#632390 (C++17) No.754 畳み込みの和

提出ソース
結果

問題	No.754 畳み込みの和
ユーザー	soraie_
提出日時	2021-03-20 10:26:30
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	872 ms / 5,000 ms
コード長	14,487 bytes
コンパイル時間	5,029 ms
コンパイル使用メモリ	273,084 KB
実行使用メモリ	21,868 KB
最終ジャッジ日時	2024-11-20 19:24:31
合計ジャッジ時間	8,980 ms
ジャッジサーバーID （参考情報）	judge1 / judge2
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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	868 ms 21,864 KB
testcase_01	AC	868 ms 21,868 KB
testcase_02	AC	872 ms 21,740 KB
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ソースコード

raw source code
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

using namespace std;
//--------------------------------------------------------------------
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(n) for(ll _=0;_<(ll)n;++_)
#define rep2(i,n) for(ll i=0;i<(ll)n;++i)
#define rep3(i,a,b) for(ll i=(ll)a;i<(ll)b;++i)
#define rep4(i,a,b,c) for(ll i=(ll)a;i<(ll)b;i+=(ll)c)
#define rep(...) overload4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#ifdef _DEBUG
#define pass(...) __VA_ARGS__ ;

#define debug1(a) cerr<<#a<<": "<<a<<"\n"
#define debug2(a,b) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cerr<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"

/*
#define debug1(a) cout<<#a<<": "<<a<<"\n"
#define debug2(a,b) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<"\n"
#define debug3(a,b,c) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<"\n"
#define debug4(a,b,c,d) cout<<#a<<": "<<a<<", "<<#b<<": "<<b<<", "<<#c<<": "<<c<<", "<<#d<<": "<<d<<"\n"
*/

#define debug(...) overload4(__VA_ARGS__,debug4,debug3,debug2,debug1)(__VA_ARGS__)
#define koko cerr << "koko\n";
#else
#define debug(...) void(0)
#define pass(...) void(0);
#define koko void(0);
#endif
#define mp make_pair
//#define fi first
//#define se second
void myset(){ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);}
void doset(int n){cout << fixed << setprecision(n);cerr << fixed << setprecision(n);}
using ll = long long;
using ld = long double;
using dou = double;
template<class First,class Second>ostream& operator<<(ostream& os,const pair<First,Second>& pp)
{return os << "{" << pp.first << "," << pp.second << "}";}
template<class T>ostream& operator<<(ostream& os,const vector<T>& VV)
{if(VV.empty())return os<<"[]";os<<"[";rep(i,VV.size())os<<VV[i]<<(i==int(VV.size()-1)?"]":",");return os;}
template<class T>ostream& operator<<(ostream& os,const set<T>& SS)
{if(SS.empty())return os<<"[]";os<<"[";auto ii=SS.begin();for(;ii!=SS.end();ii++)os<<*ii<<(ii==prev(SS.end())?"]":",");return os;}
template<class Key,class Tp>ostream& operator<<(ostream& os,const map<Key,Tp>& MM)
{if(MM.empty())return os<<"[]";os<<"[";auto ii=MM.begin();for(;ii!=MM.end();ii++)os<<"{"<<ii->first<<":"<<ii->second<<"}"<<(ii==prev(MM.end())?"]":",");return os;}
const int inf = 1 << 30;
const ll INF = 1LL << 61;
const ld pi = 3.14159265358;
const ll mod1 = 1000000007LL;
const ll mod2 = 998244353LL;
typedef pair<ll,ll> P;
template<class T, class U> inline bool chmin(T& a, const U& b){ if(a > b){ a = b; return 1; } return 0; }
template<class T, class U> inline bool chmax(T& a, const U& b){ if(a < b){ a = b; return 1; } return 0; }
ll modpow(ll n,ll m,ll MOD){
    if(m == 0)return 1;
    if(m < 0)return 0;
    ll res = 1;
    n %= MOD;
    while(m){
        if(m & 1)res = (res * n) % MOD;
        m >>= 1;
        n *= n;
        n %= MOD;
    }
    return res;
}
ll mypow(ll n,ll m){
    if(m == 0)return 1;
    if(m < 0)return -1;
    ll res = 1;
    while(m){
        if(m & 1)res = (res * n);
        m >>= 1;
        n *= n;
    }
    return res;
}

