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P2590 [ZJOI2008]树的统计
R63590620
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167
Luogu/P2590/P2590.cpp
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167
Luogu/P2590/P2590.cpp
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#include <bits/stdc++.h>
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using namespace std;
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const int N = 100005;
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int n, q, x, y, u, v, a[N];
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string op;
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vector<int> g[N];
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int cnt, id[N], w[N], top[N], son[N], dep[N], fa[N], siz[N];
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// Heavy Path Decomposition
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void dfs1(int, int);
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void dfs2(int, int);
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int query_path_sum(int, int);
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int query_path_max(int, int);
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// Segment Tree
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void pushup(int);
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void build(int, int, int);
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void modify(int, int, int);
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int query_sum(int, int, int);
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int query_max(int, int, int);
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int main() {
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cin >> n;
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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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for (int i = 1; i <= n; i++) {
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cin >> a[i];
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}
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dfs1(1, 0);
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dfs2(1, 1);
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build(1, 1, n);
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cin >> q;
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while (q--) {
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cin >> op >> u >> v;
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if (op == "CHANGE") {
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modify(1, id[u], v);
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} else if (op == "QMAX") {
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cout << query_path_max(u, v) << endl;
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} else if (op == "QSUM") {
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cout << query_path_sum(u, v) << endl;
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}
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}
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return 0;
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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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siz[u] = 1;
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for (int v : g[u]) {
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if (v == f) continue;
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dfs1(v, u);
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siz[u] += siz[v];
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if (siz[son[u]] < siz[v]) son[u] = v;
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}
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}
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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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top[u] = t;
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if (!son[u]) return;
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dfs2(son[u], t);
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for (int v : g[u]) {
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if (v == fa[u]) continue;
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if (v == son[u]) continue;
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dfs2(v, v);
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}
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}
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int query_path_max(int u, int v) {
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int res = numeric_limits<int>::min();
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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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res = max(res, query_max(1, id[top[u]], id[u]));
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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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res = max(res, query_max(1, id[v], id[u]));
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return res;
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}
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int query_path_sum(int u, int v) {
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int 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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sum += query_sum(1, id[top[u]], id[u]);
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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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sum += query_sum(1, id[v], id[u]);
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return sum;
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}
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// === Segment Tree ===
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struct node {
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int l, r, sum, max;
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node()
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: l(0), r(0), sum(0), max(numeric_limits<int>::min()) {}
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node(int _l, int _r)
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: l(_l), r(_r), sum(0), max(numeric_limits<int>::min()) {}
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} tr[N << 2];
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void pushup(int u) {
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tr[u].sum = tr[u << 1].sum + tr[u << 1 | 1].sum;
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tr[u].max = max(tr[u << 1].max, tr[u << 1 | 1].max);
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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].sum = w[l];
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tr[u].max = 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 x, int d) {
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if (tr[u].l == x && tr[u].r == x) {
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tr[u].sum = d;
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tr[u].max = d;
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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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if (x <= mid) {
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modify(u << 1, x, d);
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} else {
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modify(u << 1 | 1, x, d);
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}
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pushup(u);
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}
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int query_sum(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].sum;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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int sum = 0;
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if (l <= mid) sum += query_sum(u << 1, l, r);
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if (r > mid) sum += query_sum(u << 1 | 1, l, r);
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return sum;
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}
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int query_max(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].max;
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}
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int mid = tr[u].l + tr[u].r >> 1;
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int res = numeric_limits<int>::min();
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if (l <= mid) res = max(res, query_max(u << 1, l, r));
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if (r > mid) res = max(res, query_max(u << 1 | 1, l, r));
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return res;
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}
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