結果

問題 No.1720 Division Permutation
ユーザー 👑 Nachia
提出日時 2024-12-12 06:36:24
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 131 ms / 4,000 ms
コード長 19,363 bytes
コンパイル時間 2,225 ms
コンパイル使用メモリ 132,280 KB
最終ジャッジ日時 2025-02-26 12:14:35
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 60
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
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;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <atcoder/modint>
using Modint = atcoder::static_modint<998244353>;
#include <functional>
#include <cassert>
namespace nachia{
int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
    return __builtin_popcountll(c);
#else
    c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
    c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
    c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
    c = (c * (~0ull/257)) >> 56;
    return c;
#endif
}
// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return 63 - __builtin_clzll(x);
#else
    using u64 = unsigned long long;
    int q = (x >> 32) ? 32 : 0;
    auto m = x >> q;
    constexpr u64 hi = 0x88888888;
    constexpr u64 mi = 0x11111111;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 31;
    q += (m & 0xf) << 2;
    q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf;
    return q;
#endif
}
// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}
}
namespace nachia{
template<class T, class CompT = std::less<T>>
struct RangeMinFast{
private:
    static constexpr int B = 16;
    std::vector<T> A;
    std::vector<T> LB;
    std::vector<T> RB;
    std::vector<std::vector<T>> spa;
    CompT comp;
public:
    RangeMinFast() {}
    RangeMinFast(std::vector<T> a)
        : A(std::move(a)) , comp()
    {
        int n = (int)A.size();
        LB = A;
        for(int i=n-2; i>=0; i--) if(i%B != 0 && i%B != B-1){
            if(comp(LB[i+1],LB[i])) LB[i] = LB[i+1];
        }
        RB = A;
        for(int i=1; i<n; i++) if(i%B != 0 && i%B != B-1){
            if(comp(RB[i-1],RB[i])) RB[i] = RB[i-1];
        }
        int n2 = n / B;
        if(n2 != 0){
            int logn2 = MsbIndex(n2+1) + 1;
            spa.resize(logn2);
            for(int d=0; d<logn2; d++) spa[d].resize(n2-(1<<d)+1);
            for(int i=0; i<n2; i++) spa[0][i] = std::min(A[i*B], LB[i*B+1], comp);
            for(int d=0; d+1<logn2; d++){
                int len = spa[d+1].size();
                for(int i=0; i<len; i++){
                    spa[d+1][i] = std::min(spa[d][i], spa[d][i+(1<<d)], comp);
                }
            }
        }
    }
    T min(int l, int r) const {
        if(r-l <= B){
            T d = A[l];
            for(int j=l+1; j<r; j++) if(comp(A[j], d)) d = A[j];
            return d;
        }
        int x = std::min(LB[l], RB[r-1], comp);
        int lb = (l+(B-1)) / B;
        int rb = r / B;
        if(lb == rb) return x;
        int q = MsbIndex(rb-lb);
        return std::min(std::min(x, spa[q][lb], comp), spa[q][rb-(1<<q)], comp);
    }
};
} // namespace nachia
#include <utility>
namespace nachia {
struct CommonIntervalDecompositionTree {
    enum NodeType {
        Prime,
        Dec,
        Inc,
        One
    };
    struct Node {
        int parent;
        NodeType type;
        int l;
        int r;
        int length() const { return r-l; }
    };
    std::vector<Node> tree;
    int m_root;
    CommonIntervalDecompositionTree() : m_root(-1) {}
    CommonIntervalDecompositionTree(std::vector<int> P) : m_root(-1){
        int n = int(P.size());
        calc(n, std::move(P));
    }
    int numNodes() const { return (int)tree.size(); }
    int root() const { return m_root; }
    const Node& operator[](int v) const { return tree[v]; }
private:
    void calc(int n, std::vector<int> P){
        std::vector<int> Q(n);
