cplib-cpp
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graph/test/extended_block_cut_trees.yuki1326.test.cpp
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- Last update: 2025-01-01 21:10:39+09:00
- Problem: https://yukicoder.me/problems/no/1326
Depends on
- Extended block cut tree （Block cut tree の亜種）
(graph/extended_block_cut_trees.hpp)
- Heavy-light decomposition （HLD, 木の重軽分解）
(tree/heavy_light_decomposition.hpp)
Code
#define PROBLEM "https://yukicoder.me/problems/no/1326"
#include "../extended_block_cut_trees.hpp"
#include "../../tree/heavy_light_decomposition.hpp"
#include <atcoder/fenwicktree>
#include <iostream>
using namespace std;
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
int N, M;
cin >> N >> M;
vector<pair<int, int>> edges(M);
for (auto &[u, v] : edges) cin >> u >> v, --u, --v;
const extended_block_cut_trees bct(N, edges);
heavy_light_decomposition hld(bct.size(), bct.get_edges());
hld.build();
atcoder::fenwick_tree<int> fw(hld.V);
for (int i = 0; i < N; ++i) fw.add(hld.subtree_begin[i], 1);
int Q;
cin >> Q;
while (Q--) {
int u, v;
cin >> u >> v;
--u, --v;
int ret = 0;
if (u != v) {
ret = -2;
hld.for_each_vertex(u, v, [&](int a, int b) { ret += fw.sum(a, b + 1); });
}
cout << ret << '\n';
}
}#line 1 "graph/test/extended_block_cut_trees.yuki1326.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1326"
#line 2 "graph/extended_block_cut_trees.hpp"
#include <cassert>
#include <utility>
#include <vector>
// Construct block cut tree (or forest) from a given graph
// Complexity: O(N + M), N = |vertices|, M = |edges|
// based on this idea: https://x.com/noshi91/status/1529858538650374144
// based on this implementation: https://ssrs-cp.github.io/cp_library/graph/extended_block_cut_tree.hpp.html
struct extended_block_cut_trees {
int N; // number of vertices
int B; // number of blocks
std::vector<std::vector<int>> to; // (0, ..., N - 1): vertices, (N, ..., N + B - 1): blocks
extended_block_cut_trees(int N, const std::vector<std::pair<int, int>> &edges)
: N(N), B(0), to(N) {
std::vector<std::vector<int>> adj(N);
for (auto [u, v] : edges) {
if (u != v) adj.at(u).push_back(v), adj.at(v).push_back(u);
}
std::vector<int> dfs_next(N, -1), dist(N, -1), back_cnt(N);
auto rec1 = [&](auto &&self, int now) -> void {
for (int nxt : adj[now]) {
if (dist[nxt] == -1) {
dist[nxt] = dist[now] + 1;
dfs_next[now] = nxt;
self(self, nxt);
back_cnt[now] += back_cnt[nxt];
} else if (dist[nxt] < dist[now] - 1) {
++back_cnt[now];
--back_cnt[dfs_next[nxt]];
}
}
};
for (int i = 0; i < N; ++i) {
if (dist[i] == -1) dist[i] = 0, rec1(rec1, i);
}
std::vector<bool> used(N);
auto rec2 = [&](auto &&self, int now, int current_b) -> void {
used[now] = true;
bool ok = false;
for (int nxt : adj[now]) {
if (dist[nxt] == dist[now] + 1 and !used[nxt]) {
if (back_cnt[nxt] > 0) {
if (!ok) {
ok = true;
add_edge(now, current_b);
}
self(self, nxt, current_b);
} else {
to.push_back({});
++B;
add_edge(now, B - 1);
self(self, nxt, B - 1);
}
}
}
if (!ok and dist[now] > 0) { add_edge(now, current_b); }
};
for (int i = 0; i < N; ++i) {
if (dist[i] == 0) { rec2(rec2, i, B - 1); }
if (adj[i].empty()) {
to.push_back({});
++B;
add_edge(i, B - 1);
}
}
}
int size() const { return N + B; }
bool is_articulation_point(int vertex) const {
assert(0 <= vertex and vertex < N);
return to[vertex].size() > 1;
}
int block_size(int block) const {
assert(0 <= block and block < B);
return to[N + block].size();
}
const std::vector<int> &block_vertices(int block) const {
assert(0 <= block and block < B);
