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OI-codes/Luogu/P3178/P3178.cpp

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#include <bits/stdc++.h>
using std::cin;
using std::cout;
using std::endl;
const int N = 100005;
// Basic
int n, m, u, v, op, a[N];
std::vector<int> g[N];
// Heavy Path Decomposition
int cnt, w[N], id[N], fa[N], dep[N], son[N], siz[N], top[N];
void dfs1(int, int);
void dfs2(int, int);
void modify_path(int, int, long long);
void modify_tree(int, long long);
long long query_path(int, int);
// Segment Tree
void pushup(int);
void pushdown(int);
void build(int, int, int);
void modify(int, int, int, long long);
long long query(int, int, int);
int main() {
cin >> n >> m;
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
for (int i = 1; i < n; i++) {
cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
}
dfs1(1, 0);
dfs2(1, 1);
build(1, 1, n);
while (m--) {
cin >> op >> u;
if (op == 1) {
cin >> v;
modify_path(u, u, v);
} else if (op == 2) {
cin >> v;
modify_tree(u, v);
} else {
cout << query_path(1, u) << endl;
}
}
return 0;
}
// === Heavy Path Decomposition ===
void dfs1(int u, int f) {
fa[u] = f;
dep[u] = dep[f] + 1;
siz[u] = 1;
for (int v : g[u]) {
if (v == f) continue;
dfs1(v, u);
siz[u] += siz[v];
if (siz[son[u]] < siz[v]) son[u] = v;
}
}
void dfs2(int u, int t) {
id[u] = ++cnt;
w[cnt] = a[u];
top[u] = t;
if (!son[u]) return;
dfs2(son[u], t);
for (int v : g[u]) {
if (v == fa[u]) continue;
if (v == son[u]) continue;
dfs2(v, v);
}
}
void modify_path(int u, int v, long long d) {
while (top[u] != top[v]) {
if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
modify(1, id[top[u]], id[u], d);
u = fa[top[u]];
}
if (dep[u] < dep[v]) std::swap(u, v);
modify(1, id[v], id[u], d);
}
inline void modify_tree(int u, long long d) {
modify(1, id[u], id[u] + siz[u] - 1, d);
}
long long query_path(int u, int v) {
long long sum = 0;
while (top[u] != top[v]) {
if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
sum += query(1, id[top[u]], id[u]);
u = fa[top[u]];
}
if (dep[u] < dep[v]) std::swap(u, v);
sum += query(1, id[v], id[u]);
return sum;
}
// === Segment Tree ===
struct node {
int l, r;
long long s, d;
node()
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: l(0),
r(0),
s(0),
d(0) {}
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node(int _l, int _r)
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: l(_l),
r(_r),
s(0),
d(0) {}
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} tr[N << 2];
inline void pushup(int u) {
tr[u].s = tr[u << 1].s + tr[u << 1 | 1].s;
}
inline void pushdown(int u) {
auto &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
left.s += (left.r - left.l + 1) * root.d;
left.d += root.d;
right.s += (right.r - right.l + 1) * root.d;
right.d += root.d;
root.d = 0;
}
void build(int u, int l, int r) {
tr[u] = node(l, r);
if (l == r) {
tr[u].s = w[l];
return;
}
int mid = l + r >> 1;
build(u << 1, l, mid);
build(u << 1 | 1, mid + 1, r);
pushup(u);
}
void modify(int u, int l, int r, long long d) {
if (l <= tr[u].l && tr[u].r <= r) {
tr[u].d += d;
tr[u].s += (tr[u].r - tr[u].l + 1) * d;
return;
}
int mid = tr[u].l + tr[u].r >> 1;
pushdown(u);
if (l <= mid) modify(u << 1, l, r, d);
if (r > mid) modify(u << 1 | 1, l, r, d);
pushup(u);
}
long long query(int u, int l, int r) {
if (l <= tr[u].l && tr[u].r <= r) {
return tr[u].s;
}
int mid = tr[u].l + tr[u].r >> 1;
long long sum = 0;
pushdown(u);
if (l <= mid) sum += query(u << 1, l, r);
if (r > mid) sum += query(u << 1 | 1, l, r);
return sum;
}