inline bool isp(ll n){
    bool res = true;
    if(n == 1 || n == 0)return false;
    else{
        for(ll i = 2;i * i <= n;i++){
            if(n % i == 0){
                res = false;
                break;
            }
        }
        return res;
    }
}
inline bool Yes(bool b = 1){cout << (b ? "Yes\n":"No\n");return b;}
inline bool YES(bool b = 1){cout << (b ? "YES\n":"NO\n");return b;}
map<ll,ll> primefactor(ll n){
    map<ll,ll> ma;
    if(n <= 1)return ma;
    ll m = n;
    for(ll i = 2;i * i <= n;i++){
        while(m % i == 0){
            ma[i]++;
            m /= i;
        }
    }
    if(m != 1)ma[m]++;
    return ma;
}
vector<ll> divisor(ll n,bool sorted = true,bool samein = false){
    vector<ll> res;
    for(ll i = 1;i * i <= n;i++){
        if(n % i == 0){
            res.push_back(i);
            if(i * i != n || samein)res.push_back(n / i);
        }
    }
    if(sorted)sort(all(res));
    return res;
}

ll __lcm(ll a,ll b){return a / __gcd(a,b) * b;}

template<class T>T sum(const vector<T> &V){T r=0;for(auto x:V)r+=x;return r;}
template<class T>T sum(const initializer_list<T> &V){T r=0;for(auto x:V)r+=x;return r;}


//#include <atcoder/all>
//#include "atcoder/lazysegtree.hpp"
//using namespace atcoder;


//--------------------------------------------------------------------













long long extgcd(long long a,long long b,long long &x,long long &y){
    if(b == 0){
        x = 1;
        y = 0;
        return a;
    }
    long long d = extgcd(b,a % b,y,x);
    y -= a / b * x;
    return d;
}

long long modinv(long long a,long long p){
    long long b = p, u = 1, v = 0;
    while(b){
        long long t = a / b;
        a -= t * b;std::swap(a, b);
        u -= t * v;std::swap(u, v);
    }
    u %= p;
    if(u < 0)u += p;
    return u;
}



/**
 * @brief garner precalc
 * @return long long 
 */
long long pregarner(std::vector<long long> &rems,std::vector<long long> &mods,long long MOD){
    assert(rems.size() == mods.size());
    for(int i = 0;i < int(rems.size());i++){
        for(int j = 0;j < i;j++){
            long long g = std::gcd(mods[i],mods[j]);
            if((rems[i] - rems[j]) % g != 0)return -1;
            mods[i] /= g;mods[j] /= g;
            long long gi = std::gcd(g,mods[i]),gj = g / gi;
            do{
                g = std::gcd(gi,gj);
                gi *= g;gj /= g;
            }while(g != 1);
            mods[i] *= gi;mods[j] *= gj;
            rems[i] %= mods[i];rems[j] %= mods[j];
        }
    }
    long long res = 1;
    for(long long &a : mods)res = res * a % MOD;
    return res;
}

/**
 * @brief returns a integer where rems[i](mod.mods[i]).
 * @return long long 
 */
long long garner(std::vector<long long> rems,std::vector<long long> mods,long long MOD){
    assert(rems.size() == mods.size());
    mods.push_back(MOD);
    int sz = mods.size();
    std::vector<long long> cof(sz,1LL),con(sz,0LL);
    for(int i = 0;i < sz - 1;i++){
        long long cur = (rems[i] - con[i]) * modinv(cof[i],mods[i]) % mods[i];
        if(cur < 0)cur += mods[i];
        for(int j = i + 1;j < sz;j++){
            con[j] = (con[j] + cur * cof[j]) % mods[j];
            cof[j] = cof[j] * mods[i] % mods[j];
        }
    }
    return con.back();
}










