Petrozavodsk Winter 2022. Day 5. Yandex Cup

Author: Macesuted

QOJ/2596.cpp

@@ -0,0 +1,83 @@
+/**
+ * @file 2596.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2025-10-29
+ *
+ * @copyright Copyright (c) 2025
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+
+#define maxn 1000005
+
+using pii = pair<int, int>;
+
+vector<int> graph[maxn];
+int f[maxn][3];
+
+void dfs(int p, int pre = -1) {
+    vector<int> rec[2];
+    int sum = 0;
+
+    for (auto q : graph[p]) {
+        if (q == pre) continue;
+        dfs(q, p);
+        sum += f[q][2];
+        if (f[q][0] != INT_MAX) rec[0].push_back(f[q][0] - f[q][2]);
+        if (f[q][1] != INT_MAX) rec[1].push_back(f[q][1] - f[q][2]);
+    }
+    sort(rec[0].begin(), rec[0].end()), sort(rec[1].begin(), rec[1].end());
+
+    f[p][0] = f[p][1] = f[p][2] = INT_MAX;
+    if (rec[1].size() >= 0) {
+        f[p][0] = sum;
+        for (size_t i = 0; i < rec[1].size() && rec[1][i] < 0; i++) f[p][0] += rec[1][i];
+    }
+    if (rec[0].size() >= 1) {
+        f[p][1] = sum + rec[0][0];
+        for (size_t i = 1; i < rec[0].size() && rec[0][i] < 0; i++) f[p][1] += rec[0][i];
+    }
+
+    if (rec[0].size() >= 2) {
+        int val = 1 + sum + rec[0][0] + rec[0][1];
+        for (size_t i = 2; i < rec[0].size() && rec[0][i] < 0; i++) val += rec[0][i];
+        f[p][2] = min(f[p][2], val);
+    }
+    if (rec[1].size() >= 0) {
+        int val = 1 + sum;
+        for (size_t i = 0; i < rec[1].size() && rec[1][i] < 0; i++) val += rec[1][i];
+        f[p][2] = min(f[p][2], val);
+    }
+
+    return;
+}
+
+void solve(void) {
+    int n;
+    cin >> n;
+    for (int i = 1, x, y; i < n; i++) cin >> x >> y, graph[x].push_back(y), graph[y].push_back(x);
+
+    if (n <= 2) return cout << n - 1 << endl, void();
+
+    int root = 1;
+    while (graph[root].size() == 1) root++;
+
+    dfs(root);
+
+    cout << f[root][2] - 1 << endl;
+
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}

QOJ/2598.cpp

@@ -0,0 +1,48 @@
+/**
+ * @file 2598.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2025-10-29
+ *
+ * @copyright Copyright (c) 2025
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+
+void solve(void) {
+    int n;
+    cin >> n;
+
+    if (n == 1) return cout << "NO" << endl, void();
+
+    vector<vector<int>> a(1 << n, vector<int>(1 << n));
+
+    for (int i = 0, cnt = 0; i < (1 << n); i++)
+        for (int j = 0; j < (1 << n); j++) a[i][j] = ++cnt;
+
+    for (int i = 0; i < (1 << n); i += 2)
+        for (int j = 0; j < (1 << (n - 1)); j++) swap(a[i][j], a[i][j | (1 << (n - 1))]);
+
+    for (int i = 0; i < (1 << (n - 1)); i++)
+        for (int j = 0; j < (1 << n); j += 2) swap(a[i][j], a[i | (1 << (n - 1))][j]);
+
+    cout << "YES" << endl;
+    for (int i = 0; i < (1 << n); i++) {
+        for (int j = 0; j < (1 << n); j++) cout << a[i][j] << ' ';
+        cout << endl;
+    }
+
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}

QOJ/2602.cpp

@@ -0,0 +1,111 @@
+/**
+ * @file 2602.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2025-10-29
+ *
+ * @copyright Copyright (c) 2025
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define endl '\n'
+
+#define maxn 300005
+
+using pii = pair<int, int>;
+
+class SegmentTree {
+   private:
+    int sum[maxn << 2], val[maxn << 2];
+    int n;
+
+    void pushUp(int p) {
+        sum[p] = sum[p << 1] + sum[p << 1 | 1];
+        val[p] = min(val[p << 1] + sum[p << 1 | 1], val[p << 1 | 1]);
+        return;
+    }
+    void build(int p, int l, int r) {
+        if (l == r) return sum[p] = +1, val[p] = 0, void();
+        int mid = (l + r) >> 1;
+        build(p << 1, l, mid), build(p << 1 | 1, mid + 1, r);
+        return pushUp(p);
+    }
+    void update(int p, int l, int r, int qp, int v) {
+        if (l == r) return val[p] = min(0, sum[p] += v), void();
+        int mid = (l + r) >> 1;
+        qp <= mid ? update(p << 1, l, mid, qp, v) : update(p << 1 | 1, mid + 1, r, qp, v);
+        return pushUp(p);
+    }
+
+   public:
+    void resize(int _n) { return n = _n, void(); }
+    void build(void) { return build(1, 1, n); }
+    void update(int p, int v) { return update(1, 1, n, p, v); }
+    int query(void) { return val[1]; }
+} SGT;
+
+vector<pii> ins[maxn], del[maxn];
+vector<int> pos[maxn];
+int vmax[maxn][2];
+bool mark[maxn];
+
+void solve(void) {
+    int n, m;
+    cin >> n >> m;
+
+    for (int i = 1, c, l, r; i <= m; i++) cin >> c >> l >> r, ins[l].emplace_back(c, i), del[r].emplace_back(c, i);
+
+    multiset<pii> S;
+    for (int i = 1; i <= n; i++) {
+        for (auto v : ins[i]) S.insert(v);
+
+        vmax[i][0] = vmax[i][1] = 1;
+        if (S.size() >= 1) vmax[i][0] = S.rbegin()->first, pos[S.rbegin()->second].push_back(i);
+        if (S.size() >= 2) vmax[i][1] = next(S.rbegin())->first;
+
+        for (auto v : del[i]) S.erase(S.find(v));
+    }
+
+    SGT.resize(n), SGT.build();
+
+    for (int i = 1; i <= n; i++) SGT.update(vmax[i][0], -1);
+
+    auto check = [&](void) -> void {
+        if (SGT.query() != 0) return;
+
+        set<int> S;
+        for (int i = 1; i <= n; i++) S.insert(i);
+
+        cout << "YES" << endl;
+        for (int i = 1; i <= n; i++) {
+            auto p = S.lower_bound(vmax[i][mark[i]]);
+            cout << *p << ' ', S.erase(p);
+        }
+        cout << endl;
+
+        exit(0);
+    };
+
+    check();
+
+    for (int i = 1; i <= m; i++) {
+        for (auto p : pos[i]) mark[p] = true, SGT.update(vmax[p][0], +1), SGT.update(vmax[p][1], -1);
+        check();
+        for (auto p : pos[i]) mark[p] = false, SGT.update(vmax[p][0], -1), SGT.update(vmax[p][1], +1);
+    }
+
+    cout << "NO" << endl;
+
+    return;
+}
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+
+    int _ = 1;
+    while (_--) solve();
+
+    return 0;
+}