K - Innovations

https://codeforces.com/gym/102439/submission/176106742

Gym/102439/K/K.cpp

@@ -0,0 +1,148 @@
+#include <iostream>
+#include <cmath>
+#include <string>
+#include <vector>
+
+using std::cin;
+using std::cout;
+using std::endl;
+
+const int N = 2e5 + 5;
+const int mod = 1e9 + 7;
+
+int n, m, a[N], f[N];
+int cnt, id[N], rid[N], fa[N], dep[N], siz[N], son[N], top[N];
+std::vector<std::pair<int, int>> g[N];
+
+struct node {
+    int l, r, v, max, sum;
+
+    node() = default;
+
+    node(int _l, int _r)
+        : l(_l), r(_r), v(0), max(0), sum(0) {}
+} tr[N << 2];
+
+void pushup(int u) {
+    tr[u].max = std::max(tr[u << 1].max, tr[u << 1 | 1].max);
+    tr[u].sum = (tr[u << 1].sum + tr[u << 1 | 1].sum) % mod;
+}
+
+void build(int u, int l, int r) {
+    tr[u] = node(l, r);
+
+    if (l == r) {
+        tr[u].max = a[rid[l]];
+        tr[u].sum = static_cast<long long>(tr[u].max) * f[rid[l]] % mod;
+
+        return;
+    }
+
+    int mid = l + r >> 1;
+
+    build(u << 1, l, mid);
+    build(u << 1 | 1, mid + 1, r);
+
+    pushup(u);
+}
+
+void dfs1(int u, int f) {
+    fa[u] = f;
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+
+    for (auto e : g[u]) {
+        int v = e.first,
+            w = e.second;
+
+        if (v == f) continue;
+
+        a[v] = w;
+        dfs1(v, u);
+        siz[u] += siz[v];
+
+        if (siz[son[u]] < siz[v]) son[u] = v;
+    }
+
+    ::f[u] = static_cast<long long>(siz[u]) * (n - siz[u]) % mod;
+}
+
+void dfs2(int u, int t) {
+    rid[id[u] = ++cnt] = u;
+    top[u] = t;
+
+    if (!son[u]) return;
+
+    dfs2(son[u], t);
+
+    for (auto e : g[u]) {
+        int v = e.first;
+
+        if (v == fa[u]) continue;
+        if (v == son[u]) continue;
+
+        dfs2(v, v);
+    }
+}
+
+void modify(int u, int l, int r) {
+    if (tr[u].max <= 1) return;
+
+    if (tr[u].l == tr[u].r) {
+        tr[u].max = std::sqrt(tr[u].max);
+        tr[u].sum = static_cast<long long>(tr[u].max) * f[rid[tr[u].l]] % mod;
+
+        return;
+    }
+
+    int mid = tr[u].l + tr[u].r >> 1;
+
+    if (l <= mid) modify(u << 1, l, r);
+    if (r > mid) modify(u << 1 | 1, l, r);
+
+    pushup(u);
+}
+
+void modify_path(int u, int v) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        modify(1, id[top[u]], id[u]);
+        u = fa[top[u]];
+    }
+
+    if (u == v) return;
+    if (dep[u] < dep[v]) std::swap(u, v);
+    modify(1, id[v] + 1, id[u]);
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1, u, v, w; i < n; i++) {
+        cin >> u >> v >> w;
+
+        g[u].emplace_back(v, w);
+        g[v].emplace_back(u, w);
+    }
+
+    dfs1(1, 1);
+    dfs2(1, 1);
+    build(1, 1, n);
+
+    cout << tr[1].sum << endl;
+
+    while (m--) {
+        int u, v;
+
+        cin >> u >> v;
+
+        modify_path(u, v);
+
+        cout << tr[1].sum << endl;
+    }
+
+    return 0;
+}