#389131 (C++17) No.907 Continuous Kadomatu

提出ソース
結果

問題	No.907 Continuous Kadomatu
ユーザー	beet
提出日時	2019-10-11 22:47:26
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	15,702 bytes
コンパイル時間	3,371 ms
コンパイル使用メモリ	249,216 KB
実行使用メモリ	13,760 KB
最終ジャッジ日時	2024-05-04 02:34:31
合計ジャッジ時間	9,952 ms
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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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 13,760 KB
testcase_01	AC	2 ms 6,940 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,940 KB
testcase_05	WA	-
testcase_06	WA	-
testcase_07	WA	-
testcase_08	WA	-
testcase_09	WA	-
testcase_10	WA	-
testcase_11	TLE	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
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ソースコード

raw source code
#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;}


struct FastIO{
  FastIO(){
    cin.tie(0);
    ios::sync_with_stdio(0);
  }
}fastio_beet;


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;}

  static Mint comb(long long n,int k){
    Mint num(1),dom(1);
    for(int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};
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;}


template<typename V>
V compress(V v){
  sort(v.begin(),v.end());
  v.erase(unique(v.begin(),v.end()),v.end());
  return v;
}
template<typename T>
map<T, int> dict(const vector<T> &v){
  map<T, int> res;
  for(int i=0;i<(int)v.size();i++)
    res[v[i]]=i;
  return res;
}
map<char, int> dict(const string &v){
  return dict(vector<char>(v.begin(),v.end()));
}


namespace FFT{
  using dbl = double;

  struct num{
    dbl x,y;
    num(){x=y=0;}
    num(dbl x,dbl y):x(x),y(y){}
  };

  inline num operator+(num a,num b){
    return num(a.x+b.x,a.y+b.y);
  }
  inline num operator-(num a,num b){
    return num(a.x-b.x,a.y-b.y);
  }
  inline num operator*(num a,num b){
    return num(a.x*b.x-a.y*b.y,a.x*b.y+a.y*b.x);
  }
  inline num conj(num a){
    return num(a.x,-a.y);
  }

  int base=1;
  vector<num> rts={{0,0},{1,0}};
  vector<int> rev={0,1};

  const dbl PI=acosl(-1.0);

  void ensure_base(int nbase){
    if(nbase<=base) return;

    rev.resize(1<<nbase);
    for(int i=0;i<(1<<nbase);i++)
      rev[i]=(rev[i>>1]>>1)+((i&1)<<(nbase-1));

    rts.resize(1<<nbase);
    while(base<nbase){
      dbl angle=2*PI/(1<<(base+1));
      for(int i=1<<(base-1);i<(1<<base);i++){
        rts[i<<1]=rts[i];
        dbl angle_i=angle*(2*i+1-(1<<base));
        rts[(i<<1)+1]=num(cos(angle_i),sin(angle_i));
      }
      base++;
    }
  }

  void fft(vector<num> &a,int n=-1){
    if(n==-1) n=a.size();
    assert((n&(n-1))==0);

    int zeros=__builtin_ctz(n);
    ensure_base(zeros);
    int shift=base-zeros;
    for(int i=0;i<n;i++)
      if(i<(rev[i]>>shift))
        swap(a[i],a[rev[i]>>shift]);

    for(int k=1;k<n;k<<=1){
      for(int i=0;i<n;i+=2*k){
        for(int j=0;j<k;j++){
          num z=a[i+j+k]*rts[j+k];
          a[i+j+k]=a[i+j]-z;
          a[i+j]=a[i+j]+z;
        }
      }
    }
  }

  vector<num> fa;

  vector<long long> multiply(vector<int> &a,vector<int> &b){
    int need=a.size()+b.size()-1;
    int nbase=0;
    while((1<<nbase)<need) nbase++;
    ensure_base(nbase);

    int sz=1<<nbase;
    if(sz>(int)fa.size()) fa.resize(sz);
    for(int i=0;i<sz;i++){
      int x=(i<(int)a.size()?a[i]:0);
      int y=(i<(int)b.size()?b[i]:0);
      fa[i]=num(x,y);
    }
    fft(fa,sz);

    num r(0,-0.25/sz);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      num z=(fa[j]*fa[j]-conj(fa[i]*fa[i]))*r;
      if(i!=j)
        fa[j]=(fa[i]*fa[i]-conj(fa[j]*fa[j]))*r;
      fa[i]=z;
    }
    fft(fa,sz);

    vector<long long> res(need);
    for(int i=0;i<need;i++)
      res[i]=fa[i].x+0.5;

    return res;
  }

};


template<typename T>
struct ArbitraryModConvolution{
  using dbl=FFT::dbl;
  using num=FFT::num;

