#876114 (C++17) No.2342 Triple Tree Query (Hard)

提出ソース
結果

問題	No.2342 Triple Tree Query (Hard)
ユーザー	👑 Nachia
提出日時	2023-05-30 21:07:25
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	541 ms / 10,000 ms
コード長	18,906 bytes
コンパイル時間	2,147 ms
コンパイル使用メモリ	122,284 KB
実行使用メモリ	28,700 KB
最終ジャッジ日時	2024-06-08 20:40:06
合計ジャッジ時間	16,410 ms
ジャッジサーバーID （参考情報）	judge1 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
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	7 ms 5,376 KB
testcase_03	AC	7 ms 5,376 KB
testcase_04	AC	6 ms 5,376 KB
testcase_05	AC	6 ms 5,376 KB
testcase_06	AC	7 ms 5,376 KB
testcase_07	AC	343 ms 28,444 KB
testcase_08	AC	387 ms 28,492 KB
testcase_09	AC	358 ms 28,576 KB
testcase_10	AC	364 ms 28,528 KB
testcase_11	AC	355 ms 28,568 KB
testcase_12	AC	355 ms 28,588 KB
testcase_13	AC	360 ms 28,536 KB
testcase_14	AC	365 ms 28,532 KB
testcase_15	AC	352 ms 28,480 KB
testcase_16	AC	360 ms 28,568 KB
testcase_17	AC	433 ms 28,568 KB
testcase_18	AC	419 ms 28,444 KB
testcase_19	AC	418 ms 28,508 KB
testcase_20	AC	437 ms 28,484 KB
testcase_21	AC	418 ms 28,572 KB
testcase_22	AC	207 ms 28,572 KB
testcase_23	AC	216 ms 28,636 KB
testcase_24	AC	222 ms 28,692 KB
testcase_25	AC	515 ms 28,548 KB
testcase_26	AC	540 ms 28,572 KB
testcase_27	AC	528 ms 28,524 KB
testcase_28	AC	541 ms 28,520 KB
testcase_29	AC	535 ms 28,524 KB
testcase_30	AC	218 ms 28,700 KB
testcase_31	AC	216 ms 28,576 KB
testcase_32	AC	227 ms 28,572 KB
testcase_33	AC	278 ms 28,584 KB
testcase_34	AC	283 ms 28,568 KB
testcase_35	AC	291 ms 28,568 KB
testcase_36	AC	299 ms 28,664 KB
testcase_37	AC	273 ms 28,700 KB
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ソースコード

raw source code
#line 1 "..\\Main.cpp"

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <tuple>
#include <atcoder/modint>
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\csr-array.hpp"
#include <utility>
#line 5 "D:\\Programming\\VSCode\\competitive-cpp\\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 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\graph\\graph.hpp"
#include <cassert>
#line 6 "D:\\Programming\\VSCode\\competitive-cpp\\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, int m = 0) : m_n(n), m_e(m), 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 };
    }
    template<class Cin>
    static Graph Input(Cin& cin, int n, bool undirected, int m, bool offset = 0){
        Graph res(n, undirected, m);
        for(int i=0; i<m; i++){
            int u, v; cin >> u >> v;
            res[i].from = u - offset;
            res[i].to = v - offset;
        }
        return res;
    }
    int numVertices() const noexcept { return m_n; }
    int numEdges() const noexcept { return int(m_e.size()); }
    int addNode() noexcept { return m_n++; }
    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]; }
        m_n = newV;
    }
    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 6 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\tree\\heavy-light-decomposition.hpp"

namespace nachia{

struct HeavyLightDecomposition{
private:

    int N;
    std::vector<int> P;
    std::vector<int> PP;
    std::vector<int> PD;
    std::vector<int> D;
    std::vector<int> I;

    std::vector<int> rangeL;
    std::vector<int> rangeR;

public:

    HeavyLightDecomposition(const CsrArray<int>& E = CsrArray<int>::Construct(1, {}), int root = 0){
        N = E.size();
        P.assign(N, -1);
        I = {root};
        I.reserve(N);
        for(int i=0; i<(int)I.size(); i++){
            int p = I[i];
            for(int e : E[p]) if(P[p] != e){
                I.push_back(e);
                P[e] = p;
            }
        }
        std::vector<int> Z(N, 1);
        std::vector<int> nx(N, -1);
        PP.resize(N);
        for(int i=0; i<N; i++) PP[i] = i;
        for(int i=N-1; i>=1; i--){
            int p = I[i];
            Z[P[p]] += Z[p];
            if(nx[P[p]] == -1) nx[P[p]] = p;
            if(Z[nx[P[p]]] < Z[p]) nx[P[p]] = p;
        }

        for(int p : I) if(nx[p] != -1) PP[nx[p]] = p;

