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cp-templates/graph/hld.cc

99 lines
3.0 KiB
C++

template <typename Info, typename Tag>
struct HLD {
struct node_info {
int father, depth, hson, size, head, dfn = -1;
};
int n;
vector<int> seq;
vector<node_info> info;
segtree<Info, Tag> tr;
// returns: (dfs sequence, node info)
// node numbering starts from `1`
// if `dfn(v) == -1`, then node `v` is never accessed.
HLD(const vector<vector<int>>& ch, const vector<Info>& init, int root = 0) : n(ch.size() - 1), seq(), info(n + 1), tr(n + 1) {
vector<node_info> res(n + 1);
auto dfs1 = [&] (auto dfs1, int v, int pa) -> void {
res[v].father = pa;
res[v].depth = res[pa].depth + 1;
res[v].size = 1;
int mx = 0;
for (auto&& u : ch[v]) {
if (u == pa) continue;
dfs1(dfs1, u, v);
res[v].size += res[u].size;
if (res[u].size > mx) {
mx = res[u].size;
res[v].hson = u;
}
}
};
dfs1(dfs1, root, root);
int tm = 0;
auto dfs2 = [&] (auto dfs2, int v, int head) -> void {
res[v].dfn = tm++;
seq.emplace_back(v);
res[v].head = head;
if (not res[v].hson) return;
dfs2(dfs2, res[v].hson, head);
for (auto&& u : ch[v]) {
if (u == res[v].father or u == res[v].hson) continue;
dfs2(dfs2, u, u);
}
};
dfs2(dfs2, root, root);
info = res;
for (int i = 1; i <= n; ++i) {
tr.set(info[i].dfn, init[i]);
}
}
void set(int v, const Info& t) {
tr.set(info[v].dfn, t);
}
void apply(int v, const Tag& t) {
tr.apply(info[v].dfn, t);
}
Info query(int v) {
return tr.query(info[v].dfn);
}
void path_apply(int u, int v, const Tag& t) {
while (info[u].head != info[v].head) {
if (info[info[u].head].depth < info[info[v].head].depth) {
swap(u, v);
}
tr.range_apply(info[info[u].head].dfn, info[u].dfn, t);
u = info[info[u].head].father;
}
if (info[u].depth < info[v].depth) swap(u, v);
tr.range_apply(info[v].dfn, info[u].dfn, t);
}
Info path_query(int u, int v) {
Info res;
while (info[u].head != info[v].head) {
if (info[info[u].head].depth < info[info[v].head].depth) {
swap(u, v);
}
res = res + tr.range_query(info[info[u].head].dfn, info[u].dfn);
u = info[info[u].head].father;
}
if (info[u].depth < info[v].depth) swap(u, v);
res = res + tr.range_query(info[v].dfn, info[u].dfn);
return res;
}
void subtree_apply(int v, const Tag& t) {
tr.range_apply(info[v].dfn, info[v].dfn + info[v].size - 1, t);
}
Info subtree_query(int v) {
return tr.range_query(info[v].dfn, info[v].dfn + info[v].size - 1);
}
};