  vector<T> multiply(vector<T> as,vector<T> bs){
    int need=as.size()+bs.size()-1;
    int sz=1;
    while(sz<need) sz<<=1;
    vector<num> fa(sz),fb(sz);
    for(int i=0;i<(int)as.size();i++)
      fa[i]=num(as[i].v&((1<<15)-1),as[i].v>>15);
    for(int i=0;i<(int)bs.size();i++)
      fb[i]=num(bs[i].v&((1<<15)-1),bs[i].v>>15);

    fft(fa,sz);fft(fb,sz);

    dbl ratio=0.25/sz;
    num r2(0,-1),r3(ratio,0),r4(0,-ratio),r5(0,1);
    for(int i=0;i<=(sz>>1);i++){
      int j=(sz-i)&(sz-1);
      num a1=(fa[i]+conj(fa[j]));
      num a2=(fa[i]-conj(fa[j]))*r2;
      num b1=(fb[i]+conj(fb[j]))*r3;
      num b2=(fb[i]-conj(fb[j]))*r4;
      if(i!=j){
        num c1=(fa[j]+conj(fa[i]));
        num c2=(fa[j]-conj(fa[i]))*r2;
        num d1=(fb[j]+conj(fb[i]))*r3;
        num d2=(fb[j]-conj(fb[i]))*r4;
        fa[i]=c1*d1+c2*d2*r5;
        fb[i]=c1*d2+c2*d1;
      }
      fa[j]=a1*b1+a2*b2*r5;
      fb[j]=a1*b2+a2*b1;
    }
    fft(fa,sz);fft(fb,sz);

    vector<T> cs(need);
    using ll = long long;
    for(int i=0;i<need;i++){
      ll aa=T(llround(fa[i].x)).v;
      ll bb=T(llround(fb[i].x)).v;
      ll cc=T(llround(fa[i].y)).v;
      cs[i]=T(aa+(bb<<15)+(cc<<30));
    }
    return cs;
  }
};


template<typename T>
struct FormalPowerSeries{
  using Poly = vector<T>;
  using Conv = function<Poly(Poly, Poly)>;
  Conv conv;
  FormalPowerSeries(Conv conv):conv(conv){}

  Poly pre(const Poly &as,int deg){
    return Poly(as.begin(),as.begin()+min((int)as.size(),deg));
  }

  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);
  }

  Poly mul(Poly as,T k){
    for(auto &a:as) a*=k;
    return as;
  }

  // F(0) must not be 0
  Poly inv(Poly as,int deg){
    assert(as[0]!=T(0));
    Poly rs({T(1)/as[0]});
    for(int i=1;i<deg;i<<=1)
      rs=pre(sub(add(rs,rs),mul(mul(rs,rs),pre(as,i<<1))),i<<1);
    return rs;
  }

  // not zero
  Poly div(Poly as,Poly bs){
    while(as.back()==T(0)) as.pop_back();
    while(bs.back()==T(0)) bs.pop_back();
    if(bs.size()>as.size()) return Poly();
    reverse(as.begin(),as.end());
    reverse(bs.begin(),bs.end());
    int need=as.size()-bs.size()+1;
    Poly ds=pre(mul(as,inv(bs,need)),need);
    reverse(ds.begin(),ds.end());
    return ds;
  }

  // F(0) must be 1
  Poly sqrt(Poly as,int deg){
    assert(as[0]==T(1));
    T inv2=T(1)/T(2);
    Poly ss({T(1)});
    for(int i=1;i<deg;i<<=1){
      ss=pre(add(ss,mul(pre(as,i<<1),inv(ss,i<<1))),i<<1);
      for(T &x:ss) x*=inv2;
    }
    return ss;
  }

  Poly diff(Poly as){
    int n=as.size();
    Poly rs(n-1);
    for(int i=1;i<n;i++) rs[i-1]=as[i]*T(i);
    return rs;
  }

  Poly integral(Poly as){
    int n=as.size();
    Poly rs(n+1);
    rs[0]=T(0);
    for(int i=0;i<n;i++) rs[i+1]=as[i]/T(i+1);
    return rs;
  }

  // F(0) must be 1
  Poly log(Poly as,int deg){
    return pre(integral(mul(diff(as),inv(as,deg))),deg);
  }

  // F(0) must be 0
  Poly exp(Poly as,int deg){
    Poly f({T(1)});
    as[0]+=T(1);
    for(int i=1;i<deg;i<<=1)
      f=pre(mul(f,sub(pre(as,i<<1),log(f,i<<1))),i<<1);
    return f;
  }

  Poly partition(int n){
    Poly rs(n+1);
    rs[0]=T(1);
    for(int k=1;k<=n;k++){
      if(1LL*k*(3*k+1)/2<=n) rs[k*(3*k+1)/2]+=T(k%2?-1LL:1LL);
      if(1LL*k*(3*k-1)/2<=n) rs[k*(3*k-1)/2]+=T(k%2?-1LL:1LL);
    }
    return inv(rs,n+1);
  }

