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P3384 【模板】轻重链剖分/树链剖分
R65189455
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@ -1,10 +1,63 @@
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#include <bits/stdc++.h>
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#include <iostream>
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#include <vector>
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using namespace std;
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using std::cin;
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using std::cout;
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using std::endl;
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int n, m, r, p, a[100005], x, y, op, u, v, k;
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vector<int> g[100005];
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int cnt, dep[100005], fa[100005], siz[100005], son[100005], id[100005], top[100005], w[100005];
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const int N = 100005;
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int p, a[N];
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std::vector<int> g[N];
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// Segment Tree
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void build(int, int, int);
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// Heavy Path Decomposition
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int cnt, id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
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void dfs1(int, int);
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void dfs2(int, int);
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void modify_path(int, int, int);
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void modify_tree(int, int);
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long long query_path(int, int);
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long long query_tree(int);
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int main() {
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int n, m, r;
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cin >> n >> m >> r >> p;
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for (int i = 1; i <= n; i++) {
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cin >> a[i];
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}
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for (int i = 1; i < n; i++) {
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int x, y;
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cin >> x >> y;
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g[x].push_back(y);
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g[y].push_back(x);
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}
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dfs1(r, r);
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dfs2(r, r);
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build(1, 1, n);
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while (m--) {
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int op, x, y, z;
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cin >> op;
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if (op == 1) {
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cin >> x >> y >> z;
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modify_path(x, y, z);
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} else if (op == 2) {
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cin >> x >> y;
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cout << query_path(x, y) << endl;
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} else if (op == 3) {
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cin >> x >> z;
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modify_tree(x, z);
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} else {
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cin >> x;
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cout << query_tree(x) << endl;
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}
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}
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return 0;
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}
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// === Segment Tree ===
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struct node {
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int l, r;
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@ -14,11 +67,61 @@ struct 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[100005 << 2];
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} tr[N << 2];
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inline void pushup(int u) {
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tr[u].s = (tr[u << 1].s + tr[u << 1 | 1].s) % p;
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}
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inline void pushdown(int u) {
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node &root = tr[u], &left = tr[u << 1], &right = tr[u << 1 | 1];
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left.s = (left.s + (left.r - left.l + 1) * root.d) % p;
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left.d = (left.d + root.d) % p;
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right.s = (right.s + (right.r - right.l + 1) * root.d) % p;
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right.d = (right.d + root.d) % p;
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root.d = 0;
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}
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void build(int u, int l, int r) {
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tr[u] = node(l, r);
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if (l == r) {
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tr[u].s = a[rid[l]] % p;
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return;
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}
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int mid = l + r >> 1;
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build(u << 1, l, mid);
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build(u << 1 | 1, mid + 1, r);
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pushup(u);
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}
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void modify(int u, int l, int r, int d) {
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if (l <= tr[u].l && tr[u].r <= r) {
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tr[u].s = (tr[u].s + (tr[u].r - tr[u].l + 1) * d) % p;
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tr[u].d = (tr[u].d + d) % p;
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return;
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}
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pushdown(u);
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int mid = tr[u].l + tr[u].r >> 1;
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if (l <= mid) modify(u << 1, l, r, d);
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if (r > mid) modify(u << 1 | 1, l, r, d);
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pushup(u);
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}
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long long query(int u, int l, int r) {
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if (l <= tr[u].l && tr[u].r <= r) return tr[u].s % p;
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pushdown(u);
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int mid = tr[u].l + tr[u].r >> 1;
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long long res = 0;
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if (l <= mid) res = (res + query(u << 1, l, r)) % p;
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if (r > mid) res = (res + query(u << 1 | 1, l, r)) % p;
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return res;
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}
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// == Heavy Path Decomposition ===
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void dfs1(int u, int f) {
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dep[u] = dep[f] + 1;
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fa[u] = f;
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dep[u] = dep[f] + 1;
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siz[u] = 1;
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for (int v : g[u]) {
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if (v == f) continue;
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@ -30,7 +133,7 @@ void dfs1(int u, int f) {
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void dfs2(int u, int t) {
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id[u] = ++cnt;
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w[cnt] = a[u];
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rid[id[u]] = u;
