Codeforces: 1981D

Turtle and Multiplication

Codeforces/1981D.cpp

@@ -0,0 +1,83 @@
+/**
+ * @file 1981D.cpp
+ * @author Macesuted (i@macesuted.moe)
+ * @date 2024-07-01
+ *
+ * @copyright Copyright (c) 2024
+ *
+ */
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#ifndef LOCAL
+#define endl '\n'
+#endif
+
+bool mem1;
+
+#define maxn 1000005
+#define maxv 300005
+
+bool notPrime[maxv];
+vector<int> prime, path;
+vector<unordered_set<int>> graph;
+
+void construct(int n) {
+    graph.clear(), graph.resize(n + 1);
+    for (int i = 1; i <= n; i++)
+        for (int j = 1; j <= i; j++) graph[i].insert(j), graph[j].insert(i);
+    if (n & 1) return;
+    for (int i = 2; i < n; i += 2) graph[i].erase(i - 1), graph[i - 1].erase(i);
+}
+void dfs(int p) {
+    while (!graph[p].empty()) {
+        int q = *graph[p].begin();
+        graph[p].erase(q), graph[q].erase(p);
+        dfs(q);
+    }
+    path.push_back(p);
+    return;
+}
+
+void solve(void) {
+    int n;
+    cin >> n;
+    int l = 0, r = prime.size();
+    while (l + 1 < r) {
+        int mid = (l + r) >> 1;
+        int64_t val = (int64_t)mid * (mid + 1) / 2 - ((mid & 1) ? 0 : mid / 2 - 1);
+        (val < n - 1 ? l : r) = mid;
+    }
+    construct(r);
+    path.clear(), dfs(r);
+    for (int i = 0; i < n; i++) cout << prime[path[i] - 1] << ' ';
+    cout << endl;
+    return;
+}
+
+bool mem2;
+
+int main() {
+    ios::sync_with_stdio(false), cin.tie(nullptr);
+#ifdef LOCAL
+    cerr << "Memory Cost: " << abs(&mem1 - &mem2) / 1024. / 1024. << "MB" << endl;
+#endif
+
+    for (int i = 2; i < maxv; i++) {
+        if (!notPrime[i]) prime.push_back(i);
+        for (auto j = prime.begin(); j != prime.end() && i * *j < maxv; j++) {
+            notPrime[i * *j] = true;
+            if (i % *j == 0) break;
+        }
+    }
+
+    int _ = 1;
+    cin >> _;
+    while (_--) solve();
+
+#ifdef LOCAL
+    cerr << "Time Cost: " << clock() * 1000. / CLOCKS_PER_SEC << "MS" << endl;
+#endif
+    return 0;
+}