#10138. 「一本通 4.5 例 1」树的统计

https://loj.ac/s/1310660

LibreOJ/10138/10138.cpp

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