return to[N + block];
}
std::vector<std::vector<int>> biconnected_components() const {
return std::vector<std::vector<int>>(to.begin() + N, to.end());
}
// first < N (vertices), second >= N (blocks)
std::vector<std::pair<int, int>> get_edges() const {
std::vector<std::pair<int, int>> edges;
for (int i = 0; i < N; ++i) {
for (int j : to[i]) edges.emplace_back(i, j);
}
return edges;
}
private:
void add_edge(int vertex, int block) {
assert(0 <= vertex and vertex < N);
assert(0 <= block and block < B);
to[vertex].push_back(N + block);
to[N + block].push_back(vertex);
}
};
#line 2 "tree/heavy_light_decomposition.hpp"
#include <algorithm>
#line 4 "tree/heavy_light_decomposition.hpp"
#include <functional>
#include <queue>
#include <stack>
#line 9 "tree/heavy_light_decomposition.hpp"
// Heavy-light decomposition of trees (forest)
// Based on http://beet-aizu.hatenablog.com/entry/2017/12/12/235950
struct heavy_light_decomposition {
int V;
int k;
std::vector<std::vector<int>> e;
std::vector<int> par; // par[i] = parent of vertex i (Default: -1)
std::vector<int> depth; // depth[i] = distance between root and vertex i
std::vector<int> subtree_sz; // subtree_sz[i] = size of subtree whose root is i
std::vector<int> heavy_child; // heavy_child[i] = child of vertex i on heavy path (Default: -1)
std::vector<int> tree_id; // tree_id[i] = id of tree vertex i belongs to
// subtree_begin[i] = aligned id for vertex i (consecutive on heavy edges)
std::vector<int> subtree_begin, subtree_end;
std::vector<int> vis_order; // vis_order[subtree_begin[i]] = i
std::vector<int> head; // head[i] = id of vertex on heavy path of vertex i, nearest to root
heavy_light_decomposition(int n, const std::vector<std::pair<int, int>> &edges)
: V(n), k(0), e(n), par(n), depth(n), subtree_sz(n), heavy_child(n), tree_id(n, -1),
subtree_begin(n), subtree_end(n), vis_order(0), head(n) {
for (auto [u, v] : edges) {
assert(u != v);
e.at(u).emplace_back(v);
e.at(v).emplace_back(u);
}
}
void _build_dfs_1(int root) {
std::vector<std::pair<int, int>> st;
par[root] = -1;
depth[root] = 0;
st.emplace_back(root, 0);
while (!st.empty()) {
int now = st.back().first;
int &i = st.back().second;
if (i < (int)e[now].size()) {
int nxt = e[now][i++];
if (nxt == par[now]) continue;
par[nxt] = now;
depth[nxt] = depth[now] + 1;
st.emplace_back(nxt, 0);
} else {
st.pop_back();
int max_sub_sz = 0;
subtree_sz[now] = 1;
heavy_child[now] = -1;
for (auto nxt : e[now]) {
if (nxt == par[now]) continue;
subtree_sz[now] += subtree_sz[nxt];
if (max_sub_sz < subtree_sz[nxt]) {
max_sub_sz = subtree_sz[nxt], heavy_child[now] = nxt;
}
}
}
}
}
void _build_dfs_2(int now, int tree_id_now) {
std::vector<std::pair<int, bool>> st;
st.emplace_back(now, true);
head[now] = now;
while (!st.empty()) {
auto [now, mode] = st.back();
st.pop_back();
if (mode) {
tree_id[now] = tree_id_now;
subtree_begin[now] = k++;
vis_order.push_back(now);
st.emplace_back(now, false);
for (int nxt : e[now]) {
if (nxt == par[now] or nxt == heavy_child[now]) continue;
head[nxt] = nxt;
st.emplace_back(nxt, true);
}
if (heavy_child[now] != -1) {
head[heavy_child[now]] = head[now];
st.emplace_back(heavy_child[now], true);
}
} else {
subtree_end[now] = k;
}
}
}
void build(std::vector<int> roots = {0}) {
int tree_id_now = 0;
for (int r : roots) {
_build_dfs_1(r);
_build_dfs_2(r, tree_id_now++);
}
}
template <class T> std::vector<T> segtree_rearrange(const std::vector<T> &data) const {
assert(int(data.size()) == V);
std::vector<T> ret;
ret.reserve(vis_order.size());
