#936732 (C++17) No.2578 Jewelry Store

提出ソース

結果

問題	No.2578 Jewelry Store
ユーザー	👑 Nachia
提出日時	2023-12-06 00:58:37
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,418 ms / 3,500 ms
コード長	6,550 bytes
コンパイル時間	1,349 ms
コンパイル使用メモリ	110,500 KB
実行使用メモリ	9,348 KB
最終ジャッジ日時	2023-12-06 00:58:49
合計ジャッジ時間	11,046 ms
ジャッジサーバーID （参考情報）	judge14 / judge13

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 6,548 KB
testcase_01	AC	2 ms 6,548 KB
testcase_02	AC	11 ms 6,548 KB
testcase_03	AC	6 ms 6,548 KB
testcase_04	AC	32 ms 6,548 KB
testcase_05	AC	5 ms 6,548 KB
testcase_06	AC	11 ms 6,548 KB
testcase_07	AC	32 ms 6,548 KB
testcase_08	AC	6 ms 6,548 KB
testcase_09	AC	32 ms 6,548 KB
testcase_10	AC	63 ms 6,548 KB
testcase_11	AC	5 ms 6,548 KB
testcase_12	AC	7 ms 6,548 KB
testcase_13	AC	5 ms 6,548 KB
testcase_14	AC	5 ms 6,548 KB
testcase_15	AC	5 ms 6,548 KB
testcase_16	AC	63 ms 6,548 KB
testcase_17	AC	32 ms 6,548 KB
testcase_18	AC	5 ms 6,548 KB
testcase_19	AC	18 ms 6,548 KB
testcase_20	AC	32 ms 6,548 KB
testcase_21	AC	32 ms 6,548 KB
testcase_22	AC	9 ms 6,548 KB
testcase_23	AC	17 ms 6,548 KB
testcase_24	AC	7 ms 6,548 KB
testcase_25	AC	10 ms 6,548 KB
testcase_26	AC	8 ms 6,548 KB
testcase_27	AC	115 ms 6,548 KB
testcase_28	AC	193 ms 6,548 KB
testcase_29	AC	189 ms 6,548 KB
testcase_30	AC	266 ms 6,548 KB
testcase_31	AC	115 ms 6,548 KB
testcase_32	AC	84 ms 6,784 KB
testcase_33	AC	102 ms 6,548 KB
testcase_34	AC	131 ms 6,548 KB
testcase_35	AC	34 ms 6,548 KB
testcase_36	AC	105 ms 7,412 KB
testcase_37	AC	89 ms 6,548 KB
testcase_38	AC	99 ms 6,548 KB
testcase_39	AC	93 ms 6,548 KB
testcase_40	AC	97 ms 6,548 KB
testcase_41	AC	94 ms 6,548 KB
testcase_42	AC	87 ms 6,548 KB
testcase_43	AC	109 ms 6,548 KB
testcase_44	AC	80 ms 6,548 KB
testcase_45	AC	101 ms 6,548 KB
testcase_46	AC	91 ms 6,548 KB
testcase_47	AC	552 ms 6,548 KB
testcase_48	AC	158 ms 9,348 KB
testcase_49	AC	1,418 ms 6,548 KB
testcase_50	AC	1,399 ms 6,548 KB
testcase_51	AC	84 ms 6,548 KB
testcase_52	AC	227 ms 6,548 KB
testcase_53	AC	47 ms 6,548 KB

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ソースコード

raw source code

#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <utility>
#include <queue>
#include <array>
#include <cmath>
#include <atcoder/modint>
using namespace std;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(i64 i=0; i<(i64)(n); i++)
#define repr(i,n) for(i64 i=(i64)(n)-1; i>=0; i--)
const i64 INF = 1001001001001001001;
const char* yn(bool x){ return x ? "Yes" : "No"; }
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
template<typename A> using nega_queue = priority_queue<A,vector<A>,greater<A>>;
using Modint = atcoder::static_modint<998244353>;
//#include "nachia/vec.hpp"

namespace nachia{

int Popcount(unsigned long long c) noexcept {
#ifdef __GNUC__
    return __builtin_popcountll(c);
#else
    c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));
    c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));
    c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));
    c = (c * (~0ull/257)) >> 56;
    return c;
#endif
}

// please ensure x != 0
int MsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return 63 - __builtin_clzll(x);
#else
    using u64 = unsigned long long;
    int q = (n >> 32) ? 32 : 0;
    auto m = n >> q;
    constexpr u64 hi = 0x8888'8888;
    constexpr u64 mi = 0x1111'1111;
    m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;
    m = (((m | ~(hi - (n & ~hi))) & hi) * mi) >> 31;
    q += (m & 0xf) << 2;
    q += 0x3333'3333'2222'1100 >> (((n >> q) & 0xf) << 2) & 0xf
    return q;
#endif
}

// please ensure x != 0
int LsbIndex(unsigned long long x) noexcept {
#ifdef __GNUC__
    return __builtin_ctzll(x);
#else
    return MsbIndex(x & -x);
#endif
}

