#1160337 (C++23) No.3506 All Distance is Square Number

• 問題: No.3506 All Distance is Square Number
• ユーザー: はじっこゆーれー
• 提出日時: 2026-04-19 05:41:13
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: TLE
• 実行時間: -
• コード長: 3,950 bytes
• コンパイル時間: 2,027 ms
• コンパイル使用メモリ: 202,928 KB
• 実行使用メモリ: 9,856 KB
• 最終ジャッジ日時: 2026-04-19 05:41:47
• 合計ジャッジ時間: 7,663 ms
• ジャッジサーバーID （参考情報）: judge2_0 / judge1_1

ファイルパターン	結果
other	AC * 7 TLE * 1 -- * 21

ソースコード

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <random>
using namespace std;
const int MAX_SUM = 50000;
bool is_sq_arr[MAX_SUM + 5];
inline bool is_sq(int n) {
    if (n < 0 || n > MAX_SUM) return false;
    return is_sq_arr[n];
}
int N;
int W[105];
int Dist[105][105];
vector<int> get_tree_path(int a, int b) {
    vector<int> path;
    if (a < b) {
        for (int k = a; k < b; ++k) path.push_back(k);
    } else {
        for (int k = a - 1; k >= b; --k) path.push_back(k);
    }
    return path;
}
inline int get_shortcut_id(int x) {
    if (x == 2) return 1;
    return N + x - 3;
}
struct Pair {
    int u, v;
};
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    for (int i = 0; i * i <= MAX_SUM; ++i) {
        is_sq_arr[i * i] = true;
    }
    if (!(cin >> N)) return 0;
    if (N == 2) {
        cout << 1 << "\n";
        cout << 1 << " " << 2 << " " << 1 << "\n";
        cout << 1 << " " << 1 << "\n";
        return 0;
    }
    for (int i = 1; i <= N; ++i) {
        for (int j = 1; j <= N; ++j) {
            Dist[i][j] = abs((i - 1) * (i - 1) - (j - 1) * (j - 1));
        }
    }
    vector<int> evens;
    for (int i = 2; i <= 200; i += 2) {
        evens.push_back(i);
    }
    vector<Pair> pairs_to_check;
    for (int d = 1; d <= N - 1; ++d) {
        for (int u = 2; u + d <= N; ++u) {
            pairs_to_check.push_back({u, u + d});
        }
    }
    mt19937 rng(42);
    while (true) {
        shuffle(evens.begin(), evens.end(), rng);
        for (int i = 3; i <= N; ++i) {
            W[i] = evens[i - 3];
        }
        W[2] = 1;
        bool all_ok = true;
        for (const auto& p : pairs_to_check) {
            int u = p.u;
            int v = p.v;
            if (is_sq_arr[Dist[u][v]]) continue;
            bool found = false;
            for (int x = 2; x < v; ++x) {
                int left_part = Dist[u][x] + W[x];
                int start_y = max(u, x) + 1;
                for (int y = start_y; y <= N; ++y) {
                    if (is_sq_arr[left_part + W[y] + Dist[y][v]]) {
                        found = true;
                        break;
                    }
                }
                if (found) break;
            }
            if (!found) {
                all_ok = false;
                break;
            }
        }
        if (all_ok) break;
    }
    int M = 2 * N - 3;
    cout << M << "\n";
    for (int i = 1; i < N; ++i) {
        cout << i << " " << i + 1 << " " << 2 * i - 1 << "\n";
    }
    for (int i = 3; i <= N; ++i) {
        cout << 1 << " " << i << " " << W[i] << "\n";
    }
    for (int u = 1; u <= N; ++u) {
        for (int v = u + 1; v <= N; ++v) {
            if (u == 1 || is_sq_arr[Dist[u][v]]) {
                vector<int> path = get_tree_path(u, v);
                cout << path.size();
                for (int e : path) cout << " " << e;
                cout << "\n";
                continue;
            }
            bool printed = false;
            for (int x = 2; x < v && !printed; ++x) {
                int start_y = max(u, x) + 1;
                for (int y = start_y; y <= N && !printed; ++y) {
                    if (is_sq_arr[Dist[u][x] + W[x] + W[y] + Dist[y][v]]) {
                        vector<int> path;
                        vector<int> p1 = get_tree_path(u, x);
                        path.insert(path.end(), p1.begin(), p1.end());
                        path.push_back(get_shortcut_id(x));
                        path.push_back(get_shortcut_id(y));
                        vector<int> p2 = get_tree_path(y, v);
                        path.insert(path.end(), p2.begin(), p2.end());
                        cout << path.size();
                        for (int e : path) cout << " " << e;
                        cout << "\n";
                        printed = true;
                    }
                }
            }
        }
    }
    return 0;
}