結果

問題 No.8046 yukicoderの過去問
ユーザー beetbeet
提出日時 2019-09-08 18:00:31
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 415 ms / 2,000 ms
コード長 9,454 bytes
コンパイル時間 4,475 ms
コンパイル使用メモリ 265,208 KB
実行使用メモリ 67,584 KB
最終ジャッジ日時 2024-06-27 15:05:38
合計ジャッジ時間 7,360 ms
ジャッジサーバーID
(参考情報)
judge1 / judge5
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 3 ms
5,248 KB
testcase_01 AC 2 ms
5,376 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 408 ms
67,060 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 AC 399 ms
66,932 KB
testcase_06 AC 415 ms
67,584 KB
testcase_07 AC 408 ms
67,260 KB
testcase_08 AC 413 ms
67,456 KB
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ソースコード

diff #

#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}
//BEGIN CUT HERE
template<typename T>
struct FormalPowerSeries{
  using Poly = vector<T>;
  using Conv = function<Poly(Poly, Poly)>;
  Conv conv;
  FormalPowerSeries(Conv conv):conv(conv){}

  Poly add(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,T(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]+=bs[i];
    return cs;
  }

  Poly sub(Poly as,Poly bs){
    int sz=max(as.size(),bs.size());
    Poly cs(sz,T(0));
    for(int i=0;i<(int)as.size();i++) cs[i]+=as[i];
    for(int i=0;i<(int)bs.size();i++) cs[i]-=bs[i];
    return cs;
  }

  Poly mul(Poly as,Poly bs){
    return conv(as,bs);
  }

  // F(0) must not be 0
  Poly inv(Poly as,int deg){
    assert(as[0]!=T(0));
    Poly rs({T(1)/as[0]});
    int sz=1;
    while(sz<deg){
      sz<<=1;
      Poly ts(min(sz,(int)as.size()));
      for(int i=0;i<(int)ts.size();i++) ts[i]=as[i];
      rs=sub(add(rs,rs),mul(mul(rs,rs),ts));
      rs.resize(sz);
    }
    return rs;
  }

  // Only for divisable
  Poly div(Poly as,Poly bs){
    reverse(as.begin(),as.end());
    reverse(bs.begin(),bs.end());
    while(bs.back()==T(0)){
      assert(as.back()==T(0));
      as.pop_back();
      bs.pop_back();
    }
    reverse(as.begin(),as.end());
    reverse(bs.begin(),bs.end());
    int need=as.size()-bs.size()+1;
    return mul(as,inv(bs,need));
  }

  // as[0] must be 1
  Poly sqrt(Poly as,int deg){
    assert(as[0]==T(1));

    int sz=1;
    T inv2=T(1)/T(2);
    Poly ss({T(1)});
    while(sz<deg){
      sz<<=1;
      Poly ts(min(sz,(int)as.size()));
      for(int i=0;i<(int)ts.size();i++) ts[i]=as[i];
      ss=add(ss,mul(ts,inv(ss,sz)));
      ss.resize(sz);
      for(T &x:ss) x*=inv2;
    }
    return ss;
  }
};
//END CUT HERE

template<typename T,T MOD = 1000000007>
struct Mint{
  static constexpr T mod = MOD;
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }

  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}

  Mint inv(){return pow(MOD-2);}

  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}

  Mint operator+(Mint a) const{return Mint(v)+=a;};
  Mint operator-(Mint a) const{return Mint(v)-=a;};
  Mint operator*(Mint a) const{return Mint(v)*=a;};
  Mint operator/(Mint a) const{return Mint(v)/=a;};