template<long long MOD = 1000000007>
struct modint {
    using mint = modint<MOD>;
    long long x;
    modint(long long a = 0):x((a % MOD + MOD) % MOD){}
    inline constexpr modint operator-()const noexcept{return modint(-x);}
    inline constexpr modint &operator+=(const modint &a)noexcept{
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    inline constexpr modint &operator-=(const modint &a)noexcept{
        if ((x -= a.x) < 0) x += MOD;
        return *this;
    }
    inline constexpr modint &operator*=(const modint &a)noexcept{
        (x *= a.x) %= MOD;
        return *this;
    }
    inline constexpr modint &operator++()noexcept{
        x++;
        if(x == MOD)x = 0;
        return *this;
    }
    inline constexpr modint operator++(int)noexcept{
        modint res(*this);
        operator++();
        return res;
    }
    inline constexpr modint &operator--()noexcept{
        x--;
        if(x == -1)x = MOD - 1;
        return *this;
    }
    inline constexpr modint operator--(int)noexcept{
        modint res(*this);
        operator--();
        return res;
    }
    inline constexpr modint operator+(const modint &a)const noexcept{
        modint res(*this);
        return res += a;
    }
    inline constexpr modint operator-(const modint &a)const noexcept{
        modint res(*this);
        return res -= a;
    }
    inline constexpr modint operator*(const modint &a)const noexcept{
        modint res(*this);
        return res *= a;
    }
    inline constexpr modint inv()const{
        long long a = x,b = MOD,u = 1,v = 0;
        while(b){
            long long t = a / b;
            a -= t * b;std::swap(a,b);
            u -= t * v;std::swap(u,v);
        }
        return u;
    }
    inline constexpr modint &operator/=(const modint &a)noexcept{return (*this) *= a.inv();}
    inline constexpr modint operator/(const modint &a)const noexcept{
        modint res(*this);
        return res /= a;
    }
    inline constexpr bool operator==(const modint &a)const noexcept{return x == a.x;}
    friend std::istream &operator>>(std::istream &is,modint &a) {
        is >> a.x;
        a.x = (a.x % MOD + MOD) % MOD;
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os,const modint &a){
        os << a.x;
        return os;
    }
    long long getmod(){return MOD;}
    friend mint modpow(mint a,long long b)noexcept{
        mint res(1);
        while(b){
            if(b & 1)res *= a;
            a *= a;
            b >>= 1;
        }
        return res;
    }
};
//using mint = modint<1'000'000'007>::mint;




//ex. (2013265921,137,27),(998244353,31,23),(469762049,30,26)
template<long long MOD,int base,int max_exp>
struct NTT_primitive{
    using mint = modint<MOD>;
    std::vector<mint> bases,invs;
    NTT_primitive(){
        bases.resize(max_exp + 1);invs.resize(max_exp + 1);
        bases[max_exp] = base;
        invs[max_exp] = mint(base).inv();
        for(int i = max_exp - 1;i >= 0;i--){
            bases[i] = bases[i + 1] * bases[i + 1];
            invs[i] = invs[i + 1] * invs[i + 1];
        }
    }
    void dft(std::vector<mint>& vec,int t){
        int sz = vec.size();
        if(sz == 1)return;
        std::vector<mint> veca,vecb;
        for(int i = 0;i < sz / 2;i++){
            veca.push_back(vec[i * 2]);
            vecb.push_back(vec[i * 2 + 1]);
        }
        dft(veca,t);
        dft(vecb,t);
        
        int e = __builtin_ffsll(sz) - 1;
        mint now = 1,zeta = (t == 1 ? bases[e]:invs[e]);
        for(int i = 0;i < sz;i++){
            vec[i] = veca[i % (sz / 2)] + now * vecb[i % (sz / 2)];
            now *= zeta;
        }
    }
    std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
        assert(A.size() == B.size());
        int sz = 1;
        while(sz < int(A.size() + B.size()))sz <<= 1;
        std::vector<mint> f(sz),g(sz);
        for(int i = 0;i < int(A.size());i++){
            f[i] = A[i];
            g[i] = B[i];
        }
        dft(f,1);dft(g,1);
        for(int i = 0;i < sz;i++)f[i] = f[i] * g[i];
        dft(f,-1);
        mint inv = mint(sz).inv();
        for(int i = 0;i < sz;i++)f[i] *= inv;
        return f;
    }
    void dft(std::vector<long long>& vec,int t){
        int sz = vec.size();
        if(sz == 1)return;
        std::vector<long long> veca,vecb;
        for(int i = 0;i < sz / 2;i++){
            veca.push_back(vec[i * 2]);
            vecb.push_back(vec[i * 2 + 1]);
        }
        dft(veca,t);
        dft(vecb,t);
        
