#2125. 「HAOI2015」树上操作

https://loj.ac/s/1312868

LibreOJ/2125/2125.cpp

@@ -0,0 +1,169 @@
+#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()
+        : 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;
+}
+
+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;
+}