for (int v : vis_order) ret.emplace_back(data[v]);
return ret;
}
void for_vertex(int u, const std::function<void(int)> &f) const { f(subtree_begin[u]); }
// query for vertices on path [u, v] (INCLUSIVE)
void
for_each_vertex(int u, int v, const std::function<void(int ancestor, int descendant)> &f) const {
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
f(std::max(subtree_begin[head[v]], subtree_begin[u]), subtree_begin[v]);
if (head[u] == head[v]) break;
v = par[head[v]];
}
}
void for_each_vertex_noncommutative(
int from, int to, const std::function<void(int ancestor, int descendant)> &fup,
const std::function<void(int ancestor, int descendant)> &fdown) const {
int u = from, v = to;
const int lca = lowest_common_ancestor(u, v), dlca = depth[lca];
while (u >= 0 and depth[u] > dlca) {
const int p = (depth[head[u]] > dlca ? head[u] : lca);
fup(subtree_begin[p] + (p == lca), subtree_begin[u]), u = par[p];
}
static std::vector<std::pair<int, int>> lrs;
int sz = 0;
while (v >= 0 and depth[v] >= dlca) {
const int p = (depth[head[v]] >= dlca ? head[v] : lca);
if (int(lrs.size()) == sz) lrs.emplace_back(0, 0);
lrs.at(sz++) = {p, v}, v = par.at(p);
}
while (sz--) fdown(subtree_begin[lrs.at(sz).first], subtree_begin[lrs.at(sz).second]);
}
// query for edges on path [u, v]
void for_each_edge(int u, int v, const std::function<void(int, int)> &f) const {
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
if (head[u] != head[v]) {
f(subtree_begin[head[v]], subtree_begin[v]);
v = par[head[v]];
} else {
if (u != v) f(subtree_begin[u] + 1, subtree_begin[v]);
break;
}
}
}
// query for vertices in subtree rooted at u
void for_subtree(int u, const std::function<void(int, int)> &f) const {
f(subtree_begin[u], subtree_end[u] - 1);
}
// lowest_common_ancestor: O(log V)
int lowest_common_ancestor(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
while (true) {
if (subtree_begin[u] > subtree_begin[v]) std::swap(u, v);
if (head[u] == head[v]) return u;
v = par[head[v]];
}
}
int distance(int u, int v) const {
assert(tree_id[u] == tree_id[v] and tree_id[u] >= 0);
return depth[u] + depth[v] - 2 * depth[lowest_common_ancestor(u, v)];
}
// Level ancestor, O(log V)
// if k-th parent is out of range, return -1
int kth_parent(int v, int k) const {
if (k < 0) return -1;
while (v >= 0) {
int h = head.at(v), len = depth.at(v) - depth.at(h);
if (k <= len) return vis_order.at(subtree_begin.at(v) - k);
k -= len + 1, v = par.at(h);
}
return -1;
}
// Jump on tree, O(log V)
int s_to_t_by_k_steps(int s, int t, int k) const {
if (k < 0) return -1;
if (k == 0) return s;
int lca = lowest_common_ancestor(s, t);
if (k <= depth.at(s) - depth.at(lca)) return kth_parent(s, k);
return kth_parent(t, depth.at(s) + depth.at(t) - depth.at(lca) * 2 - k);
}
};
#line 4 "graph/test/extended_block_cut_trees.yuki1326.test.cpp"
#include <atcoder/fenwicktree>
#include <iostream>
using namespace std;
int main() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
int N, M;
cin >> N >> M;
vector<pair<int, int>> edges(M);
for (auto &[u, v] : edges) cin >> u >> v, --u, --v;
const extended_block_cut_trees bct(N, edges);
heavy_light_decomposition hld(bct.size(), bct.get_edges());
hld.build();
atcoder::fenwick_tree<int> fw(hld.V);
for (int i = 0; i < N; ++i) fw.add(hld.subtree_begin[i], 1);
int Q;
cin >> Q;
while (Q--) {
int u, v;
cin >> u >> v;
--u, --v;
int ret = 0;
if (u != v) {
ret = -2;
hld.for_each_vertex(u, v, [&](int a, int b) { ret += fw.sum(a, b + 1); });
}
cout << ret << '\n';
}
}