        PD.assign(N,N);
        PD[root] = 0;
        D.assign(N,0);
        for(int p : I) if(p != root){
            PP[p] = PP[PP[p]];
            PD[p] = std::min(PD[PP[p]], PD[P[p]]+1);
            D[p] = D[P[p]]+1;
        }
        
        rangeL.assign(N,0);
        rangeR.assign(N,0);
        
        for(int p : I){
            rangeR[p] = rangeL[p] + Z[p];
            int ir = rangeR[p];
            for(int e : E[p]) if(P[p] != e) if(e != nx[p]){
                rangeL[e] = (ir -= Z[e]);
            }
            if(nx[p] != -1){
                rangeL[nx[p]] = rangeL[p] + 1;
            }
        }

        I.resize(N);
        for(int i=0; i<N; i++) I[rangeL[i]] = i;
    }
    
    HeavyLightDecomposition(const Graph& tree, int root = 0)
        : HeavyLightDecomposition(tree.getAdjacencyArray(true), root) {}

    int numVertices() const { return N; }
    int depth(int p) const { return D[p]; }
    int toSeq(int vertex) const { return rangeL[vertex]; }
    int toVtx(int seqidx) const { return I[seqidx]; }
    int toSeq2In(int vertex) const { return rangeL[vertex] * 2 - D[vertex]; }
    int toSeq2Out(int vertex) const { return rangeR[vertex] * 2 - D[vertex] - 1; }
    int parentOf(int v) const { return P[v]; }
    int heavyRootOf(int v) const { return PP[v]; }
    int heavyChildOf(int v) const {
        if(toSeq(v) == N-1) return -1;
        int cand = toVtx(toSeq(v) + 1);
        if(PP[v] == PP[cand]) return cand;
        return -1;
    }

    int lca(int u, int v) const {
        if(PD[u] < PD[v]) std::swap(u, v);
        while(PD[u] > PD[v]) u = P[PP[u]];
        while(PP[u] != PP[v]){ u = P[PP[u]]; v = P[PP[v]]; }
        return (D[u] > D[v]) ? v : u;
    }

    int dist(int u, int v) const {
        return depth(u) + depth(v) - depth(lca(u,v)) * 2;
    }

    std::vector<std::pair<int,int>> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
        if(PD[c] < PD[r]) return {};
        std::vector<std::pair<int,int>> res(PD[c]-PD[r]+1);
        for(int i=0; i<(int)res.size()-1; i++){
            res[i] = std::make_pair(rangeL[PP[c]], rangeL[c]+1);
            c = P[PP[c]];
        }
        if(PP[r] != PP[c] || D[r] > D[c]) return {};
        res.back() = std::make_pair(rangeL[r]+(include_root?0:1), rangeL[c]+1);
        if(res.back().first == res.back().second) res.pop_back();
        if(!reverse_path) std::reverse(res.begin(),res.end());
        else for(auto& a : res) a = std::make_pair(N - a.second, N - a.first);
        return res;
    }

    std::pair<int,int> subtree(int p){
        return std::make_pair(rangeL[p], rangeR[p]);
    }

    int median(int x, int y, int z) const {
        return lca(x,y) ^ lca(y,z) ^ lca(x,z);
    }

    int la(int from, int to, int d) const {
        if(d < 0) return -1;
        int g = lca(from,to);
        int dist0 = D[from] - D[g] * 2 + D[to];
        if(dist0 < d) return -1;
        int p = from;
        if(D[from] - D[g] < d){ p = to; d = dist0 - d; }
        while(D[p] - D[PP[p]] < d){
            d -= D[p] - D[PP[p]] + 1;
            p = P[PP[p]];
        }
        return I[rangeL[p] - d];
    }
};

} // namespace nachia
#line 1 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\dual-segment-tree.hpp"

#line 3 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\array\\dual-segment-tree.hpp"

namespace nachia{

template<
    class F,
    F composition(F f, F x)
>
struct DualSegtree {

    struct Node { F f; bool propagated; };
    int N;
    int logN;
    std::vector<Node> A;

    void mapf(Node& a, F f) {
        a.propagated = false;
        a.f = composition(f, a.f);
    }
    void spread(int i) {
        if(A[i].propagated || !(i < N)) return;
        mapf(A[i*2], A[i].f);
        mapf(A[i*2+1], A[i].f);
        A[i] = A[0];
    }

