From fcc9ddbee923a6c37682714aacf5798afab36947 Mon Sep 17 00:00:00 2001
From: Baoshuo <i@baoshuo.ren>
Date: Sat, 4 Feb 2023 17:06:45 +0800
Subject: [PATCH] =?UTF-8?q?P6072=20=E3=80=8EMdOI=20R1=E3=80=8FPath?=
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https://www.luogu.com.cn/record/101440281
---
 Luogu/P6072/P6072.cpp | 177 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 177 insertions(+)
 create mode 100644 Luogu/P6072/P6072.cpp

diff --git a/Luogu/P6072/P6072.cpp b/Luogu/P6072/P6072.cpp
new file mode 100644
index 00000000..5afb67ab
--- /dev/null
+++ b/Luogu/P6072/P6072.cpp
@@ -0,0 +1,177 @@
+#include <iostream>
+#include <algorithm>
+#include <cmath>
+#include <tuple>
+#include <utility>
+#include <vector>
+
+using std::cin;
+using std::cout;
+const char endl = '\n';
+
+const int N = 3e4 + 5;
+
+int n, t, c, tot, id[N], siz[N], dis[N << 1], pos[N << 1], ans[N << 1];
+std::vector<std::pair<int, int>> g[N];
+std::tuple<int, int, int> qs[N << 1];
+int tr[N * 30][2], cnt[N * 30];
+
+void insert(int x) {
+    static int tot = 1;
+    int p = 1;
+
+    for (int i = 30; i >= 0; i--) {
+        bool ch = (x >> i) & 1;
+
+        if (!tr[p][ch]) {
+            tr[p][ch] = ++tot;
+        }
+
+        p = tr[p][ch];
+        cnt[p]++;
+    }
+}
+
+int query(int x) {
+    int p = 1;
+    int res = 0;
+
+    for (int i = 30; i >= 0; i--) {
+        int ch = (x >> i) & 1;
+
+        if (cnt[tr[p][ch ^ 1]]) {
+            res |= 1 << i;
+            p = tr[p][ch ^ 1];
+        } else {
+            p = tr[p][ch];
+        }
+    }
+
+    return res;
+}
+
+void remove(int x) {
+    int p = 1;
+
+    for (int i = 30; i >= 0; i--) {
+        int ch = (x >> i) & 1;
+
+        p = tr[p][ch];
+        cnt[p]--;
+    }
+}
+
+void dfs(int u, int f, int w) {
+    static int cnt = 0;
+
+    id[u] = ++cnt;
+    siz[u] = 1;
+    dis[id[u]] = dis[id[f]] ^ w;
+
+    std::for_each(g[u].rbegin(), g[u].rend(), [&](auto e) {
+        int v = e.first,
+            w = e.second;
+
+        if (v == f) return;
+
+        dfs(v, u, w);
+
+        siz[u] += siz[v];
+    });
+}
+
+int calc(int l, int r) {
+    int res = 0;
+
+    for (int i = l; i <= r; i++) {
+        res = std::max(res, query(dis[i]));
+        insert(dis[i]);
+    }
+
+    for (int i = l; i <= r; i++) {
+        remove(dis[i]);
+    }
+
+    return res;
+}
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    cin >> n;
+
+    for (int i = 1, x, y, w; i < n; i++) {
+        cin >> x >> y >> w;
+
+        g[x].emplace_back(y, w);
+        g[y].emplace_back(x, w);
+    }
+
+    dfs(1, 0, 0);
+
+    for (int i = 2; i <= n; i++) {
+        qs[++tot] = {id[i], id[i] + siz[i] - 1, i};
+        qs[++tot] = {id[i] + siz[i], id[i] + n - 1, i};
+    }
+
+    std::copy_n(dis + 1, n, dis + 1 + n);
+
+    n <<= 1;
+    t = std::sqrt(n);
+
+    for (int i = 1; i <= n; i++) {
+        pos[i] = (i - 1) / t + 1;
+    }
+
+    std::sort(qs + 1, qs + tot + 1, [&](auto lhs, auto rhs) -> bool {
+        int p = pos[std::get<0>(lhs)],
+            q = pos[std::get<0>(rhs)];
+        int x = std::get<1>(lhs),
+            y = std::get<1>(rhs);
+
+        return p == q ? x < y : p < q;
+    });
+
+    for (int i = 1, p = 1; i <= pos[n]; i++) {
+        int r = std::min(i * t, n),
+            x = r + 1,
+            y = r,
+            res = 0;
+
+        for (; pos[std::get<0>(qs[p])] == i; p++) {
+            int ql, qr, id;
+
+            std::tie(ql, qr, id) = qs[p];
+
+            if (pos[qr] == i) {
+                ans[id] += calc(ql, qr);
+
+                continue;
+            }
+
+            while (y < qr) {
+                res = std::max(res, query(dis[++y]));
+                insert(dis[y]);
+            }
+
+            int tmp = res;
+
+            while (x > ql) {
+                res = std::max(res, query(dis[--x]));
+                insert(dis[x]);
+            }
+
+            while (x <= r) remove(dis[x++]);
+
+            ans[id] += res;
+            res = tmp;
+        }
+
+        while (y > r) remove(dis[y--]);
+    }
+
+    cout << *std::max_element(ans + 1, ans + 1 + n) << endl;
+
+    return 0;
+}