#1116475 (C++17) No.2770 Coupon Optimization

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結果

問題	No.2770 Coupon Optimization
コンテスト
ユーザー	GOTKAKO
提出日時	2025-09-01 10:05:27
言語	C++17 (gcc 13.3.0 + boost 1.87.0)
結果	AC
実行時間	344 ms / 3,000 ms
コード長	15,394 bytes
コンパイル時間	3,864 ms
コンパイル使用メモリ	241,976 KB
実行使用メモリ	38,272 KB
最終ジャッジ日時	2025-09-01 10:05:37
合計ジャッジ時間	9,931 ms
ジャッジサーバーID （参考情報）	judge2 / judge5
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 * 2
other	AC * 16
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ソースコード

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

//入力が必ず-mod<a<modの時.
template<const int mod>
struct modint{ //mod変更が不可能.
    public:
    long long v = 0;
    static void setmod(int m){} //飾り.
    static constexpr long long getmod(){return mod;}
    modint(){v = 0;} modint(int a){v = a<0?a+mod:a;} modint(long long a){v = a<0?a+mod:a;}
    modint(unsigned int a){v = a;} modint(unsigned long long a){v = a;}
    long long val()const{return v;}
 
    modint &operator=(const modint &b) = default;
    modint operator+()const{return (*this);}
    modint operator-()const{return modint(0)-(*this);}
    modint operator+(const modint b)const{return modint(v)+=b;}
    modint operator-(const modint b)const{return modint(v)-=b;}
    modint operator*(const modint b)const{return modint(v)*=b;}
    modint operator/(const modint b)const{return modint(v)/=b;}
    modint operator+=(const modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    modint operator-=(const modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    modint operator*=(const modint b){v = v*b.v%mod; return *this;}
    modint operator/=(modint b){ //b!=0 mod素数が必須.
        if(b == 0) assert(false);
        int left = mod-2;
        while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
        return *this;
    }
    modint operator++(){*this += 1; return *this;}
    modint operator--(){*this -= 1; return *this;}
    modint operator++(int){modint ret = (*this); *this += 1; return ret;}
    modint operator--(int){modint ret = (*this); *this -= 1; return ret;}
    bool operator==(const modint b)const{return v == b.v;}
    bool operator!=(const modint b)const{return v != b.v;}
    bool operator>(const modint b)const{return v > b.v;}
    bool operator>=(const modint b)const{return v >= b.v;}
    bool operator<(const modint b)const{return v < b.v;}
    bool operator<=(const modint b)const{return v <= b.v;}
    modint pow(long long n)const{
        modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    modint inv()const{return modint(1)/v;} //素数mod必須.
};
 
template<int idx> //modが入力で与えられる場合. 
struct dynamic_modint{ //mod変更が可能 最初にsetmod必須 idxで複数個所持が可能.
    private:
    static int mod;
    public:
    long long v = 0;
    static constexpr long long getmod(){return mod;}
    static void setmod(int m){
        assert(m > 0);
        mod = m;
    }
    dynamic_modint(){v = 0;}
    dynamic_modint(int a){v = a<0?a+mod:a;} dynamic_modint(long long a){v = a<0?a+mod:a;}
    dynamic_modint(unsigned int a){v = a;}
    dynamic_modint(unsigned long long a){v = a;}
    long long val()const{return v;}
 
    dynamic_modint &operator=(const dynamic_modint &b) = default;
    dynamic_modint operator+()const{return (*this);}
    dynamic_modint operator-()const{return dynamic_modint(0)-(*this);}
    dynamic_modint operator+(const dynamic_modint b)const{return dynamic_modint(v)+=b;}
    dynamic_modint operator-(const dynamic_modint b)const{return dynamic_modint(v)-=b;}
    dynamic_modint operator*(const dynamic_modint b)const{return dynamic_modint(v)*=b;}
    dynamic_modint operator/(const dynamic_modint b)const{return dynamic_modint(v)/=b;}
    dynamic_modint operator+=(const dynamic_modint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    dynamic_modint operator-=(const dynamic_modint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    dynamic_modint operator*=(const dynamic_modint b){v = v*b.v%mod; return *this;}
    dynamic_modint operator/=(dynamic_modint b){ //b!=0 mod素数が必須.
        if(b == 0) assert(false);
        int left = mod-2;
        while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
        return *this;
    }
    dynamic_modint operator++(){*this += 1; return *this;}
    dynamic_modint operator--(){*this -= 1; return *this;}
    dynamic_modint operator++(int){dynamic_modint ret = *this; *this += 1; return ret;}
    dynamic_modint operator--(int){dynamic_modint ret = *this; *this -= 1; return ret;}
    bool operator==(const dynamic_modint b)const{return v == b.v;}
    bool operator!=(const dynamic_modint b)const{return v != b.v;}
    bool operator>(const dynamic_modint b)const{return v > b.v;}
    bool operator>=(const dynamic_modint b)const{return v >= b.v;}
    bool operator<(const dynamic_modint b)const{return v < b.v;}
    bool operator<=(const dynamic_modint b)const{return v <= b.v;}
    dynamic_modint pow(long long n)const{
        dynamic_modint ret = 1,p = v;
        if(n < 0) p = p.inv(),n = -n;
        while(n){
            if(n&1) ret *= p;
            p *= p; n >>= 1;
        }
        return ret;
    }
    dynamic_modint inv()const{return dynamic_modint(1)/v;} //素数mod必須.
};
template<int idx> int dynamic_modint<idx>::mod=998244353;
using mint = modint<998244353>; const long long mod = 998244353;
//using mint = modint<1000000007>; const long long mod = 1000000007;
//using mint = dynamic_modint<0>;

