#996533 (C++17) No.2817 Competition

提出ソース

結果

問題	No.2817 Competition
ユーザー	GOTKAKO
提出日時	2024-07-20 09:46:43
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,515 ms / 2,000 ms
コード長	11,859 bytes
コンパイル時間	3,249 ms
コンパイル使用メモリ	229,868 KB
実行使用メモリ	16,644 KB
最終ジャッジ日時	2024-08-13 04:24:52
合計ジャッジ時間	17,384 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 5,248 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	1 ms 5,376 KB
testcase_03	AC	1,506 ms 16,516 KB
testcase_04	AC	1,498 ms 16,644 KB
testcase_05	AC	1,515 ms 16,520 KB
testcase_06	AC	1,486 ms 16,516 KB
testcase_07	AC	1,482 ms 16,516 KB
testcase_08	AC	144 ms 5,376 KB
testcase_09	AC	309 ms 6,724 KB
testcase_10	AC	485 ms 8,448 KB
testcase_11	AC	854 ms 11,648 KB
testcase_12	AC	3 ms 5,376 KB
testcase_13	AC	355 ms 7,064 KB
testcase_14	AC	551 ms 9,088 KB
testcase_15	AC	271 ms 6,144 KB
testcase_16	AC	602 ms 9,344 KB
testcase_17	AC	385 ms 7,296 KB
testcase_18	AC	1,509 ms 16,516 KB
testcase_19	AC	2 ms 5,376 KB
testcase_20	AC	2 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB

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ソースコード

raw source code

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

long long mod = 998244353;
//入力が必ずmod未満の時に使う.
struct mint{
    long long v = 0;
    mint(){} mint(int a){v = a;} mint(long long a){v = a;} mint(unsigned long long a){v = a;}
    long long val(){return v;}
    void modu(){v %= mod;}
 
    mint repeat2mint(const long long a,long long b){
        mint ret = 1,p = a;
        while(b){
            if(b&1) ret *= p;
            p *= p; b >>= 1;
        }
        return ret;
    };
 
    mint operator+(const mint b){return mint(v)+=b;}
    mint operator-(const mint b){return mint(v)-=b;}
    mint operator*(const mint b){return mint(v)*=b;}
    mint operator/(const mint b){return mint(v)/=b;}
 
    mint operator+=(const mint b){
        v += b.v; if(v >= mod) v -= mod;
        return *this;
    }
    mint operator-=(const mint b){
        v -= b.v; if(v < 0) v += mod; 
        return *this;
    }   
    mint operator*=(const mint b){v = v*b.v%mod; return *this;}
    mint operator/=(mint b){
        if(b == 0) assert(false);
        int left = mod-2;
        while(left){if(left&1) *this *= b; b *= b; left >>= 1;}
        return *this;
    }
 
    mint operator++(int){*this += 1; return *this;}
    mint operator--(int){*this -= 1; return *this;}
    bool operator==(const mint b){return v == b.v;}
    bool operator!=(const mint b){return v != b.v;}
    bool operator>(const mint b){return v > b.v;}
    bool operator>=(const mint b){return v >= b.v;}
    bool operator<(const mint b){return v < b.v;}
    bool operator<=(const mint b){return v <= b.v;}
    
    mint pow(const long long x){return repeat2mint(v,x);}
    mint inv(){return mint(1)/v;}
};
 
namespace to_fold{ //纏めて折り畳むためのやつ 苦労したが結局ほぼACLの写経.
    __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};
}
 
long long Garner(vector<long long> &A,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);
}
struct fftinfo{
    vector<mint> root,iroot,rate2,irate2,rate3,irate3;
    fftinfo(mint g){
        int rank2 = countzero(mod-1);
        root.resize(rank2+1),iroot = root;
        rate2.resize(max(0,rank2-2+1)); irate2 = rate2;
        rate3.resize(max(0,rank2-3+1)); irate3 = rate3;
 
