CP-templates
This documentation is automatically generated by online-judge-tools/verification-helper
tree/HLD.cpp
- View this file on GitHub
- Last update: 2026-02-03 04:18:40+08:00
Verified with
- test/jump_on_tree_2.test.cpp
- test/jump_on_tree_3.test.cpp
- test/lca_4.test.cpp
- test/vertex_add_path_sum.test.cpp
- test/vertex_add_subtree_sum.test.cpp
- test/vertex_set_path_composite.test.cpp
Code
struct HLD {
static const int MSK = (1 << 30);
vi dep, p_head, tin, tout, inv_tin;
inline int head(int v) const { return (p_head[v] & MSK) ? v : p_head[v]; }
inline int head_parent(int v) const { return p_head[head(v)] & (MSK - 1); }
HLD(vc<pii> e, int root = 0) {
const int n = ssize(e) + 1;
dep = p_head = tin = tout = vi(n);
vi sz(n, 1), mx_child_sz(n, -1);
{
vi d(n);
for(auto [u, v] : e)
p_head[u] ^= v, p_head[v] ^= u, d[u]++, d[v]++;
d[root] = 0;
for(int i = 0; i < n; i++) {
int v = i;
while(d[v] == 1) {
d[v] = 0, d[p_head[v]]--, p_head[p_head[v]] ^= v;
sz[p_head[v]] += sz[v];
chmax(mx_child_sz[p_head[v]], sz[v]);
v = p_head[v];
}
}
}
vi ord(n);
{
vi f(n + 2);
for(int x : sz) f[x + 1]++;
pSum(f);
for(int v = 0; v < n; v++)
ord[n - 1 - (f[sz[v]]++)] = v;
}
{
p_head[root] = (root | MSK), tout[root] = n;
vi add(n, 1);
for(int v : ord | views::drop(1)) {
dep[v] = dep[p_head[v]] + 1;
tin[v] = tin[p_head[v]] + add[p_head[v]];
add[p_head[v]] += sz[v];
tout[v] = tin[v] + sz[v];
if (mx_child_sz[p_head[v]] == sz[v])
mx_child_sz[p_head[v]] = 0, p_head[v] = head(p_head[v]);
else
p_head[v] |= MSK;
}
}
inv_tin = invPerm(tin);
}
auto query_path(int u, int v, bool edge = false) {
vc<pii> lr;
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)])
swap(u, v);
lr.emplace_back(tin[head(v)], tin[v] + 1);
v = head_parent(v);
}
if (tin[u] > tin[v]) swap(u, v);
if (tin[u] + edge <= tin[v])
lr.emplace_back(tin[u] + edge, tin[v] + 1);
return lr;
}
//l < r: op(l, op(l + 1, ...))
//l > r: op(r - 1, op(r - 2, ...))
auto query_path_non_commutative(int u, int v, bool edge = false) {
vc<pii> lr1, lr2;
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)]) {
lr1.emplace_back(tin[u] + 1, tin[head(u)]);
u = head_parent(u);
} else {
lr2.emplace_back(tin[head(v)], tin[v] + 1);
v = head_parent(v);
}
}
if (tin[u] + edge <= tin[v])
lr2.emplace_back(tin[u] + edge, tin[v] + 1);
else if (tin[v] + edge <= tin[u])
lr1.emplace_back(tin[u] + 1, tin[v] + edge);
lr1.insert(end(lr1), lr2.rbegin(), lr2.rend());
return lr1;
}
auto query_subtree(int v) { return pii(tin[v], tout[v]); }
int query_point(int v) { return tin[v]; }
int lca(int u, int v) {
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)])
swap(u, v);
v = head_parent(v);
}
return tin[u] < tin[v] ? u : v;
}
int kth(int s, int t, int k) {
int l = lca(s, t);
if (int d = dep[s] + dep[t] - 2 * dep[l]; k > d)
return -1;
else if (k > dep[s] - dep[l])
k = d - k, swap(s, t);
while(k > dep[s] - dep[head(s)]) {
k -= dep[s] - dep[head(s)] + 1;
s = head_parent(s);
}
return inv_tin[tin[s] - k];