namespace to_fold{
__int128_t safemod(__int128_t a,long long m){a %= m; if(a < 0) a += m; return a;}
pair<long long,long long> invgcd(long long a,long long b){
    //return {gcd(a,b),x} (xa≡g(mod b))
    a = safemod(a,b);
    if(a == 0) return {b,0};
    long long x = 0,y = 1,memob = b;
    while(a){
        long long q = b/a;
        b -= a*q;
        swap(x,y); y -= q*x;
        swap(a,b);
    }
    if(x < 0) x += memob/b;
    return {b,x};
}
template<long long mod>
long long Garner(const vector<long long> &A,const vector<long long> &M){
    __int128_t mulM = 1,x = A.at(0)%M.at(0); //Mの要素のペア互いに素必須.
    for(int i=1; i<A.size(); i++){
        //assert(gcd(mulM,M.at(i-1)) == 1);
        mulM *= M.at(i-1); //2乗がオーバーフローする時__int128_t
        long long t = safemod((A.at(i)-x)*invgcd(mulM,M.at(i)).second,M.at(i));
        x += t*mulM;
    }
    return x%mod;
}
int countzero(unsigned long long x){
    if(x == 0) return 64;
    else return __popcount((x&-x)-1);
}
template<typename mint>
struct fftinfo{
    static bool First;
    static mint g,sum_e[30],sum_ie[30]; //sum_e[i]=Π[j=0~i-1]ies[j] * es[i],sum_ie[i]=Π[i=0~j-1]es[j] * ies[i].
    static mint divpow2[30]; //div[i] = 1/(2^i).
    static mint Zeta[30];
    fftinfo(){
        if(!First) return;
        First = false;
        const long long mod = mint::getmod();
        if(mod == 998244353) g = 3;
        else if(mod == 754974721) g = 11;
        else if(mod == 167772161) g = 3;
        else if(mod == 469762049) g = 3;
        else assert(false); //現状RE.
        mint es[30],ies[30]; //es[i]^(2^(2+i))=1.
        int cnt2 = countzero(mod-1);
        mint e = g.pow((mod-1)>>cnt2),ie = e.inv();
        for(int i=cnt2; i>=2; i--){ //e^(2^i)=1;
            es[i-2] = e,e *= e;
            ies[i-2] = ie,ie *= ie;
        }
        mint rot = 1;
        for(int i=0; i<=cnt2-2; i++) sum_e[i] = es[i]*rot,rot *= ies[i];
        rot = 1;
        for(int i=0; i<=cnt2-2; i++) sum_ie[i] = ies[i]*rot,rot *= es[i];
        mint div2n = 1,div2 = mint(1)/2;
        for(int i=0; i<30; i++) divpow2[i] = div2n,div2n *= div2;
        for(int i=0; i<=cnt2; i++) Zeta[i] = g.pow((mod-1)/(2<<i));
    }
};
template<typename mint> bool fftinfo<mint>::First=true;
template<typename mint> mint fftinfo<mint>::g;
template<typename mint> mint fftinfo<mint>::sum_e[30];
template<typename mint> mint fftinfo<mint>::sum_ie[30];
template<typename mint> mint fftinfo<mint>::divpow2[30];
template<typename mint> mint fftinfo<mint>::Zeta[30];
template<typename mint>
void NTT(vector<mint> &A){ //ACLを超参考にしてる.
    int n = A.size();
    assert((n&-n) == n);
    fftinfo<mint> info;
    int h = countzero(n);
    for(int ph=1; ph<=h; ph++){
        int w = 1<<(ph-1),p = 1<<(h-ph);
        mint rot = 1;
        for(int s=0; s<w; s++){
            int offset = s<<(h-ph+1);
            for(int i=0; i<p; i++){
                mint l = A.at(i+offset),r = A.at(i+offset+p)*rot;
                A.at(i+offset) = l+r;
                A.at(i+offset+p) = l-r;
            }
            rot *= info.sum_e[countzero(~(unsigned int)(s))];
        }
    }
}
template<typename mint>
void INTT(vector<mint> &A){
    int n = A.size();
    assert((n&-n) == n);
    fftinfo<mint> info;
    const unsigned int mod = mint::getmod();
