1, 4},
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{1, 2, 7}
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};
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/* ------------ */
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HLD<int64_t> hld(n);
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hld.set_node_val(node_values);
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for(int i = 0; i < n - 1; i++) {
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int u = edges[i][0], v = edges[i][1];
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hld.add_edge(u-1, v-1);
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}
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hld.init();
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for(const auto& q : queries) {
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int type = q[0];
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if(type == 1) {
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int p = q[1], x = q[2];
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hld.update(p - 1, x);
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}
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else if(type == 2) {
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int p = q[1];
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std::cout << hld.query(0, p - 1) << std::endl;
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}
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else {
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continue;
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}
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}
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}
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int main() {
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test_1();
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test_2();
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return 0;
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}
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/*
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* Sample Output 1:
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* 11
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* 8
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*
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* Sample Output 2:
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* 27
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* 11
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* 45
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* 9
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* 34
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*/
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