結果

問題 No.2504 NOT Path Painting
ユーザー suisen
提出日時 2023-02-21 11:50:51
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
RE  
実行時間 -
コード長 2,844 bytes
コンパイル時間 1,523 ms
コンパイル使用メモリ 116,888 KB
最終ジャッジ日時 2025-02-10 19:40:45
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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ファイルパターン 結果
other RE * 8 MLE * 13
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ソースコード

diff #
プレゼンテーションモードにする

#include <deque>
#include <iostream>
#include <tuple>
#include <vector>
#include <atcoder/modint>
using mint = atcoder::modint998244353;
int edge_num(int n) {
    return (n * (n + 1)) >> 1;
}
auto find_path_on_tree(const std::vector<std::vector<int>> &g, int u, int v) {
    std::vector<int> res;
    auto dfs = [&](auto dfs, int cur, int par) -> bool {
        res.push_back(cur);
        if (cur == v) return true;
        for (int nxt : g[cur]) if (nxt != par and dfs(dfs, nxt, cur)) return true;
        res.pop_back();
        return false;
    };
    dfs(dfs, u, -1);
    return res;
}
#include <algorithm>
#include <map>
int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    int n;
    std::cin >> n;
    std::vector<std::vector<int>> g(n);
    for (int i = 0; i < n - 1; ++i) {
        int u, v;
        std::cin >> u >> v;
        --u, --v;
        g[u].push_back(v);
        g[v].push_back(u);
    }
    const int m = edge_num(n);
    const mint inv_m = mint(m).inv();
    std::map<std::pair<int, int>, std::vector<int>> paths;
    std::map<std::pair<int, int>, std::vector<int>> compl_paths;
    std::map<std::vector<int>, std::pair<int, int>> rev_paths;
    for (int x = 0; x < n; ++x) for (int y = 0; y <= x; ++y) {
        std::vector<int> path = find_path_on_tree(g, x, y);
        std::sort(path.begin(), path.end());
        std::vector<int> compl_path;
        for (int i = 0, j = 0; i < n; ++i) {
            if (j < int(path.size()) and path[j] == i) {
                ++j;
                continue;
            }
            compl_path.push_back(i);
        }
        paths[std::make_pair(x, y)] = path;
        rev_paths[path] = std::make_pair(x, y);
        compl_paths[std::make_pair(x, y)] = compl_path;
    }
    std::map<std::pair<int, int>, mint> dp;
    auto rec = [&](auto rec, int x, int y) -> mint {
        if (auto it = dp.find(std::make_pair(x, y)); it != dp.end()) {
            return it->second;
        }
        mint a = 1, b = 1;
        std::vector<int> path = paths[std::make_pair(x, y)];
        for (const auto &[_, compl_path] : compl_paths) {
            std::vector<int> next_path;
            std::set_difference(path.begin(), path.end(), compl_path.begin(), compl_path.end(), std::back_inserter(next_path));
            if (next_path.size()) {
                if (next_path.size() == path.size()) {
                    a -= inv_m;
                } else {
                    auto [nx, ny] = rev_paths[next_path];
                    b += inv_m * rec(rec, nx, ny);
                }
            }
        }
        return dp[std::make_pair(x, y)] = b * a.inv();
    };
    mint ans = 1;
    for (int x = 0; x < n; ++x) for (int y = 0; y <= x; ++y) {
        ans += rec(rec, x, y) * inv_m;
    }
    std::cout << ans.val() << std::endl;
    return 0;
}
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