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top[u] = t;
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if (!son[u]) return;
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dfs2(son[u], t);
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@ -41,113 +144,32 @@ void dfs2(int u, int t) {
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}
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}
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void pushup(int u) {
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tr[u].s = (tr[u << 1].s + tr[u << 1 | 1].s) % p;
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}
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void pushdown(int u) {
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if (!tr[u].d) return;
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tr[u << 1].s = (tr[u << 1].s + (tr[u << 1].r - tr[u << 1].l + 1) * tr[u].d) % p;
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tr[u << 1].d = (tr[u << 1].d + tr[u].d) % p;
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tr[u << 1 | 1].s = (tr[u << 1 | 1].s + (tr[u << 1 | 1].r - tr[u << 1 | 1].l + 1) * tr[u].d) % p;
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tr[u << 1 | 1].d = (tr[u << 1 | 1].d + tr[u].d) % p;
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tr[u].d = 0;
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}
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void build(int u, int l, int r) {
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tr[u] = node(l, r);
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if (l == r) {
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tr[u].s = w[r];
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return;
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}
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int mid = l + r >> 1;
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build(u << 1, l, mid);
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build(u << 1 | 1, mid + 1, r);
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pushup(u);
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}
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void modify(int u, int l, int r, int k) {
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if (l <= tr[u].l && tr[u].r <= r) {
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tr[u].s = (tr[u].s + (tr[u].r - tr[u].l + 1) * k) % p;
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tr[u].d = (tr[u].d + k) % p;
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return;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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pushdown(u);
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if (l <= mid) modify(u << 1, l, r, k);
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if (r > mid) modify(u << 1 | 1, l, r, k);
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pushup(u);
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}
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long long query(int u, int l, int r) {
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if (l <= tr[u].l && tr[u].r <= r) {
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return tr[u].s % p;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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long long sum = 0;
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pushdown(u);
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if (l <= mid) sum = (sum + query(u << 1, l, r)) % p;
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if (r > mid) sum = (sum + query(u << 1 | 1, l, r)) % p;
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return sum;
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}
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void modify_path(int u, int v, int k) {
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void modify_path(int u, int v, int d) {
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while (top[u] != top[v]) {
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if (dep[top[u]] < dep[top[v]]) swap(u, v);
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modify(1, id[top[u]], id[u], k);
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if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
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modify(1, id[top[u]], id[u], d);
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u = fa[top[u]];
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}
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if (dep[u] < dep[v]) swap(u, v);
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modify(1, id[v], id[u], k);
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if (dep[u] < dep[v]) std::swap(u, v);
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modify(1, id[v], id[u], d);
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}
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long long query_path(int u, int v) {
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long long sum = 0;
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while (top[u] != top[v]) {
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if (dep[top[u]] < dep[top[v]]) swap(u, v);
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if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
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sum = (sum + query(1, id[top[u]], id[u])) % p;
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u = fa[top[u]];
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}
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if (dep[u] < dep[v]) swap(u, v);
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if (dep[u] < dep[v]) std::swap(u, v);
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sum = (sum + query(1, id[v], id[u])) % p;
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return sum;
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}
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void modify_tree(int u, int k) {
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modify(1, id[u], id[u] + siz[u] - 1, k);
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inline void modify_tree(int u, int d) {
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modify(1, id[u], id[u] + siz[u] - 1, d);
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}
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long long query_tree(int u) {
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inline long long query_tree(int u) {
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return query(1, id[u], id[u] + siz[u] - 1);
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}
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int main() {
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cin >> n >> m >> r >> p;
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for (int i = 1; i <= n; i++) {
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cin >> a[i];
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}
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for (int i = 1; i < n; i++) {
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cin >> x >> y;
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g[x].push_back(y);
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g[y].push_back(x);
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}
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dfs1(r, 0);
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dfs2(r, r);
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build(1, 1, n);
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for (int i = 1; i <= m; i++) {
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cin >> op >> u;
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if (op == 1) {
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cin >> v >> k;
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modify_path(u, v, k);
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} else if (op == 2) {
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cin >> v;
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cout << query_path(u, v) % p << endl;
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} else if (op == 3) {
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cin >> k;
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modify_tree(u, k);
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} else {
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cout << query_tree(u) % p << endl;
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}
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}
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return 0;
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}
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BIN
Luogu/P3384/data/P3384_2.in
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Luogu/P3384/data/P3384_2.in
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Luogu/P3384/data/P3384_2.out
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Luogu/P3384/data/P3384_2.out
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