QOJ: 9570

Binary Tree

QOJ/9570.cpp

@@ -0,0 +1,104 @@
+/**
+ * @file 9570.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-11-06
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+bool mem1;
+
+typedef pair<int, int> pii;
+
+vector<bool> ban;
+vector<int> siz;
+vector<vector<int>> graph;
+
+int lim;
+int query(int x, int y) {
+    assert(lim--);
+    cout << "? " << x << ' ' << y << endl;
+    int ret;
+    cin >> ret;
+    return ret;
+}
+
+void getSiz(int p, int fa = -1) {
+    siz[p] = 1;
+    for (auto i : graph[p])
+        if (i != fa && !ban[i]) getSiz(i, p), siz[p] += siz[i];
+    return;
+}
+pii fndRoot(int p, int n, int fa = -1) {
+    pii cur = {n - siz[p], p}, ans = {n, 0};
+    for (auto i : graph[p])
+        if (i != fa && !ban[i]) cur.first = max(cur.first, siz[i]), ans = min(ans, fndRoot(i, n, p));
+    return min(ans, cur);
+}
+
+int solve(int p) {
+    getSiz(p), p = fndRoot(p, siz[p]).second;
+
+    vector<int> neigh;
+    for (auto i : graph[p])
+        if (!ban[i]) neigh.push_back(i);
+
+    if (neigh.empty()) return p;
+    if (neigh.size() == 1) return query(p, neigh[0]) == 0 ? p : neigh[0];
+    if (neigh.size() == 2) {
+        int ret = query(neigh[0], neigh[1]);
+        if (ret == 0) return ban[p] = true, solve(neigh[0]);
+        if (ret == 2) return ban[p] = true, solve(neigh[1]);
+        return p;
+    }
+    getSiz(p);
+
+    sort(neigh.begin(), neigh.end(), [&](int a, int b) { return siz[a] > siz[b]; });
+    int ret = query(neigh[0], neigh[1]);
+    if (ret == 0) return ban[p] = true, solve(neigh[0]);
+    if (ret == 2) return ban[p] = true, solve(neigh[1]);
+    return ban[neigh[0]] = ban[neigh[1]] = true, solve(p);
+}
+
+void solve(void) {
+    int n;
+    cin >> n;
+
+    lim = 1;
+    while (1 << (lim + 1) <= n) lim++;
+
+    ban.clear(), ban.resize(n + 1);
+    siz.clear(), siz.resize(n + 1);
+    graph.clear(), graph.resize(n + 1);
+
+    for (int i = 1, cl, cr; i <= n; i++) {
+        cin >> cl >> cr;
+        if (cl) graph[i].push_back(cl), graph[cl].push_back(i);
+        if (cr) graph[i].push_back(cr), graph[cr].push_back(i);
+    }
+    int ans = solve(1);
+    cout << "! " << ans << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    int _ = 1;
+    cin >> _;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}