    int h = countzero(n);
    for(int ph=h; ph>0; ph--){
        int w = 1<<(ph-1),p = 1<<(h-ph);
        mint irot = 1;
        for(int s=0; s<w; s++){
            int offset = s<<(h-ph+1);
            for(int i=0; i<p; i++){
                mint l = A.at(i+offset),r = A.at(i+offset+p);
                A.at(i+offset) = l+r;
                A.at(i+offset+p) = ((unsigned long long)(mod+(unsigned int)l.v-(unsigned int)r.v)*irot.v)%mod;
            }
            irot *= info.sum_ie[countzero(~(unsigned int)(s))];
        }
    }
    mint divn = info.divpow2[h];
    for(auto &a : A) a *= divn;
}
template<typename mint>
vector<mint> convolution(vector<mint> A,vector<mint> B){ //mintじゃないのを突っ込まないように!!!.
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1,N = 1;
    if(siza == 0 || sizb == 0) return {};
    if(min(siza,sizb) <= 60){ //naive.
        vector<mint> ret(sizc);
        if(siza >= sizb){for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);}
        else{for(int i=0; i<sizb; i++) for(int k=0; k<siza; k++) ret.at(i+k) += B.at(i)*A.at(k);}
        return ret;
    }
    while(N < sizc) N <<= 1;
    A.resize(N),B.resize(N);
    NTT(A); NTT(B);
    for(int i=0; i<N; i++) A.at(i) *= B.at(i);
    INTT(A); A.resize(sizc);
    return A;
}
vector<long long> convolution_ll(const vector<long long> &A,const vector<long long> &B){ //long longに収まる範囲.
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
    vector<long long> ret(sizc);
    if(min(siza,sizb) <= 200){ //naive 200はやばい?.
        vector<long long> ret(sizc);
        if(siza >= sizb){for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);}
        else{for(int i=0; i<sizb; i++) for(int k=0; k<siza; k++) ret.at(i+k) += B.at(i)*A.at(k);}
        return ret;
    }
    const unsigned long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    const unsigned long long m1m2 = mod1*mod2,m2m3 = mod2*mod3,m3m1 = mod3*mod1,m1m2m3 = mod1*mod2*mod3;
    const unsigned long long i1 = invgcd(m2m3,mod1).second,i2 = invgcd(m3m1,mod2).second,i3 = invgcd(m1m2,mod3).second;
    assert(sizc <= (1<<24));
    using mint1 = modint<mod1>;
    using mint2 = modint<mod2>;
    using mint3 = modint<mod3>;
    vector<mint1> a1(siza),b1(sizb);
    vector<mint2> a2(siza),b2(sizb);
    vector<mint3> a3(siza),b3(sizb);
    for(int i=0; i<siza; i++) a1.at(i) = A.at(i)%mod1;
    for(int i=0; i<sizb; i++) b1.at(i) = B.at(i)%mod1;
    vector<mint1> C1 = convolution(a1,b1);
    for(int i=0; i<siza; i++) a2.at(i) = A.at(i)%mod2;
    for(int i=0; i<sizb; i++) b2.at(i) = B.at(i)%mod2;
    vector<mint2> C2 = convolution(a2,b2);
    for(int i=0; i<siza; i++) a3.at(i) = A.at(i)%mod3;
    for(int i=0; i<sizb; i++) b3.at(i) = B.at(i)%mod3;
    vector<mint3> C3 = convolution(a3,b3);
    vector<unsigned long long> offset = {0,0,m1m2m3,2*m1m2m3,3*m1m2m3};
    for(int i=0; i<sizc; i++){
        unsigned long long x = 0;
        x += (C1.at(i).v*i1)%mod1*m2m3;
        x += (C2.at(i).v*i2)%mod2*m3m1;
        x += (C3.at(i).v*i3)%mod3*m1m2;
        long long diff = C1.at(i).v-((long long)x+(long long)mod1)%mod1;
        if(diff < 0) diff += mod1;
        x -= offset.at(diff%5);
        ret.at(i) = x;
    }
    return ret;
}
template<typename mint>