        for(int i=0; i<n; i++) Q[P[i]] = i;
        auto rm_h = RangeMinFast(Q);
        struct LeftBase { int l; int vl; int vr; };
        struct Common { int l; int r; int v; };
        std::vector<LeftBase> st;
        std::vector<Common> coms;
        for(int r=1; r<=n; r++){
            int a = P[r-1];
            LeftBase bs = { r-1, a, a+1 };
            while(!st.empty()){
                if(bs.vl < st.back().vl) st.back().vl = bs.vl;
                if(bs.vr > st.back().vr) st.back().vr = bs.vr;
                auto nx = st.back();
                if(rm_h.min(nx.vl, nx.vr) < nx.l){
                    st.pop_back();
                    auto& nx2 = st.back();
                    if(nx.vl < nx2.vl) nx2.vl = nx.vl;
                    if(nx.vr > nx2.vr) nx2.vr = nx.vr;
                }
                else if(nx.vr - nx.vl == r - nx.l){
                    bs = nx;
                    st.pop_back();
                    coms.push_back({ nx.l, r, nx.vl });
                }
                else break;
            }
            st.push_back(bs);
        }
        while(st.size() >= 2){
            auto nx = st.back(); st.pop_back();
            auto& nx2 = st.back();
            if(nx.vl < nx2.vl) nx2.vl = nx.vl;
            if(nx.vr > nx2.vr) nx2.vr = nx.vr;
            if(nx2.vr - nx2.vl == n - nx2.l) coms.push_back({ nx2.l, n, nx2.vl });
        }
        if(st.size() != 1) coms.push_back({ 0, n, 0 });
        st = {};
        std::vector<Node> res;
        for(int i=0; i<n; i++) res.push_back({ -1,One,i,i+1 });
        std::vector<int> nodeid(n);
        for(int i=0; i<n; i++) nodeid[i] = i;
        std::vector<int> sll(n);
        for(int i=0; i<n; i++) sll[i] = i+1;
        for(auto com : coms){
            int m = sll[com.l];
            if(sll[m] == com.r){
                int a = nodeid[com.l];
                int b = nodeid[m];
                sll[com.l] = com.r;
                auto tgty = P[com.l] < P[com.r-1] ? Inc : Dec;
                if(res[a].type == tgty){
                    res[b].parent = a;
                    res[a].r = com.r;
                } else {
                    int c = int(res.size());
                    res.push_back({ -1, tgty, com.l, com.r });
                    res[a].parent = c;
                    res[b].parent = c;
                    nodeid[com.l] = c;
                }
            } else {
                int c = int(res.size());
                res.push_back({ -1, Prime, com.l, com.r });
                for(int p=com.l; p<com.r; p=sll[p]){
                    res[nodeid[p]].parent = c;
                }
                nodeid[com.l] = c;
                sll[com.l] = com.r;
            }
        }
        std::swap(tree, res);
        m_root = nodeid[0];
    }
};
} // namespace nachia
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
namespace nachia{
struct Graph {
public:
    struct Edge{
        int from, to;
        void reverse(){ std::swap(from, to); }
        int xorval() const { return from ^ to; }
    };
    Graph() : m_n(0), m_e(0), m_isUndir(false) {}
    explicit Graph(int n, bool undirected = false, int m = 0) : m_n(n), m_e(m), m_isUndir(undirected) {}
    explicit Graph(int n, const std::vector<std::pair<int, int>>& edges, int 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, int 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
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.assign(N, 0); I[0] = root;
        int iI = 1;
        for(int i=0; i<iI; i++){
            int p = I[i];
            for(int e : E[p]) if(P[p] != e){
                I[iI++] = 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;
            }
        }
        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 vtx) const { return rangeL[vtx]; }
    int toVtx(int seqidx) const { return I[seqidx]; }