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}
};
template<typename T,T MOD> constexpr T Mint<T, MOD>::mod;
template<typename T,T MOD>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}

constexpr int bmds(int x){
  const int v[] = {1012924417, 924844033, 998244353,
                   897581057, 645922817};
  return v[x];
}
constexpr int brts(int x){
  const int v[] = {5, 5, 3, 3, 3};
  return v[x];
}

template<int X>
struct NTT{
  static constexpr int md = bmds(X);
  static constexpr int rt = brts(X);
  using M = Mint<int, md>;
  vector< vector<M> > rts,rrts;

  void ensure_base(int n){
    if((int)rts.size()>=n) return;
    rts.resize(n);rrts.resize(n);
    for(int i=1;i<n;i<<=1){
      if(!rts[i].empty()) continue;
      M w=M(rt).pow((md-1)/(i<<1));
      M rw=w.inv();
      rts[i].resize(i);rrts[i].resize(i);
      rts[i][0]=M(1);rrts[i][0]=M(1);
      for(int k=1;k<i;k++){
        rts[i][k]=rts[i][k-1]*w;
        rrts[i][k]=rrts[i][k-1]*rw;
      }
    }
  }

  void ntt(vector<M> &as,bool f,int n=-1){
    if(n==-1) n=as.size();
    assert((n&(n-1))==0);
    ensure_base(n);

    for(int i=0,j=1;j+1<n;j++){
      for(int k=n>>1;k>(i^=k);k>>=1);
      if(i>j) swap(as[i],as[j]);
    }

    for(int i=1;i<n;i<<=1){
      for(int j=0;j<n;j+=i*2){
        for(int k=0;k<i;k++){
          M z=as[i+j+k]*(f?rrts[i][k]:rts[i][k]);
          as[i+j+k]=as[j+k]-z;
          as[j+k]+=z;
        }
      }
    }

    if(f){
      M tmp=M(n).inv();
      for(int i=0;i<n;i++) as[i]*=tmp;
    }
  }

  vector<M> multiply(vector<M> as,vector<M> bs){
    int need=as.size()+bs.size()-1;
    int sz=1;
    while(sz<need) sz<<=1;
    as.resize(sz,M(0));
    bs.resize(sz,M(0));

    ntt(as,0);ntt(bs,0);
    for(int i=0;i<sz;i++) as[i]*=bs[i];
    ntt(as,1);

    as.resize(need);
    return as;
  }

  vector<int> multiply(vector<int> as,vector<int> bs){
    vector<M> am(as.size()),bm(bs.size());
    for(int i=0;i<(int)am.size();i++) am[i]=M(as[i]);
    for(int i=0;i<(int)bm.size();i++) bm[i]=M(bs[i]);
    vector<M> cm=multiply(am,bm);
    vector<int> cs(cm.size());
    for(int i=0;i<(int)cs.size();i++) cs[i]=cm[i].v;
    return cs;
  }
};
template<int X> constexpr int NTT<X>::md;
template<int X> constexpr int NTT<X>::rt;

struct ArbitraryModConvolution{
  using ll = long long;
  static NTT<0> ntt0;
  static NTT<1> ntt1;
  static NTT<2> ntt2;

  static constexpr int pow(int a,int b,int md){
    int res=1;
    a=a%md;
    while(b){
      if(b&1) res=(ll)res*a%md;
      a=(ll)a*a%md;
      b>>=1;
    }
    return res;
  }

  static constexpr int inv(int x,int md){
    return pow(x,md-2,md);
  }

  inline void garner(vector< vector<int> > &cs,int MOD){
    static constexpr int r01=inv(ntt0.md,ntt1.md);
    static constexpr int r02=inv(ntt0.md,ntt2.md);
    static constexpr int r12=inv(ntt1.md,ntt2.md);

    int m01 =(ll)ntt0.md*ntt1.md%MOD;
    size_t sz=cs[0].size();
    for(size_t i=0;i<sz;i++){
      cs[1][i]=(ll)(cs[1][i]-cs[0][i])*r01%ntt1.md;
      if(cs[1][i]<0) cs[1][i]+=ntt1.md;

      cs[2][i]=(ll)(cs[2][i]-cs[0][i])*r02%ntt2.md;
      cs[2][i]=(ll)(cs[2][i]-cs[1][i])*r12%ntt2.md;
      if(cs[2][i]<0) cs[2][i]+=ntt2.md;

      cs[0][i]+=(ll)cs[1][i]*ntt0.md%MOD;
      if(cs[0][i]>=MOD) cs[0][i]-=MOD;
      cs[0][i]+=(ll)cs[2][i]*m01%MOD;
      if(cs[0][i]>=MOD) cs[0][i]-=MOD;
    }
  }