vector<mint> convolution_llmod(const vector<mint> &A,const vector<mint> &B){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
    vector<mint> ret(sizc);
    if(min(siza,sizb) <= 200){
        for(int i=0; i<siza; i++) for(int k=0; k<sizb; k++) ret.at(i+k) += A.at(i)*B.at(k);
        return ret;
    }
    const long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    assert(sizc <= (1<<24));
    using mint1 = modint<mod1>;
    using mint2 = modint<mod2>;
    using mint3 = modint<mod3>;
    vector<mint1> a1(siza),b1(sizb);
    vector<mint2> a2(siza),b2(sizb);
    vector<mint3> a3(siza),b3(sizb);
    for(int i=0; i<siza; i++) a1.at(i) = A.at(i).v%mod1;
    for(int i=0; i<sizb; i++) b1.at(i) = B.at(i).v%mod1;
    vector<mint1> C1 = convolution(a1,b1);
    for(int i=0; i<siza; i++) a2.at(i) = A.at(i).v%mod2;
    for(int i=0; i<sizb; i++) b2.at(i) = B.at(i).v%mod2;
    vector<mint2> C2 = convolution(a2,b2);
    for(int i=0; i<siza; i++) a3.at(i) = A.at(i).v%mod3;
    for(int i=0; i<sizb; i++) b3.at(i) = B.at(i).v%mod3;
    vector<mint3> C3 = convolution(a3,b3);
    for(int i=0; i<sizc; i++){
        vector<long long> A = {C1.at(i).v,C2.at(i).v,C3.at(i).v};
        vector<long long> M = {mod1,mod2,mod3};
        ret.at(i) = Garner<mint::getmod()>(A,M);
    }
    return ret;
}
vector<int> convolution_int(const vector<int> &A,const vector<int> &B){ //intに収まる範囲.
    if(A.size() == 0 || B.size() == 0) return {};
    vector<int> ret;
    if(min(A.size(),B.size()) <= 60){
        ret.resize(A.size()+B.size()-1);
        for(int i=0; i<A.size(); i++) for(int k=0; k<B.size(); k++) ret.at(i+k) += A.at(i)*B.at(k);
    }
    else{
        using mint1 = modint<998244353>;
        vector<mint1> X(A.size()),Y(B.size()),Z;
        for(int i=0; i<A.size(); i++) X.at(i) = A.at(i);
        for(int i=0; i<B.size(); i++) Y.at(i) = B.at(i);
        Z = convolution(X,Y);
        ret.resize(Z.size());
        for(int i=0; i<Z.size(); i++) ret.at(i) = Z.at(i).v;
    }
    return ret;
}
template<typename mint> 
void NTTdoubling(vector<mint> &A){ //NTTの原理を忘れているため何やってるのか意味が分からない NTT-friendly専用.
        //INTT->resize(2倍）->NTTの代わりにcopy->INTT->謎の操作->NTT->push sizeが小さい時は効率悪いらしいよ.
        int n = A.size();
        fftinfo<mint> info;
        vector<mint> B = A;
        INTT(B);
        mint rot = 1,zeta = info.Zeta[countzero(n)];
        for(auto &v : B) v *= rot,rot *= zeta;
        NTT(B); A.reserve(n<<1);
        for(auto &v : B) A.push_back(v); 
}
bool isNTTfriendly(long long mod){
    if(mod == 998244353 || mod == 754974721 || mod == 16777216 || mod == 469762049) return true;
    return false; //現状false 原子根求める機能を追加してから.
    int have2 = countzero(mod-1);
    return have2 >= 20;//とりあえず2^20でokとする;
}
}
using namespace to_fold;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);

    int N,M; cin >> N >> M;
    vector<long long> A(N),B(M);
    for(auto &a : A) cin >> a,a /= 100;
    for(auto &b : B) cin >> b;
    sort(A.begin(),A.end());
    sort(B.rbegin(),B.rend());
    while(B.size() < N) B.push_back(0);
    while(B.size() > N) B.pop_back();

    vector<long long> C = convolution_ll(A,B);
    long long answer = 0;
    for(int i=0; i<N; i++){
        answer += A.at(i)*100;
        cout << answer-C.at(i) << "\n";
    }
}
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結果

ソースコード