  Poly bernoulli(int n){
    Poly rs(n+1,1);
    for(int i=1;i<=n;i++) rs[i]=rs[i-1]/T(i+1);
    rs=inv(rs,n+1);
    T tmp(1);
    for(int i=1;i<=n;i++){
      tmp*=T(i);
      rs[i]*=tmp;
    }
    return rs;
  }
};


template<typename M>
class Enumeration{
private:
  static vector<M> fact,finv,invs;
public:
  static void init(int n){
    n=min<decltype(M::mod)>(n,M::mod-1);

    int m=fact.size();
    if(n<m) return;

    fact.resize(n+1,1);
    finv.resize(n+1,1);
    invs.resize(n+1,1);

    if(m==0) m=1;
    for(int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i);
    finv[n]=M(1)/fact[n];
    for(int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i);
    for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];
  }

  static M Fact(int n){
    init(n);
    return fact[n];
  }
  static M Finv(int n){
    init(n);
    return finv[n];
  }
  static M Invs(int n){
    init(n);
    return invs[n];
  }

  static M C(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k]*finv[k];
  }

  static M P(int n,int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k];
  }

  static M H(int n,int k){
    if(n<0||k<0) return M(0);
    if(!n&&!k) return M(1);
    init(n+k-1);
    return C(n+k-1,k);
  }

  static M S(int n,int k){
    init(k);
    M res(0);
    for(int i=1;i<=k;i++){
      M tmp=C(k,i)*M(i).pow(n);
      if((k-i)&1) res-=tmp;
      else res+=tmp;
    }
    return res*=finv[k];
  }

  static vector< vector<M> > D(int n,int m){
    vector< vector<M> > dp(n+1,vector<M>(m+1,0));
    dp[0][0]=M(1);
    for(int i=0;i<=n;i++){
      for(int j=1;j<=m;j++){
        if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j];
        else dp[i][j]=dp[i][j-1];
      }
    }
    return dp;
  }

  static M B(int n,int k){
    if(n==0) return M(1);
    k=min(k,n);
    init(k);
    vector<M> dp(k+1);
    dp[0]=M(1);
    for(int i=1;i<=k;i++)
      dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]);
    M res(0);
    for(int i=1;i<=k;i++)
      res+=M(i).pow(n)*finv[i]*dp[k-i];
    return res;
  }

  static M montmort(int n){
    init(n);
    M res(0);
    for(int k=2;k<=n;k++){
      if(k&1) res-=finv[k];
      else res+=finv[k];
    }
    return res*=fact[n];
  }

  static M LagrangePolynomial(vector<M> &y,M t){
    int n=y.size()-1;
    if(t.v<=n) return y[t.v];
    init(n+1);
    vector<M> dp(n+1,1),pd(n+1,1);
    for(int i=0;i<n;i++) dp[i+1]=dp[i]*(t-M(i));
    for(int i=n;i>0;i--) pd[i-1]=pd[i]*(t-M(i));
    M res(0);
    for(int i=0;i<=n;i++){
      M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i];
      if((n-i)&1) res-=tmp;
      else res+=tmp;
    }
    return res;
  }
};
template<typename M>
vector<M> Enumeration<M>::fact=vector<M>();
template<typename M>
vector<M> Enumeration<M>::finv=vector<M>();
template<typename M>
vector<M> Enumeration<M>::invs=vector<M>();

//INSERT ABOVE HERE
signed main(){
  int n;
  cin>>n;
  vector<int> as(n),bs(n);
  for(int i=0;i<n;i++) cin>>as[i]>>bs[i];

  vector<int> vs;
  for(int a:as) vs.emplace_back(a);
  for(int b:bs) vs.emplace_back(b);
  vs.emplace_back(0);
  vs.emplace_back(1e9+6);

  vs=compress(vs);
  auto dc=dict(vs);
  int sz=dc.size();

  const int MOD = 1e9+7;
  using M = Mint<int, MOD>;
  ArbitraryModConvolution<M> arb;
  FormalPowerSeries<M> FPS([&](auto as,auto bs){return arb.multiply(as,bs);});

  using Poly = FormalPowerSeries<M>::Poly;

