test/yosupo/bitwise_xor_convolution.test.cpp

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• Last update: 2021-09-23 20:26:31+09:00
• Problem: https://judge.yosupo.jp/problem/bitwise_xor_convolution

Depends on

• convolution/bitwise/fwht.cpp
• convolution/bitwise/xor.cpp
• mod/mint.cpp

Code

// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#include "../../mod/mint.cpp"
#include "../../convolution/bitwise/fwht.cpp"
#include "../../convolution/bitwise/xor.cpp"
#undef call_from_test

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

  int n;
  cin>>n;

  using M = Mint<int, 998244353>;

  int sz=1<<n;
  vector<M> as(sz),bs(sz);
  for(int i=0;i<sz;i++) cin>>as[i].v;
  for(int i=0;i<sz;i++) cin>>bs[i].v;

  fwht(as,bitwise_xor::zeta);
  fwht(bs,bitwise_xor::zeta);

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

  fwht(as,bitwise_xor::zeta);
  M inv=M(sz).inv();
  for(int i=0;i<sz;i++) as[i]*=inv;

  for(int i=0;i<sz;i++){
    if(i) cout<<' ';
    cout<<as[i];
  }
  cout<<endl;
  return 0;
}

#line 1 "test/yosupo/bitwise_xor_convolution.test.cpp"
// verification-helper: PROBLEM https://judge.yosupo.jp/problem/bitwise_xor_convolution

#include <bits/stdc++.h>
using namespace std;

#define call_from_test
#line 1 "mod/mint.cpp"

#line 3 "mod/mint.cpp"
using namespace std;
#endif

//BEGIN CUT HERE
template<typename T, T MOD = 1000000007>
struct Mint{
  inline 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 *this;}
  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;}

  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>
ostream& operator<<(ostream &os,Mint<T, MOD> m){os<<m.v;return os;}
//END CUT HERE
#ifndef call_from_test
signed main(){
  return 0;
}
#endif
#line 1 "convolution/bitwise/fwht.cpp"

#line 3 "convolution/bitwise/fwht.cpp"
using namespace std;
#endif
// https://kazuma8128.hatenablog.com/entry/2018/05/31/144519
//BEGIN CUT HERE
// O(n \log n)
template<typename T, typename F>
void fwht(vector<T> &as,F f){
  int n=as.size();
  for(int d=1;d<n;d<<=1)
    for(int m=d<<1,i=0;i<n;i+=m)
      for(int j=0;j<d;j++)
        f(as[i+j],as[i+j+d]);
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 1 "convolution/bitwise/xor.cpp"

#line 3 "convolution/bitwise/xor.cpp"
using namespace std;
#endif
//BEGIN CUT HERE
namespace bitwise_xor{
  auto zeta=[](auto& lo,auto& hi){
    auto x=lo+hi,y=lo-hi;
    lo=x;
    hi=y;
  };
  auto moebius=[](auto& lo,auto& hi){
    auto x=lo+hi,y=lo-hi;
    lo=x/decltype(x)(2);
    hi=y/decltype(y)(2);
  };
}
//END CUT HERE
#ifndef call_from_test
//INSERT ABOVE HERE
signed main(){
  return 0;
}
#endif
#line 10 "test/yosupo/bitwise_xor_convolution.test.cpp"
#undef call_from_test

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

  int n;
  cin>>n;

  using M = Mint<int, 998244353>;

  int sz=1<<n;
  vector<M> as(sz),bs(sz);
  for(int i=0;i<sz;i++) cin>>as[i].v;
  for(int i=0;i<sz;i++) cin>>bs[i].v;

  fwht(as,bitwise_xor::zeta);
  fwht(bs,bitwise_xor::zeta);

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

  fwht(as,bitwise_xor::zeta);
  M inv=M(sz).inv();
  for(int i=0;i<sz;i++) as[i]*=inv;

  for(int i=0;i<sz;i++){
    if(i) cout<<' ';
    cout<<as[i];
  }
  cout<<endl;
  return 0;
}

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