    DualSegtree(int n, F id) {
        N=1; logN=0;
        while(N<n){ N *= 2; logN++; }
        A.assign(N*2, { id, true });
    }
    DualSegtree(const std::vector<F>& a) : DualSegtree(a.size()) {
        for(int i=0; i<a.size(); i++){ A[i+N].f = a[i]; A[i+N].propagated = false; }
    }

    void clear(int p) {
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        A[p] = A[0];
    }
    F get(int p){
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        return A[p].f;
    }
    void apply(int l, int r, F f){
        if(!(l < r)) return;
        if(l == 0 && r == N){ mapf(A[1], f); return; }
        l += N; r += N;
        for(int d=logN; d; d--){
            if((l >> d) << d != l) spread(l >> d);
            if((r >> d) << d != r) spread(r >> d);
        }
        while(l < r){
            if(l&1){ mapf(A[l++], f); } l /= 2;
            if(r&1){ mapf(A[--r], f); } r /= 2;
        }
    }
    void apply(int p, F f){
        p += N;
        for(int d=logN; d; d--) spread(p >> d);
        mapf(A[p], f);
    }
};

} // namespace nachia;
#line 10 "..\\Main.cpp"
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

using Modint = atcoder::static_modint<998244353>;

struct Affine {
    Modint c, d;
    static Affine Construct(int c, int d){ return Affine{ Modint::raw(c), Modint::raw(d) }; }
    Modint eval(Modint x) const { return c*x+d; }
};
Affine f1(Affine a, Affine b){
    Affine res;
    res.c = a.c * b.c;
    res.d = a.c * b.d + a.d;
    return res;
}

int naive(){
    int N, Q; cin >> N >> Q;
    auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);
    auto hld = nachia::HeavyLightDecomposition(tree);
    vector<Modint> X(N); rep(i,N){ int x; cin >> x; X[i] = x; }
    rep(i,Q){
        int t; cin >> t;
        if(t == 1){
            int v; cin >> v; v--;
            cout << X[v].val() << endl;
        }
        if(t == 2){
            int v,k,c,d; cin >> v >> k >> c >> d; v--;
            auto f = Affine::Construct(c,d);
            rep(j,N) if(hld.dist(v,j) <= k) X[j] = f.eval(X[j]);
        }
        if(t == 3){
            int v,c,d; cin >> v >> c >> d; v--;
            auto f = Affine::Construct(c,d);
            auto [l,r] = hld.subtree(v);
            for(int j=l; j<r; j++){
                int w = hld.toVtx(j);
                X[w] = f.eval(X[w]);
            }
        }
        if(t == 4){
            int v,w,c,d; cin >> v >> w >> c >> d; v--; w--;
            auto f = Affine::Construct(c,d);
            int di = hld.dist(v, w);
            rep(x,N) if(hld.dist(v,x) + hld.dist(w,x) == di) X[x] = f.eval(X[x]);
        }
    }
    return 0;
}

int main(){
    //return naive();
    int maxK = 10;

    int N, Q; cin >> N >> Q;
    auto tree = nachia::Graph::Input(cin, N, true, N-1, 1);
    auto hld = nachia::HeavyLightDecomposition(tree);
    tree = nachia::Graph(N, false);
    rep(i,N) if(hld.parentOf(i) >= 0) tree.addEdge(hld.parentOf(i), i);
    auto adj = tree.getAdjacencyArray();
    vector<int> h11(N); rep(i,N) h11[i] = (hld.depth(i) <= maxK) ? -1 : hld.toSeq(hld.la(i, 0, maxK+1));
    vector<int> ord(N); rep(i,N) ord[i] = i;
    sort(ord.begin(), ord.end(), [&](int a, int b){
        return make_tuple(h11[a], hld.depth(a), hld.toSeq(a)) < make_tuple(h11[b], hld.depth(b), hld.toSeq(b));
    });
    vector<int> pos(N); rep(i,N) pos[ord[i]] = i;
    vector<int> hdepth(N);
    rep(i,N) hdepth[i] = hld.depth(i) - hld.depth(hld.heavyRootOf(i));
    auto isOnHeavy = [&](int v){ return hdepth[v] > maxK; };