        int e = __builtin_ffsll(sz) - 1;
        long long now = 1,zeta = (t == 1 ? bases[e].x:invs[e].x);
        for(int i = 0;i < sz;i++){
            vec[i] = (veca[i % (sz / 2)] + now * vecb[i % (sz / 2)] % MOD) % MOD;
            now = now * zeta % MOD;
        }
    }
    std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
        assert(A.size() == B.size());
        int sz = 1;
        while(sz < int(A.size() + B.size()))sz <<= 1;
        std::vector<long long> f(sz),g(sz);
        for(int i = 0;i < int(A.size());i++){
            f[i] = A[i] % MOD;
            g[i] = B[i] % MOD;
        }
        dft(f,1);dft(g,1);
        for(int i = 0;i < sz;i++)f[i] = f[i] * g[i] % MOD;
        dft(f,-1);
        long long inv = modinv(sz,MOD);
        for(int i = 0;i < sz;i++)f[i] = f[i] * inv % MOD;
        return f;
    }
};





template<long long MOD>
struct NTT_all{
    NTT_primitive<2013265921,137,27> ntt1;
    NTT_primitive<998244353,31,23> ntt2;
    NTT_primitive<469762049,30,26> ntt3;
    using mint = modint<MOD>;
    using mint1 = modint<2013265921>;
    using mint2 = modint<998244353>;
    using mint3 = modint<469762049>;
    NTT_all(){}
    
    std::vector<mint> convolution(const std::vector<mint>& A,const std::vector<mint>& B){
        assert(A.size() == B.size());
        int sz = A.size();
        std::vector<mint1> A1(sz),B1(sz);
        std::vector<mint2> A2(sz),B2(sz);
        std::vector<mint3> A3(sz),B3(sz);
        for(int i = 0;i < sz;i++){
            A1[i] = A[i].x;A2[i] = A[i].x;A3[i] = A[i].x;
            B1[i] = B[i].x;B2[i] = B[i].x;B3[i] = B[i].x;
        }
        auto C1 = ntt1.convolution(A1,B1);
        auto C2 = ntt2.convolution(A2,B2);
        auto C3 = ntt3.convolution(A3,B3);
        int rs = C1.size();
        std::vector<mint> res(rs);
        for(int i = 0;i < rs;i++){
            std::vector<long long> r = {C1[i].x,C2[i].x,C3[i].x},m = {2013265921,998244353,469762049};
            res[i] = garner(r,m,MOD);
        }
        return res;
    }
    std::vector<long long> convolution(const std::vector<long long>& A,const std::vector<long long>& B){
        assert(A.size() == B.size());
        int sz = A.size();
        std::vector<long long> A1(sz),B1(sz),A2(sz),B2(sz),A3(sz),B3(sz);
        for(int i = 0;i < sz;i++){
            A1[i] = A[i] % 2013265921;B1[i] = B[i] % 2013265921;
            A2[i] = A[i] % 998244353;B2[i] = B[i] % 998244353;
            A3[i] = A[i] % 469762049;B3[i] = B[i] % 469762049;
        }
        auto C1 = ntt1.convolution(A1,B1);
        auto C2 = ntt2.convolution(A2,B2);
        auto C3 = ntt3.convolution(A3,B3);
        int rs = C1.size();
        std::vector<long long> res(rs);
        for(int i = 0;i < rs;i++){
            std::vector<long long> r = {C1[i],C2[i],C3[i]},m = {2013265921,998244353,469762049};
            res[i] = garner(r,m,MOD) % MOD;
        }
        return res;
    }
};



int main(){
    myset();
    NTT_all<mod1> ntt;
    using mint = NTT_all<mod1>::mint;
    int N;
    cin >> N;
    vector<mint> A(N + 1),B(N + 1);
    rep(i,N + 1)cin >> A[i];
    rep(i,N + 1)cin >> B[i];
    // reverse(all(A));reverse(all(B));
    auto C = ntt.convolution(A,B);
    mint ans = 0;
    rep(i,N + 1)ans += C[i];
    cout << ans << "\n";
    debug(A,B);
    debug(C);
}
yukicoder

結果

テストケース

ソースコード