}


namespace nachia{

template<class Int> Int BinaryGcd(Int a, Int b){
    if(a < 0) a = -a;
    if(b < 0) b = -b;
    if(!a || !b) return a|b;
    int q = LsbIndex(a|b);
    b >>= LsbIndex(b);
    a >>= LsbIndex(a);
    while(a!=b){
        if(a<b){ b-=a; b>>=LsbIndex(b); }
        else{ a-=b; a>>=LsbIndex(a); }
    }
    return a<<q;
}

}
#include <initializer_list>

namespace nachia{

bool IsPrime(unsigned long long x) noexcept {
    if(x <= 1) return false;
    if(x % 2 == 0) return x == 2;
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 d = x-1;
    int s = 0;
    int q = 63;
    while(!(d&1)){ d >>= 1; s++; }
    while(!(d >> q)) q--;
    u64 r = x; for(int t=0; t<6; t++) r*=2-r*x;
    u128 n2 = -(u128)x % x;
    auto red = [=](u128 t) noexcept -> u64 {
        t = (t + (u128)((u64)t*-r)*x) >> 64;
        return (t >= x) ? t-x : t;
    };
    u64 one = red(n2);
    for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){
        if(base%x==0) continue;
        u64 a = base = red(base%x*n2);
        for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); }
        if(a == one) continue;
        for(int t=1; t<s&&a!=x-one; t++) a = red((u128)a*a);
        if(a != x-one) return false;
    }
    return true;
}

} // namespace nachia

namespace nachia{

std::vector<std::pair<unsigned long long, int>> Factorize(unsigned long long x){
    if(x == 1) return {};
    if(IsPrime(x)) return {{x,1}};
    using u64 = unsigned long long;
    using u128 = __uint128_t;
    u64 X = x;
    std::vector<u64> p;
    for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; }
    u64 r=1; u128 n2=1;
    auto updX = [&](){
        r = x; for(int t=0; t<6; t++) r*=2-r*x;
        n2 = -(u128)x % x;
    };
    auto red = [&](u128 t) noexcept -> u64 {
        u64 s = ((u128)x*((u64)t*r)) >> 64;
        u64 t2 = t >> 64;
        return t2-s + (t2 < s ? x : 0);
    };
    auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); };
    auto gcd = [](u64 a, u64 b) noexcept {
        if(!a || !b) return a|b;
        int q = LsbIndex(a|b);
        b >>= LsbIndex(b);
        a >>= LsbIndex(a);
        while(a!=b){
            if(a<b){ b-=a; b>>=LsbIndex(b); }
            else{ a-=b; a>>=LsbIndex(a); }
        }
        return a<<q;
    };
    static u64 v = 7001;
    p.push_back(x);
    for(int pi=p.size()-1; pi<(int)p.size(); pi++) while(p[pi] != 1 && !IsPrime(p[pi])){
        x = p[pi]; updX();
        while(p[pi] == x){
            v^=v<<13; v^=v>>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916
            u64 c = red(v); if(c == 0) continue;
            auto f = [=](u64 a) noexcept -> u64 { return red((u128)a*a+c); };
            u64 a=0, b=f(a);
            u64 buf = 1, sz = 1, nx = 10;
            while(true){
                while(nx != sz && a != b){
                    buf = mult(buf, a<=b?b-a:a-b); sz++;
                    a = f(a); b = f(f(b));
                }
                u64 g = gcd(buf, x);
                if(g != 1){
                    while(p[pi] % g == 0) p[pi] /= g;
                    p.push_back(g);
                    break;
                }
                if(a == b) break;
                nx = sz * 3 / 2;
            }
        }
    }
    std::vector<std::pair<u64, int>> res;
    for(u64 q : p) if(q != 1){
        int e=0; while(X%q == 0){ e++; X/=q; }
        if(e) res.push_back({ q, e });
    }
    return res;
}

unsigned long long Totient(unsigned long long x){
    auto F = Factorize(x);
    for(auto f : F) x -= x / f.first;
    return x;
}

} // namespace nachia

void testcase(){
    int T; cin >> T;
    i64 M; cin >> M;
    auto pf = nachia::Factorize(M);
    int n = pf.size();
    vector<i64> pes(n, 1);
    rep(i,n) rep(j,pf[i].second) pes[i] *= pf[i].first;
    rep(caseid, T){
        int N; cin >> N;
        vector<Modint> W(N);
        {
            int b,c,d; cin >> b >> c >> d;
            W[0] = b;
            rep(i,N-1) W[i+1] = W[i] * c + d;
        }
        vector<i64> A(N);
        rep(i,N) cin >> A[i];
        rep(i,N) if(M % A[i] != 0){ A[i] = 1; W[i] = 0; }
        vector<Modint> F(1<<n, 1);
        rep(i,N){
            int q = 0;
            rep(b,n) if(A[i] % pes[b] == 0) q += 1 << b;
            F[q] *= W[i] + 1;
        }
        rep(d,n) rep(i,1<<n) if(i&(1<<d)) F[i] *= F[i-(1<<d)];
        rep(d,n) rep(i,1<<n) if(i&(1<<d)) F[i] -= F[i-(1<<d)];
        F[0] -= 1;
        cout << F.back().val() << endl;
    }
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    #ifdef NACHIA
    int T; cin >> T; for(int t=0; t<T; T!=++t?(cout<<'\n'),0:0)
    #endif
    testcase();
    return 0;
}

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結果

テストケース

ソースコード