    /*
    cout << "##" << endl;
    rep(i,N) cout << isOnHeavy(i);
    cout << endl;
    */

    vector<vector<pair<int, int>>> seq(N, vector<pair<int,int>>(maxK+1, {N,0}));
    rep(v,N){
        int w = v;
        int p = pos[v];
        for(int k=0; k<=maxK; k++){
            seq[w][k].first = min(seq[w][k].first, p);
            seq[w][k].second = max(seq[w][k].second, p+1);
            w = hld.parentOf(w);
            if(w < 0) break;
        }
    }
    rep(i,N) for(auto& a : seq[i]) if(a.first >= a.second) a = {0,0};

    /*
    cout << "###" << endl;
    cout << "h10 = ";
    rep(i,N) cout << h10[i] << " ";
    cout << endl;

    cout << "seq : " << endl;
    rep(k,maxK+1){
        cout << "  k = " << (k/10) << (k%10) << " : ";
        rep(i,N) cout << seq[i][k].first << "-" << seq[i][k].second << " ";
        cout << endl;
    } cout << endl;
    */

    vector<int> h11pos(N+1, 0);
    rep(i,N) h11pos[h11[ord[i]]+1] = i+1;
    rep(i,N) h11pos[i+1] = max(h11pos[i+1], h11pos[i]);
    vector<pair<int, int>> subtree(N, {0,0});
    rep(i,N) subtree[i] = { h11pos[hld.subtree(i).first], h11pos[hld.subtree(i).second] };

    vector<Modint> X(N);
    rep(i,N){ int x; cin >> x; X[i] = Modint::raw(x); }
    nachia::DualSegtree<Affine, f1> rq(N, Affine::Construct(1,0));
    nachia::DualSegtree<Affine, f1> rqh(N, Affine::Construct(1,0));
    auto applyVtx = [&](int v, Affine f){
        if(isOnHeavy(v)){
            rqh.apply(hld.toSeq(v), f);
        }
        else{
            rq.apply(pos[v], f);
        }
    };
    auto heavyDec = [&](int v, int k) -> int {
        int s = hld.toSeq(v);
        s += k;
        if(s >= N) return -1;
        int w = hld.toVtx(s);
        //if(hld.heavyRootOf(w) != hld.heavyRootOf(v) || !isOnHeavy(w)) return -1;
        if(!isOnHeavy(w)) return -1;
        return w;
    };
    auto applyDec = [&](int v, int k, Affine f, bool doHeavy = true){
        if(k == 0){
            if(isOnHeavy(v)){
                if(doHeavy) rqh.apply(hld.toSeq(v), f);
            }
            else{
                rq.apply(pos[v], f);
            }
            return;
        }
        if(doHeavy){
            int hd = heavyDec(v, k);
            if(hd >= 0) applyVtx(hd, f);
        }
        auto [l,r] = seq[v][k];
        if(l <= r) rq.apply(l, r, f);
    };
    auto applyPath = [&](int r, int c, Affine f){
        for(auto [a, b] : hld.path(r, c)){
            while(a < b && !isOnHeavy(hld.toVtx(a))){
                int av = hld.toVtx(a);
                applyVtx(av, f);
                a++;
            }
            rqh.apply(a, b, f);
        }
    };
    rep(i,Q){
        int t; cin >> t;
        if(t == 1){
            int v; cin >> v; v--;
            Affine f = (isOnHeavy(v) ? rqh.get(hld.toSeq(v)) : rq.get(pos[v]));
            cout << f.eval(X[v]).val() << '\n';
        }
        if(t == 2){
            int v, k, c, d; cin >> v >> k >> c >> d; v--;
            Affine af = Affine::Construct(c, d);
            while(k >= 0){
                applyDec(v, k, af);
                k--; if(k < 0) break;
                applyDec(v, k, af);
                if(hld.parentOf(v) < 0){
                    while(k > 0){
                        k--;
                        applyDec(v, k, af);
                    }
                    break;
                }
                v = hld.parentOf(v);
            }
        }
        if(t == 3){
            int v, c, d; cin >> v >> c >> d; v--;
            Affine af = Affine::Construct(c, d);
            auto st = hld.subtree(v);
            rqh.apply(st.first, st.second, af);
            for(int k=0; k<=maxK; k++) applyDec(v, k, af, false);
            rq.apply(subtree[v].first, subtree[v].second, af);
        }
        if(t == 4){
            int u, v, c, d; cin >> u >> v >> c >> d; u--; v--;
            Affine af = Affine::Construct(c, d);
            int h = hld.lca(u, v);
            applyPath(h, u, af);
            if(h != v) applyPath(hld.la(h, v, 1), v, af);
        }
    }
    return 0;
}



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

結果

テストケース

ソースコード
