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OI-codes/Luogu/P3384/P3384.cpp

176 lines
3.9 KiB
C++

#include <iostream>
#include <vector>
using std::cin;
using std::cout;
using std::endl;
const int N = 100005;
int p, a[N];
std::vector<int> g[N];
// Segment Tree
void build(int, int, int);
// Heavy Path Decomposition
int cnt, id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
void dfs1(int, int);
void dfs2(int, int);
void modify_path(int, int, int);
void modify_tree(int, int);
long long query_path(int, int);
long long query_tree(int);
int main() {
int n, m, r;
cin >> n >> m >> r >> p;
for (int i = 1; i <= n; i++) {
cin >> a[i];
}
for (int i = 1; i < n; i++) {
int x, y;
cin >> x >> y;
g[x].push_back(y);
g[y].push_back(x);
}
dfs1(r, r);
dfs2(r, r);
build(1, 1, n);
while (m--) {
int op, x, y, z;
cin >> op;
if (op == 1) {
cin >> x >> y >> z;
modify_path(x, y, z);
} else if (op == 2) {
cin >> x >> y;
cout << query_path(x, y) << endl;
} else if (op == 3) {
cin >> x >> z;
modify_tree(x, z);
} else {
cin >> x;
cout << query_tree(x) << endl;
}
}
return 0;
}
// === Segment Tree ===
struct node {
int l, r;
long long s, d;
node()
: l(0), r(0), s(0), d(0) {}
node(int _l, int _r)
: l(_l), r(_r), s(0), d(0) {}
} tr[N << 2];
inline void pushup(int u) {
tr[u].s = (tr[u << 1].s + tr[u << 1 | 1].s) % p;
}
inline void pushdown(int u) {
node &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
left.s = (left.s + (left.r - left.l + 1) * root.d) % p;
left.d = (left.d + root.d) % p;
right.s = (right.s + (right.r - right.l + 1) * root.d) % p;
right.d = (right.d + root.d) % p;
root.d = 0;
}
void build(int u, int l, int r) {
tr[u] = node(l, r);
if (l == r) {
tr[u].s = a[rid[l]] % p;
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, int d) {
if (l <= tr[u].l && tr[u].r <= r) {
tr[u].s = (tr[u].s + (tr[u].r - tr[u].l + 1) * d) % p;
tr[u].d = (tr[u].d + d) % p;
return;
}
pushdown(u);
int mid = tr[u].l + tr[u].r >> 1;
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 % p;
pushdown(u);
int mid = tr[u].l + tr[u].r >> 1;
long long res = 0;
if (l <= mid) res = (res + query(u << 1, l, r)) % p;
if (r > mid) res = (res + query(u << 1 | 1, l, r)) % p;
return res;
}
// == 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;
rid[id[u]] = 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, int 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);
}
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 = (sum + query(1, id[top[u]], id[u])) % p;
u = fa[top[u]];
}
if (dep[u] < dep[v]) std::swap(u, v);
sum = (sum + query(1, id[v], id[u])) % p;
return sum;
}
inline void modify_tree(int u, int d) {
modify(1, id[u], id[u] + siz[u] - 1, d);
}
inline long long query_tree(int u) {
return query(1, id[u], id[u] + siz[u] - 1);
}