        root[rank2] = g.pow((mod-1)>>rank2);
        iroot[rank2] = root[rank2].inv();
        for(int i=rank2-1; i>=0; i--){
            root[i] = root[i+1]*root[i+1];
            iroot[i] = iroot[i+1]*iroot[i+1];
        }
        mint mul = 1,imul = 1;
        for(int i=0; i<=rank2-2; i++){
            rate2[i] = root[i+2]*mul;
            irate2[i] = iroot[i+2]*imul;
            mul *= iroot[i+2],imul *= root[i+2];
        }
        mul = 1,imul = 1;
        for(int i=0; i<=rank2-3; i++){
            rate3[i] = root[i+3]*mul;
            irate3[i] = iroot[i+3]*imul;
            mul *= iroot[i+3],imul *= root[i+3];
        }
    }
};
mint findroot(){
    if(mod == 998244353) return mint(3);
    else if(mod == 754974721) return mint(11);
    else if(mod == 167772161) return mint(3);
    else if(mod == 469762049) return mint(3);

    long long p = mod-1;
    vector<long long> P;
    for(long long i=2; i*i<=p; i++){
        if(p%i) continue;
        while(p%i == 0) p /= i;
        P.push_back(i);
    }
    if(p != 1) P.push_back(p);
    p = mod-1;
 
    random_device rnd; mt19937 mt(rnd());
    while(true){
        mint ret = mt()%mod;
        if(ret == 1 || ret == 0) continue;
        if(ret.pow(p) != 1) continue;
 
        bool ok = true;
        for(auto check : P) if(ret.pow(p/check) == 1){ok = false; break;}
        if(ok) return ret;
    } //O(√P)らしいです.
}
void NTT(vector<mint> &A,fftinfo &info){
    int N = A.size(),ln = countzero(N);
    int dep = 0;
    while(dep < ln){
        if(ln-dep == 1){
            int p = 1<<(ln-dep-1);
            mint rot = 1;
            for(int o=0; o<(1<<dep); o++){
                int offset = o<<(ln-dep);
                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;
                }
                if(o+1 != (1<<dep)) rot *= info.rate2[countzero(~(unsigned int)o)];
            }
            dep++;
        }
        else{
            int p = 1<<(ln-dep-2);
            mint rot = 1,imag = info.root[2];
            for(int o=0; o<(1<<dep); o++){
                mint rot2 = rot*rot,rot3 = rot2*rot;
                int offset = o<<(ln-dep);
                for(int i=0; i<p; i++){
                    auto mod2 = 1ULL*mod*mod;
                    auto a0 = 1ULL*A.at(i+offset).v;
                    auto a1 = 1ULL*A.at(i+offset+p).v*rot.v;
                    auto a2 = 1ULL*A.at(i+offset+p+p).v*rot2.v;
                    auto a3 = 1ULL*A.at(i+offset+p+p+p).v*rot3.v;
                    auto a1m2a3im = 1ULL*(a1+mod2-a3+mod)%mod*imag.v;
                    auto m2a2 = mod2-a2;
                    A.at(i+offset) = (long long)((a0+a2+a1+a3)%mod);
                    A.at(i+offset+p) = (long long)((a0+a2+(2*mod2-(a1+a3)))%mod);
                    A.at(i+offset+p+p) = (long long)((a0+m2a2+a1m2a3im)%mod);
                    A.at(i+offset+p+p+p) = (long long)((a0+m2a2+(mod2-a1m2a3im))%mod);
                }
                if(o+1 != (1<<dep)) rot *= info.rate3[countzero(~(unsigned int)o)];
            }
            dep += 2;
        }
    }
}
void INTT(vector<mint> &A,fftinfo &info){
    int N = A.size(),ln = countzero(N);
 
    int dep = ln;
    while(dep){
        if(dep == 1){
            int p = 1<<(ln-dep);
            mint irot = 1;
            for(int o=0; o<(1<<(dep-1)); o++){
                int offset = o<<(ln-dep+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) = (long long)((unsigned long long)((mod+l.v-r.v)*irot.v)%mod);
                }
                if(o+1 != (1<<(dep-1))) irot *= info.irate2[countzero(~(unsigned int)o)];
            }
            dep--;
        }
        else{
            int p = 1<<(ln-dep);
            mint irot = 1,iimag = info.iroot[2];
            for(int o=0; o<(1<<(dep-2)); o++){
                mint irot2 = irot*irot,irot3 = irot2*irot;
                int offset = o<<(ln-dep+2);
                for(int i=0; i<p; i++){
                    auto a0 = 1ULL*A.at(i+offset).v,a1 = 1ULL*A.at(i+offset+p).v;
                    auto a2 = 1ULL*A.at(i+offset+p+p).v,a3 = 1ULL*A.at(i+offset+p+p+p).v;
                    auto gotyagotya = 1ULL*((mod+a2-a3)*iimag.v%mod);
                    A.at(i+offset) = (long long)((a0+a1+a2+a3)%mod);
                    A.at(i+offset+p) = (long long)((a0+(mod-a1)+gotyagotya)*irot.v%mod);
                    A.at(i+offset+p+p) = (long long)((a0+a1+(mod-a2)+(mod-a3))*irot2.v%mod);
                    A.at(i+offset+p+p+p) = (long long)((a0+(mod-a1)+(mod-gotyagotya))*irot3.v%mod);
                }
                if(o+1 != (1<<(dep-2))) irot *= info.irate3[countzero(~(unsigned int)o)];
            }
            dep -= 2;
        }
    }
}
 