    int toSeq2In(int vtx) const { return rangeL[vtx] * 2 - D[vtx]; }
    int toSeq2Out(int vtx) const { return rangeR[vtx] * 2 - D[vtx] - 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;
    }
    struct Range{
        int l; int r;
        int size() const { return r-l; }
        bool includes(int x) const { return l <= x && x < r; }
    };
    std::vector<Range> path(int r, int c, bool include_root = true, bool reverse_path = false) const {
        if(PD[c] < PD[r]) return {};
        std::vector<Range> res(PD[c]-PD[r]+1);
        for(int i=0; i<(int)res.size()-1; i++){
            res[i] = { rangeL[PP[c]], rangeL[c]+1 };
            c = P[PP[c]];
        }
        if(PP[r] != PP[c] || D[r] > D[c]) return {};
        res.back() = { rangeL[r]+(include_root?0:1), rangeL[c]+1 };
        if(res.back().l == res.back().r) res.pop_back();
        if(!reverse_path) std::reverse(res.begin(),res.end());
        else for(auto& a : res) a = { N - a.r, N - a.l };
        return res;
    }
    Range subtree(int p) const { return { 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];
    }
    struct ChildrenIterRange {
    struct Iter {
        const HeavyLightDecomposition& hld; int s;
        int operator*() const { return hld.toVtx(s); }
        Iter& operator++(){
            s += hld.subtree(hld.I[s]).size();
            return *this;
        }
        Iter operator++(int) const { auto a = *this; return ++a; }
        bool operator==(Iter& r) const { return s == r.s; }
        bool operator!=(Iter& r) const { return s != r.s; }
    };
        const HeavyLightDecomposition& hld; int v;
        Iter begin() const { return { hld, hld.rangeL[v] + 1 }; }
        Iter end() const { return { hld, hld.rangeR[v] }; }
    };
    ChildrenIterRange children(int v) const {
        return ChildrenIterRange{ *this, v };
    }
};
} // namespace nachia
void testcase(){
    int N, K; cin >> N >> K;
    vector<int> A(N); rep(i,N){ cin >> A[i]; A[i]--; }
    auto pt = nachia::CommonIntervalDecompositionTree(A);
    int M = pt.numNodes();
    auto tree = nachia::Graph(M, false);
    rep(i,M) if(i != pt.root()) tree.addEdge(pt[i].parent, i);
    auto hld = nachia::HeavyLightDecomposition(tree, pt.root());
    auto adj = tree.getAdjacencyArray();
    vector<vector<Modint>> dp(M);
    for(int i=M-1; i>=0; i--){
        int v = hld.toVtx(i);
        if(v < N){
            dp[v].resize(2);
            dp[v][1] = 1;
            continue;
        }
        sort(adj[v].begin(), adj[v].end(), [&](int l, int r){ return pt[l].l < pt[r].l; });
        vector<Modint> tmp(1);
        tmp[0] = 1;
        int t = 0;
        if(pt[v].type == pt.Prime){
            for(int c : adj[v]){
                auto& dpc = dp[c];
                int k = min(K, t + int(dpc.size() - 1));
                vector<Modint> xtmp(k+1);
                rep(a,tmp.size()) rep(b,dpc.size()) if(a+b<=k){
                    xtmp[a+b] += tmp[a] * dpc[b];
                }
                swap(tmp, xtmp);
                t = k;
            }
            tmp[1] += 1;
        } else {
            vector<Modint> cx(K+1);
            for(int c : adj[v]){
                rep(i,t+1) cx[i] += tmp[i];
                auto& dpc = dp[c];
                int k = min(K, t + int(dpc.size() - 1));
                vector<Modint> xtmp(k+1);
                dpc[1] -= 1;
                rep(a,tmp.size()) rep(b,dpc.size()) if(a+b<=k){
                    xtmp[a+b] += tmp[a] * dpc[b];
                }
                swap(tmp, xtmp);
                t = k;
                rep(i,t) tmp[i+1] += cx[i];
            }
        }
        swap(dp[v], tmp);
    }
    for(int k=1; k<=K; k++){
        cout << dp[pt.root()][k].val() << '\n';
    }
}
int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0