#812274 (C++17) No.2115 Making Forest Easy

• 問題: No.2115 Making Forest Easy
• ユーザー: 👑 Nachia
• 提出日時: 2022-10-28 23:19:24
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 725 ms / 2,000 ms
• コード長: 7,483 bytes
• コンパイル時間: 1,247 ms
• コンパイル使用メモリ: 97,456 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-06 02:34:20
• 合計ジャッジ時間: 18,307 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	434 ms; 5,376 KB
testcase_03	AC	347 ms; 5,376 KB
testcase_04	AC	515 ms; 5,376 KB
testcase_05	AC	415 ms; 5,376 KB
testcase_06	AC	440 ms; 5,376 KB
testcase_07	AC	709 ms; 5,376 KB
testcase_08	AC	444 ms; 5,376 KB
testcase_09	AC	346 ms; 5,376 KB
testcase_10	AC	433 ms; 5,376 KB
testcase_11	AC	350 ms; 5,376 KB
testcase_12	AC	344 ms; 5,376 KB
testcase_13	AC	276 ms; 5,376 KB
testcase_14	AC	346 ms; 5,376 KB
testcase_15	AC	688 ms; 5,376 KB
testcase_16	AC	357 ms; 5,376 KB
testcase_17	AC	5 ms; 5,376 KB
testcase_18	AC	14 ms; 5,376 KB
testcase_19	AC	135 ms; 5,376 KB
testcase_20	AC	475 ms; 5,376 KB
testcase_21	AC	5 ms; 5,376 KB
testcase_22	AC	17 ms; 5,376 KB
testcase_23	AC	258 ms; 5,376 KB
testcase_24	AC	345 ms; 5,376 KB
testcase_25	AC	99 ms; 5,376 KB
testcase_26	AC	341 ms; 5,376 KB
testcase_27	AC	97 ms; 5,376 KB
testcase_28	AC	699 ms; 5,376 KB
testcase_29	AC	7 ms; 5,376 KB
testcase_30	AC	725 ms; 5,376 KB
testcase_31	AC	525 ms; 5,376 KB
testcase_32	AC	435 ms; 5,376 KB
testcase_33	AC	445 ms; 5,376 KB
testcase_34	AC	7 ms; 5,376 KB
testcase_35	AC	24 ms; 5,376 KB
testcase_36	AC	431 ms; 5,376 KB
testcase_37	AC	89 ms; 5,376 KB
testcase_38	AC	28 ms; 5,376 KB
testcase_39	AC	76 ms; 5,376 KB
testcase_40	AC	703 ms; 5,376 KB
testcase_41	AC	343 ms; 5,376 KB
testcase_42	AC	342 ms; 5,376 KB
testcase_43	AC	127 ms; 5,376 KB
testcase_44	AC	27 ms; 5,376 KB
testcase_45	AC	379 ms; 5,376 KB
testcase_46	AC	350 ms; 5,376 KB
testcase_47	AC	100 ms; 5,376 KB
testcase_48	AC	523 ms; 5,376 KB
testcase_49	AC	497 ms; 5,376 KB
testcase_50	AC	128 ms; 5,376 KB
testcase_51	AC	55 ms; 5,376 KB

ソースコード

#line 1 "Main.cpp"
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <atcoder/modint>
#line 4 "nachia\\graph\\graph.hpp"
#include <cassert>
#line 5 "nachia\\array\\csr-array.hpp"

namespace nachia{

template<class Elem>
class CsrArray{
public:
    struct ListRange{
        using iterator = typename std::vector<Elem>::iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        Elem& operator[](int i) const { return begi[i]; }
    };
    struct ConstListRange{
        using iterator = typename std::vector<Elem>::const_iterator;
        iterator begi, endi;
        iterator begin() const { return begi; }
        iterator end() const { return endi; }
        int size() const { return (int)std::distance(begi, endi); }
        const Elem& operator[](int i) const { return begi[i]; }
    };
private:
    int m_n;
    std::vector<Elem> m_list;
    std::vector<int> m_pos;
public:
    CsrArray() : m_n(0), m_list(), m_pos() {}
    static CsrArray Construct(int n, std::vector<std::pair<int, Elem>> items){
        CsrArray res;
        res.m_n = n;
        std::vector<int> buf(n+1, 0);
        for(auto& [u,v] : items){ ++buf[u]; }
        for(int i=1; i<=n; i++) buf[i] += buf[i-1];
        res.m_list.resize(buf[n]);
        for(int i=(int)items.size()-1; i>=0; i--){
            res.m_list[--buf[items[i].first]] = std::move(items[i].second);
        }
        res.m_pos = std::move(buf);
        return res;
    }
    static CsrArray FromRaw(std::vector<Elem> list, std::vector<int> pos){
        CsrArray res;
        res.m_n = pos.size() - 1;
        res.m_list = std::move(list);
        res.m_pos = std::move(pos);
        return res;
    }
    ListRange operator[](int u) { return ListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    ConstListRange operator[](int u) const { return ConstListRange{ m_list.begin() + m_pos[u], m_list.begin() + m_pos[u+1] }; }
    int size() const { return m_n; }
    int fullSize() const { return (int)m_list.size(); }
};

