P4114 Qtree1

R65026671

Luogu/P4114/P4114.cpp

@@ -0,0 +1,137 @@
+#include <iostream>
+#include <string>
+#include <vector>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 100005;
+
+int n, x, t, a, b, u[N], v[N], w[N];
+std::string op;
+std::vector<int> g[N];
+
+// Heavy Path Decomposition
+int cnt, id[N], fa[N], dep[N], son[N], siz[N], top[N];
+void dfs1(int, int);
+void dfs2(int, int);
+int query_path(int, int);
+
+// Segment Tree
+void pushup(int);
+void pushdown(int);
+void build(int, int, int);
+void change(int, int, int);
+int query(int, int, int);
+
+int main() {
+    cin >> n;
+    for (int i = 1; i < n; i++) {
+        cin >> u[i] >> v[i] >> w[i];
+        g[u[i]].push_back(v[i]);
+        g[v[i]].push_back(u[i]);
+    }
+    dfs1(1, 1);
+    dfs2(1, 1);
+    build(1, 1, n);
+    for (int i = 1; i < n; i++) {
+        if (dep[u[i]] < dep[v[i]]) std::swap(u[i], v[i]);
+        change(1, id[u[i]], w[i]);
+    }
+    while (cin >> op, op != "DONE") {
+        if (op == "CHANGE") {
+            cin >> x >> t;
+            change(1, id[u[x]], t);
+        } else {
+            cin >> a >> b;
+            cout << (a == b ? 0 : query_path(a, b)) << 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;
+    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(int u, int v) {
+    int res = 0;
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        res = std::max(res, query(1, id[top[u]], id[u]));
+        u = fa[top[u]];
+    }
+    if (dep[u] < dep[v]) std::swap(u, v);
+    res = std::max(res, query(1, id[son[v]], id[u]));
+    return res;
+}
+
+// === Segment Tree ===
+
+struct node {
+    int l, r, m;
+
+    node()
+        : l(0), r(0), m(0) {}
+    node(int _l, int _r)
+        : l(_l), r(_r), m(0) {}
+} tr[N << 2];
+
+inline void pushup(int u) {
+    tr[u].m = std::max(tr[u << 1].m, tr[u << 1 | 1].m);
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+    if (l == r) return;
+    int mid = l + r >> 1;
+    build(u << 1, l, mid);
+    build(u << 1 | 1, mid + 1, r);
+    pushup(u);
+}
+
+void change(int u, int x, int d) {
+    if (tr[u].l == tr[u].r) {
+        tr[u].m = d;
+        return;
+    }
+    int mid = tr[u].l + tr[u].r >> 1;
+    if (x <= mid) {
+        change(u << 1, x, d);
+    } else {
+        change(u << 1 | 1, x, d);
+    }
+    pushup(u);
+}
+
+int query(int u, int l, int r) {
+    if (l <= tr[u].l && tr[u].r <= r) return tr[u].m;
+    int mid = tr[u].l + tr[u].r >> 1;
+    int res = 0;
+    if (l <= mid) res = std::max(res, query(u << 1, l, r));
+    if (r > mid) res = std::max(res, query(u << 1 | 1, l, r));
+    return res;
+}