#857461 (C++17) No.2264 Gear Coloring

提出ソース

結果

問題	No.2264 Gear Coloring
ユーザー	👑 Nachia
提出日時	2023-04-07 22:20:15
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	143 ms / 2,000 ms
コード長	8,649 bytes
コンパイル時間	1,339 ms
コンパイル使用メモリ	99,912 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-04-10 17:20:53
合計ジャッジ時間	2,343 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

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 6,816 KB
testcase_01	AC	2 ms 6,812 KB
testcase_02	AC	1 ms 6,816 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	3 ms 6,944 KB
testcase_06	AC	1 ms 6,944 KB
testcase_07	AC	3 ms 6,940 KB
testcase_08	AC	1 ms 6,940 KB
testcase_09	AC	2 ms 6,940 KB
testcase_10	AC	2 ms 6,940 KB
testcase_11	AC	1 ms 6,940 KB
testcase_12	AC	1 ms 6,944 KB
testcase_13	AC	2 ms 6,940 KB
testcase_14	AC	98 ms 6,944 KB
testcase_15	AC	8 ms 6,940 KB
testcase_16	AC	143 ms 6,940 KB
testcase_17	AC	4 ms 6,944 KB
testcase_18	AC	3 ms 6,940 KB
testcase_19	AC	7 ms 6,944 KB
testcase_20	AC	2 ms 6,940 KB
testcase_21	AC	2 ms 6,940 KB

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ソースコード

raw source code

#line 1 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\enumerate-divisors.hpp"
#include <vector>
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\isprime.hpp"
#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
#line 3 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\misc\\bit-operations.hpp"
#include <algorithm>

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
    int res = 0;
    for(int d=32; d>0; d>>=1) if(x >> d){ res |= d; x >>= d; }
    return res;
#endif
}

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

}

#line 5 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\factorize.hpp"
#include <utility>

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
#line 2 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\gcd.hpp"

#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\gcd.hpp"

namespace nachia{

template<class Int> Int Gcd(Int a, Int b){
    if(a < 0) a = -a;
    if(b < 0) b = -b;
    if(!a || !b) return a + b;
    while(b){ a %= b; std::swap(a, b); }
    return a;
}

}
#line 4 "D:\\Programming\\VSCode\\competitive-cpp\\nachia\\math\\enumerate-divisors.hpp"

namespace nachia{

struct EnumerateDivisors{
    using u64 = unsigned long long;
    u64 raw;
    std::vector<u64> divord;
    std::vector<int> dims;
    std::vector<int> dimcum;
    std::vector<std::pair<u64, int>> I;
    EnumerateDivisors(std::vector<std::pair<unsigned long long, int>> pf){
        raw = 1;
        int n = pf.size();
        dims.resize(n);
        dimcum.assign(n+1, 1);
        divord = {1};
        for(int i=0; i<n; i++){
            dims[i] = pf[i].second;
            dimcum[i+1] = dimcum[i] * (dims[i] + 1);
            int q = dimcum[i];
            for(int t=q; t<dimcum[i+1]; t++) divord.push_back(divord[t-q] * pf[i].first);
            for(int t=0; t<pf[i].second; t++) raw *= pf[i].first;
        }
        I.resize(divord.size());
        for(int i=0; i<dimcum.back(); i++) I[i] = std::make_pair(divord[i], i);
        std::sort(I.begin(), I.end());
    }
    int id(unsigned long long d) const {
        d = Gcd(d, raw);
        return std::lower_bound(I.begin(), I.end(), d, [](std::pair<u64, int> e, u64 v){ return e.first < v; })->second;
    }
    int numDivisors() const { return dimcum.back(); }
    unsigned long long divisor(int i){ return divord[i]; }
    template<class Elem>
    void Zeta(std::vector<Elem>& A) const {
        int Z = numDivisors();
        for(int d=0; d<(int)dims.size(); d++){
            int w = dims[d] * dimcum[d];
            int y = dimcum[d];
            for(int i=0; i<Z; i+=dimcum[d+1]){
                for(int j=0; j<w; j++) A[i+j+y] += A[i+j];
            }
        }
    }
    template<class Elem>
    void RevZeta(std::vector<Elem>& A) const {
        int Z = numDivisors();
        for(int d=0; d<(int)dims.size(); d++){
            int w = dims[d] * dimcum[d];
            int y = dimcum[d];
            for(int i=0; i<Z; i+=dimcum[d+1]){
                for(int j=w-1; j>=0; j--) A[i+j] += A[i+j+y];
            }
        }
    }
    template<class Elem>
    void Mobius(std::vector<Elem>& A) const {
        int Z = numDivisors();
        for(int d=0; d<(int)dims.size(); d++){
            int w = dims[d] * dimcum[d];
            int y = dimcum[d];
            for(int i=0; i<Z; i+=dimcum[d+1]){
                for(int j=w-1; j>=0; j--) A[i+j+y] -= A[i+j];
            }
        }
    }
    template<class Elem>
    void RevMobius(std::vector<Elem>& A) const {
        int Z = numDivisors();
        for(int d=0; d<(int)dims.size(); d++){
            int w = dims[d] * dimcum[d];
            int y = dimcum[d];
            for(int i=0; i<Z; i+=dimcum[d+1]){
                for(int j=0; j<w; j++) A[i+j] -= A[i+j+y];
            }
        }
    }
};

}
#line 2 "..\\Main.cpp"

#include <iostream>
#include <string>
#line 7 "..\\Main.cpp"
#include <atcoder/modint>
using namespace std;
using i32 = int;
using u32 = unsigned int;
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<(int)(n); i++)
const i64 INF = 1001001001001001001;

using Modint = atcoder::static_modint<998244353>;


int main(){
    int N, M; cin >> N >> M;
    vector<i64> A(N); rep(i,N) cin >> A[i];
    i64 lcm = 1;
    for(i64 a : A) lcm = lcm / nachia::Gcd(lcm, a) * a;
    auto divs = nachia::EnumerateDivisors(nachia::Factorize(lcm));
    vector<i64> cnt(divs.numDivisors());
    rep(i,cnt.size()) cnt[i] = lcm / divs.divisor(i);
    divs.RevMobius(cnt);
    Modint ans = 0;
    rep(i,cnt.size()){
        Modint tmp = cnt[i];
        i64 div = divs.divisor(i);
        for(i64 a : A) tmp *= Modint(M).pow(nachia::Gcd(div, a));
        ans += tmp;
    }
    ans /= lcm;
    cout << ans.val() << endl;
    return 0;
}



struct ios_do_not_sync{
    ios_do_not_sync(){
        ios::sync_with_stdio(false);
        cin.tie(nullptr);
    }
} ios_do_not_sync_instance;

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結果

テストケース

ソースコード