From 98a5b912e9984ac4b3855b004b254ce1330beada Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Tue, 20 Dec 2022 16:35:29 +0800
Subject: [PATCH] =?UTF-8?q?P4556=20[Vani=E6=9C=89=E7=BA=A6=E4=BC=9A]?=
 =?UTF-8?q?=E9=9B=A8=E5=A4=A9=E7=9A=84=E5=B0=BE=E5=B7=B4=20/=E3=80=90?=
 =?UTF-8?q?=E6=A8=A1=E6=9D=BF=E3=80=91=E7=BA=BF=E6=AE=B5=E6=A0=91=E5=90=88?=
 =?UTF-8?q?=E5=B9=B6?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

https://www.luogu.com.cn/record/97677125
---
 Luogu/P4556/P4556.cpp | 228 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 228 insertions(+)
 create mode 100644 Luogu/P4556/P4556.cpp

diff --git a/Luogu/P4556/P4556.cpp b/Luogu/P4556/P4556.cpp
new file mode 100644
index 00000000..e50e4765
--- /dev/null
+++ b/Luogu/P4556/P4556.cpp
@@ -0,0 +1,228 @@
+#include <iostream>
+#include <cassert>
+#include <functional>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 1e5 + 5;
+
+class SegmentTree {
+  private:
+    int L, R;
+
+    static bool cmp(std::pair<int, int> a, std::pair<int, int> b) {
+        return a.first == b.first ? a.second > b.second : a.first < b.first;
+    }
+
+    struct node {
+        std::pair<int, int> o;
+        node *lchild, *rchild;
+
+        node()
+            : o(0, 0), lchild(nullptr), rchild(nullptr) {}
+
+        void pushup() {
+            o = {0, 0};
+
+            if (lchild) o = std::max(o, lchild->o, cmp);
+            if (rchild) o = std::max(o, rchild->o, cmp);
+        }
+    };
+
+    node *root;
+
+    void modify(node *&cur, int l, int r, int pos, int val) {
+        if (!cur) cur = new node();
+
+        if (l == r) {
+            cur->o.first += val;
+            cur->o.second = l;
+
+            return;
+        }
+
+        int mid = l + r >> 1;
+
+        if (pos <= mid) modify(cur->lchild, l, mid, pos, val);
+        else modify(cur->rchild, mid + 1, r, pos, val);
+
+        cur->pushup();
+    }
+
+    std::pair<int, int> query(node *cur, int l, int r, int ql, int qr) {
+        if (!cur) return {0, 0};
+        if (ql <= l && r <= qr) return cur->o;
+
+        int mid = l + r >> 1;
+        std::pair<int, int> res;
+
+        if (ql <= mid) res = std::max(res, query(cur->lchild, l, mid, ql, qr), cmp);
+        if (qr > mid) res = std::max(res, query(cur->rchild, mid + 1, r, ql, qr), cmp);
+
+        return res;
+    }
+
+    node *merge(node *&cur_a, node *&cur_b, int l, int r) {
+        if (!cur_a) return cur_b;
+        if (!cur_b) return cur_a;
+
+        node *cur = new node();
+
+        if (l == r) {
+            cur->o.first = cur_a->o.first + cur_b->o.first;
+            cur->o.second = l;
+
+            delete cur_a;
+            delete cur_b;
+            cur_a = cur_b = nullptr;
+
+            return cur;
+        }
+
+        int mid = l + r >> 1;
+
+        cur->lchild = merge(cur_a->lchild, cur_b->lchild, l, mid);
+        cur->rchild = merge(cur_a->rchild, cur_b->rchild, mid + 1, r);
+
+        delete cur_a;
+        delete cur_b;
+        cur_a = cur_b = nullptr;
+
+        cur->pushup();
+
+        return cur;
+    }
+
+    void _delete(node *&cur) {
+        if (cur->lchild) _delete(cur->lchild);
+        if (cur->rchild) _delete(cur->rchild);
+        delete cur;
+    }
+
+  public:
+    SegmentTree(const int &_L = 0, const int _R = 0)
+        : L(_L), R(_R), root(nullptr) {}
+
+    ~SegmentTree() {
+        // if (root) _delete(root);
+    }
+
+    void modify(int pos, int val) {
+        modify(root, L, R, pos, val);
+    }
+
+    std::pair<int, int> query(int ql, int qr) {
+        return query(root, L, R, ql, qr);
+    }
+
+    void merge(SegmentTree &b) {
+        assert(L == b.L && R == b.R);
+
+        root = merge(root, b.root, L, R);
+    }
+};
+
+int n, m, x[N], y[N], z[N], max, ans[N];
+int fa[N], dep[N], siz[N], son[N], top[N];
+std::vector<int> g[N];
+
+void dfs1(int u, int f) {
+    dep[u] = dep[f] + 1;
+    siz[u] = 1;
+    fa[u] = f;
+
+    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) {
+    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 lca(int u, int v) {
+    while (top[u] != top[v]) {
+        if (dep[top[u]] < dep[top[v]]) std::swap(u, v);
+        u = fa[top[u]];
+    }
+
+    return dep[u] < dep[v] ? u : v;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n >> m;
+
+    for (int i = 1, u, v; i < n; i++) {
+        cin >> u >> v;
+
+        g[u].emplace_back(v);
+        g[v].emplace_back(u);
+    }
+
+    dfs1(1, 0);
+    dfs2(1, 1);
+
+    for (int i = 1; i <= m; i++) {
+        cin >> x[i] >> y[i] >> z[i];
+
+        max = std::max(max, z[i]);
+    }
+
+    std::vector<SegmentTree> tr(n + 1, SegmentTree(1, max));
+
+    for (int i = 1; i <= m; i++) {
+        int p = lca(x[i], y[i]);
+
+        tr[x[i]].modify(z[i], 1);
+        tr[y[i]].modify(z[i], 1);
+        tr[p].modify(z[i], -1);
+        if (fa[p]) tr[fa[p]].modify(z[i], -1);
+    }
+
+    std::function<void(int)> dfs = [&](int u) {
+        for (int v : g[u]) {
+            if (v == fa[u]) continue;
+
+            if (dep[v] > dep[u]) {
+                dfs(v);
+
+                tr[u].merge(tr[v]);
+            }
+        }
+
+        auto res = tr[u].query(1, max);
+
+        if (res.second) ans[u] = res.second;
+    };
+
+    dfs(1);
+
+    for (int i = 1; i <= n; i++) {
+        cout << ans[i] << endl;
+    }
+
+    return 0;
+}