} // namespace nachia
#line 6 "nachia\\graph\\graph.hpp"

namespace nachia{


struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
    };
    using Base = std::vector<std::pair<int, int>>;
    Graph(int n = 0, bool undirected = false) : m_n(n), m_e(), m_isUndir(undirected) {}
    Graph(int n, const std::vector<std::pair<int, int>>& edges, bool undirected = false) : m_n(n), m_isUndir(undirected){
        m_e.resize(edges.size());
        for(std::size_t i=0; i<edges.size(); i++) m_e[i] = { edges[i].first, edges[i].second };
    }
    Graph(int n, const std::vector<Edge>& edges, bool undirected = false) : m_n(n), m_e(edges), m_isUndir(undirected) {}
    Graph(int n, std::vector<Edge>&& edges, bool undirected = false) : m_n(n), m_e(edges), m_isUndir(undirected) {}
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addEdge(int from, int to){ m_e.push_back({ from, to }); return numEdges() - 1; }
    Edge& operator[](int ei) noexcept { return m_e[ei]; }
    const Edge& operator[](int ei) const noexcept { return m_e[ei]; }
    Edge& at(int ei) { return m_e.at(ei); }
    const Edge& at(int ei) const { return m_e.at(ei); }
    auto begin(){ return m_e.begin(); }
    auto end(){ return m_e.end(); }
    auto begin() const { return m_e.begin(); }
    auto end() const { return m_e.end(); }
    bool isUndirected() const noexcept { return m_isUndir; }
    void reverseEdges() noexcept { for(auto& e : m_e) e.reverse(); }
    void contract(int newV, const std::vector<int>& mapping){
        assert(numVertices() == int(mapping.size()));
        for(int i=0; i<numVertices(); i++) assert(0 <= mapping[i] && mapping[i] < newV);
        for(auto& e : m_e){ e.from = mapping[e.from]; e.to = mapping[e.to]; }
    }
    std::vector<Graph> induce(int num, const std::vector<int>& mapping) const {
        int n = numVertices();
        assert(n == int(mapping.size()));
        for(int i=0; i<n; i++) assert(-1 <= mapping[i] && mapping[i] < num);
        std::vector<int> indexV(n), newV(num);
        for(int i=0; i<n; i++) if(mapping[i] >= 0) indexV[i] = ++newV[mapping[i]];
        std::vector<Graph> res; res.reserve(num);
        for(int i=0; i<num; i++) res.emplace_back(newV[i], isUndirected());
        for(auto e : m_e) if(mapping[e.from] == mapping[e.to] && mapping[e.to] >= 0) res[mapping[e.to]].addEdge(indexV[e.from], indexV[e.to]);
        return res;
    }
    CsrArray<int> getEdgeIndexArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(int i=0; i<numEdges(); i++){
            auto e = operator[](i);
            src.emplace_back(e.from, i);
            if(undirected) src.emplace_back(e.to, i);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getEdgeIndexArray() const { return getEdgeIndexArray(isUndirected()); }
    CsrArray<int> getAdjacencyArray(bool undirected) const {
        std::vector<std::pair<int, int>> src;
        src.reserve(numEdges() * (undirected ? 2 : 1));
        for(auto e : m_e){
            src.emplace_back(e.from, e.to);
            if(undirected) src.emplace_back(e.to, e.from);
        }
        return CsrArray<int>::Construct(numVertices(), src);
    }
    CsrArray<int> getAdjacencyArray() const { return getAdjacencyArray(isUndirected()); }
private:
    int m_n;
    std::vector<Edge> m_e;
    bool m_isUndir;
};

} // namespace nachia
#line 8 "Main.cpp"

using namespace std;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
#define rep(i,n) for(int i=0; i<(int)(n); i++)

const i64 INF = 1001001001001001001;
using Modint = atcoder::static_modint<998244353>;

int main(){
    int N; cin >> N;
    vector<Modint> A(N);
    rep(i,N){ int a; cin >> a; A[i] = Modint::raw(a); }
    nachia::Graph G(N);
    rep(i,N-1){ int u,v; cin >> u >> v; G.addEdge(u-1, v-1); }
    auto adj = G.getAdjacencyArray(true);
    vector<int> closed(N, 0);
    vector<int> ord(N); rep(i,N) ord[i] = i;
    sort(ord.begin(), ord.end(), [&](int l, int r){ return A[l].val() > A[r].val(); });
    Modint INV2 = Modint(2).inv();
    vector<int> bfs(N);
    vector<int> par(N);
    vector<Modint> dpE(N);
    vector<Modint> dpX(N);
    Modint anssum = 0;
    Modint off = Modint(2).pow(N-1);
    for(int v : ord){
        int p2=0;
        fill(par.begin(), par.end(), -1);
        fill(dpE.begin(), dpE.end(), Modint(1));
        fill(dpX.begin(), dpX.end(), Modint(1));
        bfs[p2++] = v;
        for(int w : bfs) for(int x : adj[w]) if(par[w] != x){ bfs[p2++] = x; par[x] = w; }
        for(int i=N-1; i>=1; i--){
            int w = bfs[i], p = par[w];
            if(closed[w]){ dpX[w] = 0; dpE[w] = 0; }
            Modint xw = 1 - (1 - dpX[w]) * INV2;
            dpE[p] = dpE[w] * INV2 * dpX[p] + dpE[p] * xw;
            dpX[p] *= xw;
        }
        Modint ans = dpE[v] * off;
        anssum += ans * A[v];
        closed[v] = 1;
    }
    cout << anssum.val() << endl;
    return 0;
}


struct ios_do_not_sync{
    ios_do_not_sync(){
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
    }
} ios_do_not_sync_instance;