  Poly sum({1,1,500000004,333333336,208333335,933333340,384722225,953769848,884027784,28425375,878389832,120295265,667416506,229082322,168690037,792301837,189791907,537322580,270492550,482909819,434964639,603347984,256069033,40542057,910866921,438756389,689225591,456092267,413439436,942741942,190664686,782031312,604476028,573671381,838163729,26381583,992375502,930241799,68659206,750162938,475025082,44106509,953003110,354749308,929548052,773716788,337410579,936852063,239751572,561034786,757300345,866130835,553348107,173690227,339768055,709994974,599133150,808467741,396950722,936881852,933909478,737746550,781678380,976953545,580850150,325446247,537865815,281759879,678254613,501070706,851777585,443897119,629314534,760221421,466210161,508261591,65379122,70860701,553561602,854155236,407075847,92305888,282144425,99940577,300342438,587223921,290386237,874023958,985911658,291238936,785218916,678035252,407108295,192101397,507631876,885193819,934834163,385372845,417450165,966951672,684237800,52565350,530411501,135801688,482549358,210734100,761667073,954034475,693540720,576600855,148510276,919026764,583465058,956106104,181054957,41348431,224860616,517912143,860599260,727279538,906355640,153963332,118864415,34582699,44891509,32565076,105784827,928923967,903694428,235385416,883778964,689231689,547905546,909455137,465865460,662952760,195582959,432129855,680896262,758700879,501176266,776382822,454182726,365978689,459511347,816227295,999967985,931726294,294000060,267169976,42254724,349482774,808670797,253898299,508920118,703775403,785503876,423332329,660157859,247972241,450442033,165002242,361442380,392196376,978825741,920083817,560637228,355209713,832930192,440150331,375967478,305763913,635609914,188334856,10887821,335431951,444798249,529525353,226380424,33966925,136881343,434803890,922586534,569205127,117755704,850230335,9409131,93257910,499343559,777515079,650212468,412857608,653792744,679126849,627912655,420312949,612153221,845955439,166961824,673224688,890626117,315980351,994489857,197421005,255024280,293965643,551312195,954953948,756212493,145912941,421627841,799494402,930555555,355649848,186846433,48886853,726884935,842271550,621329810,400463499,99728277,259919265,910183168,345461687,647722720,465173355,355332005,670027204,429411872,891988152,9169256,451160948,499408796,131168601,198918642,129056918,498922473,98755571,915188909,895498700,154447049,565728210,321328855,10010840,606569580,973703597,842226469,741226137,421029601,247331280,864146768,199266677,950280814,999665342,469919529,13609624});
  /*
  const int deg = 1<<8;
  {
    for(int l=0;l<deg;l++){
      Poly res({M(1)});
      Poly bs({M(1),M(1)});
      bs=FPS.inv(bs,deg);
      Poly tmp({M(1)});
      for(int i=1;i<=l;i++){
        tmp=FPS.pre(FPS.mul(tmp,bs),deg);
        res=FPS.pre(FPS.mul(res,FPS.sub(Poly({M(1)}),tmp)),deg);
      }
      sum=FPS.add(sum,res);
    }
    using E = Enumeration<M>;
    E::init(deg);
    for(int i=0;i<deg;i++) sum[i]*=E::Finv(i);
    for(int i=0;i<deg;i++) cout<<sum[i]<<",";
  }
  */


  vector< vector<M> > dp(n+1,vector<M>(sz,0));

  for(int j=0;j+1<sz;j++)
    if(as[0]<=vs[j]&&vs[j+1]<=bs[0])
      dp[1][j]=M(vs[j+1]-vs[j])/M(bs[0]-as[0]);

  for(int i=1;i<n;i++){
    M rev=M(bs[i]-as[i]).inv();
    vector< vector<M> > nx(n+1,vector<M>(sz,0));

    if(i&1){
      for(int l=1;l<n;l++){
        for(int j=0;j+1<sz;j++){
          nx[l+1][j]+=dp[l][j]*
            M(as[i]<=vs[j]&&vs[j+1]<=bs[i])*M(vs[j+1]-vs[j])*rev;

          for(int k=j+1;k+1<sz;k++)
            nx[1][k]+=sum[l]*dp[l][j]
              *M(as[i]<=vs[k]&&vs[k+1]<=bs[i])*M(vs[k+1]-vs[k])*rev;
        }
      }
    }else{
      for(int l=1;l<n;l++){
        for(int j=0;j+1<sz;j++){
          nx[l+1][j]+=dp[l][j]*
            M(as[i]<=vs[j]&&vs[j+1]<=bs[i])*M(vs[j+1]-vs[j])*rev;

          for(int k=j-1;k>=0;k--)
            nx[1][k]+=sum[l]*dp[l][j]
              *M(as[i]<=vs[k]&&vs[k+1]<=bs[i])*M(vs[k+1]-vs[k])*rev;
        }
      }
    }
    swap(dp,nx);
  }

  M ans{0};
  for(int i=1;i<=n;i++)
    for(int j=0;j+1<sz;j++)
      ans+=dp[i][j]*sum[i];

  if(0){
    for(int i=1;i<=n;i++)
      for(int j=0;j+1<sz;j++)
        cout<<i<<" "<<j<<":"<<dp[i][j]<<" "<<sum[i]<<endl;
  }
  cout<<ans<<endl;
  return 0;
}
yukicoder

結果

テストケース

ソースコード