vector<mint> convolutionnaive(vector<mint> &A,vector<mint> &B){
    vector<mint> ret(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);
    return ret;
}
vector<mint> convolution(vector<mint> &A,vector<mint> &B){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1,N = 1;
    if(siza == 0 || sizb == 0) return {};
    while(N <= sizc) N <<= 1;
    vector<mint> ca = A,cb = B;
    ca.resize(N),cb.resize(N);
    if(min(siza,sizb) <= 40) return convolutionnaive(A,B);
    assert((mod-1)%N == 0);
 
    mint root = findroot();
    fftinfo info(root);
    NTT(ca,info); NTT(cb,info);
    for(int i=0; i<N; i++) ca.at(i) *= cb.at(i);
    INTT(ca,info); ca.resize(sizc);
 
    mint divN = mint(N).inv();
    for(int i=0; i<sizc; i++) ca.at(i) *= divN;
    return ca;
}
vector<long long> convolution_ll(vector<long long> &A,vector<long long> &B){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
 
    unsigned long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    unsigned long long m1m2 = mod1*mod2,m2m3 = mod2*mod3,m3m1 = mod3*mod1,m1m2m3 = mod1*mod2*mod3;
    unsigned long long i1 = invgcd(m2m3,mod1).second,i2 = invgcd(m3m1,mod2).second,i3 = invgcd(m1m2,mod3).second;
    assert(sizc <= (1<<24));
 
    mod = mod1;
    vector<mint> a(siza),b(sizb);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
    vector<mint> C1 = convolution(a,b);
    mod = mod2;
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
    vector<mint> C2 = convolution(a,b);
    mod = mod3;
    for(int i=0; i<siza; i++) a.at(i) = A.at(i)%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i)%mod;
    vector<mint> C3 = convolution(a,b);
 
    vector<long long> ret(sizc);
 
    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;
}
vector<mint> convolution_llmod(vector<mint> &A,vector<mint> &B,long long memomod){
    int siza = A.size(),sizb = B.size(),sizc = siza+sizb-1;
    if(siza == 0 || sizb == 0) return {};
 
    long long mod1 = 754974721,mod2 = 167772161,mod3 = 469762049;
    assert(sizc <= (1<<24));
 
    mod = mod1;
    vector<mint> a(siza),b(sizb);
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
    vector<mint> C1 = convolution(a,b);
    mod = mod2;
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
    vector<mint> C2 = convolution(a,b);
    mod = mod3;
    for(int i=0; i<siza; i++) a.at(i) = A.at(i).v%mod;
    for(int i=0; i<sizb; i++) b.at(i) = B.at(i).v%mod;
    vector<mint> C3 = convolution(a,b);
 
    mod = memomod;
    vector<mint> ret(sizc);
    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(A,M);
    }
    return ret;
}
}
using namespace to_fold;

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

    int N; cin >> N;
    queue<vector<mint>> Q;
    for(int i=0; i<N; i++){
        long long a; cin >> a;
        Q.push({1,a%mod});
    }
    while(Q.size() > 1){
        auto A = Q.front(); Q.pop();
        auto B = Q.front(); Q.pop();
        Q.push(convolution(A,B));
    }

    auto &A = Q.front();
    mint answer = 0;
    for(int i=1; i<=N; i++) answer += A.at(i)*mint(i).pow(N-i);
    cout << answer.v << endl;
}

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結果

テストケース

ソースコード