}
template<class M>
vc<M> reorder_init(vc<M> init) {
assert(ssize(init) == ssize(dep));
auto r = init;
for(int i = 0; i < ssize(init); i++)
r[tin[i]] = init[i];
return r;
}
};#line 1 "tree/HLD.cpp"
struct HLD {
static const int MSK = (1 << 30);
vi dep, p_head, tin, tout, inv_tin;
inline int head(int v) const { return (p_head[v] & MSK) ? v : p_head[v]; }
inline int head_parent(int v) const { return p_head[head(v)] & (MSK - 1); }
HLD(vc<pii> e, int root = 0) {
const int n = ssize(e) + 1;
dep = p_head = tin = tout = vi(n);
vi sz(n, 1), mx_child_sz(n, -1);
{
vi d(n);
for(auto [u, v] : e)
p_head[u] ^= v, p_head[v] ^= u, d[u]++, d[v]++;
d[root] = 0;
for(int i = 0; i < n; i++) {
int v = i;
while(d[v] == 1) {
d[v] = 0, d[p_head[v]]--, p_head[p_head[v]] ^= v;
sz[p_head[v]] += sz[v];
chmax(mx_child_sz[p_head[v]], sz[v]);
v = p_head[v];
}
}
}
vi ord(n);
{
vi f(n + 2);
for(int x : sz) f[x + 1]++;
pSum(f);
for(int v = 0; v < n; v++)
ord[n - 1 - (f[sz[v]]++)] = v;
}
{
p_head[root] = (root | MSK), tout[root] = n;
vi add(n, 1);
for(int v : ord | views::drop(1)) {
dep[v] = dep[p_head[v]] + 1;
tin[v] = tin[p_head[v]] + add[p_head[v]];
add[p_head[v]] += sz[v];
tout[v] = tin[v] + sz[v];
if (mx_child_sz[p_head[v]] == sz[v])
mx_child_sz[p_head[v]] = 0, p_head[v] = head(p_head[v]);
else
p_head[v] |= MSK;
}
}
inv_tin = invPerm(tin);
}
auto query_path(int u, int v, bool edge = false) {
vc<pii> lr;
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)])
swap(u, v);
lr.emplace_back(tin[head(v)], tin[v] + 1);
v = head_parent(v);
}
if (tin[u] > tin[v]) swap(u, v);
if (tin[u] + edge <= tin[v])
lr.emplace_back(tin[u] + edge, tin[v] + 1);
return lr;
}
//l < r: op(l, op(l + 1, ...))
//l > r: op(r - 1, op(r - 2, ...))
auto query_path_non_commutative(int u, int v, bool edge = false) {
vc<pii> lr1, lr2;
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)]) {
lr1.emplace_back(tin[u] + 1, tin[head(u)]);
u = head_parent(u);
} else {
lr2.emplace_back(tin[head(v)], tin[v] + 1);
v = head_parent(v);
}
}
if (tin[u] + edge <= tin[v])
lr2.emplace_back(tin[u] + edge, tin[v] + 1);
else if (tin[v] + edge <= tin[u])
lr1.emplace_back(tin[u] + 1, tin[v] + edge);
lr1.insert(end(lr1), lr2.rbegin(), lr2.rend());
return lr1;
}
auto query_subtree(int v) { return pii(tin[v], tout[v]); }
int query_point(int v) { return tin[v]; }
int lca(int u, int v) {
while(head(u) != head(v)) {
if (dep[head(u)] > dep[head(v)])
swap(u, v);
v = head_parent(v);
}
return tin[u] < tin[v] ? u : v;
}
int kth(int s, int t, int k) {
int l = lca(s, t);
if (int d = dep[s] + dep[t] - 2 * dep[l]; k > d)
return -1;
else if (k > dep[s] - dep[l])
k = d - k, swap(s, t);
while(k > dep[s] - dep[head(s)]) {
k -= dep[s] - dep[head(s)] + 1;
s = head_parent(s);
}
return inv_tin[tin[s] - k];
}
template<class M>
vc<M> reorder_init(vc<M> init) {
assert(ssize(init) == ssize(dep));
auto r = init;
for(int i = 0; i < ssize(init); i++)
r[tin[i]] = init[i];
return r;
}
};