  vector<int> multiply(vector<int> as,vector<int> bs,int MOD){
    vector< vector<int> > cs(3);
    cs[0]=ntt0.multiply(as,bs);
    cs[1]=ntt1.multiply(as,bs);
    cs[2]=ntt2.multiply(as,bs);
    size_t sz=as.size()+bs.size()-1;
    for(auto& v:cs) v.resize(sz);
    garner(cs,MOD);
    return cs[0];
  }

  template<typename T,T MOD>
  decltype(auto) multiply(vector< Mint<T, MOD> > am,
                          vector< Mint<T, MOD> > bm){
    using M = Mint<T, MOD>;
    vector<int> as(am.size()),bs(bm.size());
    for(int i=0;i<(int)as.size();i++) as[i]=am[i].v;
    for(int i=0;i<(int)bs.size();i++) bs[i]=bm[i].v;
    vector<int> cs=multiply(as,bs,MOD);
    vector<M> cm(cs.size());
    for(int i=0;i<(int)cm.size();i++) cm[i]=M(cs[i]);
    return cm;
  }
};
NTT<0> ArbitraryModConvolution::ntt0;
NTT<1> ArbitraryModConvolution::ntt1;
NTT<2> ArbitraryModConvolution::ntt2;
//INSERT ABOVE HERE

signed HAPPYQUERY_E(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,m,q;
  cin>>n>>m>>q;
  vector<int> ls(q),rs(q);
  for(int i=0;i<q;i++) cin>>ls[i]>>rs[i],ls[i]--;

  vector<int> as(n);
  for(int i=0;i<n;i++) cin>>as[i];

  if(as==vector<int>(n,0)){
    for(int i=0;i<m;i++){
      if(i) cout<<" ";
      cout<<0;
    }
    cout<<endl;
    return 0;
  }

  vector<int> cs(n-m+1,0);
  for(int l:ls) cs[l]++;

  NTT<0> ntt;
  using M = NTT<0>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  vector<M> ps(as.size()),qs(cs.size());
  for(int i=0;i<(int)ps.size();i++) ps[i]=M(as[i]);
  for(int i=0;i<(int)qs.size();i++) qs[i]=M(cs[i]);

  auto bs=FPS.div(ps,qs);
  for(int i=0;i<m;i++){
    if(i) cout<<" ";
    cout<<bs[i];
  }
  cout<<endl;
  return 0;
}
/*
  verified on 2019/09/08
  https://www.hackerrank.com/contests/happy-query-contest/challenges/array-restoring
*/

signed CFR250_E(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int n,m;
  cin>>n>>m;
  vector<int> cs(n);
  for(int i=0;i<n;i++) cin>>cs[i];

  NTT<2> ntt;
  using M = NTT<2>::M;
  auto conv=[&](auto as,auto bs){return ntt.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  const int deg=1<<18;
  vector<M> as(deg,0);
  as[0]=M(1);
  for(int c:cs) as[c]-=M(4);

  auto bs=FPS.sqrt(as,deg);
  bs[0]+=M(1);

  vector<M> vs({2});

  auto ans=FPS.mul(vs,FPS.inv(bs,deg));
  for(int i=1;i<=m;i++) cout<<ans[i]<<"\n";
  cout<<flush;

  return 0;
}
/*
  verified on 2019/09/08
  https://codeforces.com/contest/438/problem/E
*/

signed YUKI_3046(){
  cin.tie(0);
  ios::sync_with_stdio(0);

  int k,n;
  cin>>k>>n;
  vector<int> xs(n);
  for(int i=0;i<n;i++) cin>>xs[i];

  using M = Mint<int>;
  ArbitraryModConvolution arb;
  auto conv=[&](auto as,auto bs){return arb.multiply(as,bs);};
  FormalPowerSeries<M> FPS(conv);

  const int sz=1<<17;
  vector<M> bs(sz,M(0));
  bs[0]=1;
  for(int x:xs) bs[x]-=M(1);
  cout<<FPS.inv(bs,k+1)[k]<<endl;
  return 0;
}
/*
  verified on 2019/06/29
  https://yukicoder.me/problems/no/3046
*/

signed main(){
  //HAPPYQUERY_E();
  //CFR250_E();
  YUKI_3046();
  return 0;
}
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