結果

問題 No.2075 GCD Subsequence
コンテスト
ユーザー Demystify
提出日時 2022-09-16 22:49:52
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 13,535 bytes
コンパイル時間 1,943 ms
コンパイル使用メモリ 194,480 KB
最終ジャッジ日時 2025-02-07 10:22:30
ジャッジサーバーID
（参考情報） 		judge2 / judge1
このコードへのチャレンジ
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。（リジャッジ後のコンパイルエラーは公開されます）
ただし、clay言語の場合は開発者のデバッグのため、公開されます。

コンパイルメッセージ
main.cpp: In instantiation of ‘void print(const T&) [with T = atcoder::static_modint<998244353>]’:
main.cpp:285:10:   required from here
main.cpp:67:49: error: no match for ‘operator<<’ (operand types are ‘std::ostream’ {aka ‘std::basic_ostream<char>’} and ‘const atcoder::static_modint<998244353>’)
   67 | template<class T> void print(const T& a) { cout << a << '\n'; }
      |                                            ~~~~~^~~~
In file included from /usr/include/c++/13/istream:41,
                 from /usr/include/c++/13/sstream:40,
                 from /usr/include/c++/13/complex:45,
                 from /usr/include/c++/13/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:127,
                 from main.cpp:1:
/usr/include/c++/13/ostream:110:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ostream_type& (*)(__ostream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>]’
  110 |       operator<<(__ostream_type& (*__pf)(__ostream_type&))
      |       ^~~~~~~~
/usr/include/c++/13/ostream:110:36: note:   no known conversion for argument 1 from ‘const atcoder::static_modint<998244353>’ to ‘std::basic_ostream<char>::__ostream_type& (*)(std::basic_ostream<char>::__ostream_type&)’ {aka ‘std::basic_ostream<char>& (*)(std::basic_ostream<char>&)’}
  110 |       operator<<(__ostream_type& (*__pf)(__ostream_type&))
      |                  ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/13/ostream:119:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ios_type& (*)(__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>; __ios_type = std::basic_ios<char>]’
  119 |       operator<<(__ios_type& (*__pf)(__ios_type&))
      |       ^~~~~~~~

ソースコード

diff #
raw source code 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
// --------------------------------------------------------
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort(RALL(c))
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define COUNT(c,v) count(ALL(c),(v))
#define SZ(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) __builtin_popcountll(b)
#define P0(i) (((i) & 1) == 0)
#define P1(i) (((i) & 1) == 1)
#define LB(c,v) distance((c).begin(), lower_bound(ALL(c), (v)))
#define UB(c,v) distance((c).begin(), upper_bound(ALL(c), (v)))
#define UQ(c) SORT(c), (c).erase(unique(ALL(c)), (c).end())
#define END(...) do { print(__VA_ARGS__); exit(0); } while (0)
#define elif else if
template<class T> using PQ_max = priority_queue<T>;
template<class T> using PQ_min = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = (1 << 30) - 1;   // 1073741824 - 1
constexpr ll INF = (1LL << 62) - 1;  // 4611686018427387904 - 1
#ifdef _LOCAL
    #define debug_bar cerr << "----------------------------------------\n";
    #define debug_header cerr << "[" << __FUNCTION__ << ":" << __LINE__ << "] "
    #define debug(...) do { debug_header; cerr << #__VA_ARGS__ << " = "; view(__VA_ARGS__); cerr << '\n'; } while (0)
    #define debug2(vv) do { debug_header; cerr << #vv << " = [\n"; view2d(vv); cerr << "  ]\n"; } while (0)
    #define debug3(vvv) do { debug_header; cerr << #vvv << " = [\n"; view3d(vvv); cerr << "  ]\n"; } while (0)
    void view() {}
    void view(const int& a) { if (abs(a) == inf) { cerr << "+-"[signbit(a)] << "inf"; } else { cerr << a; } }
    void view(const ll& a) { if (abs(a) == INF) { cerr << "+-"[signbit(a)] << "INF"; } else { cerr << a; } }
    template<class T> void view(const T& a) { cerr << a; }
    template<class P1, class P2> void view(const pair<P1, P2>& a) { cerr << "("; view(a.first); cerr << ", "; view(a.second); cerr << ")"; }
    template<class T1, class T2, class T3> void view(const tuple<T1, T2, T3>& a) { cerr << "("; view(get<0>(a)); cerr << ", "; view(get<1>(a)); cerr << ", "; view(get<2>(a)); cerr << ")"; }
    template<class T1, class T2, class T3, class T4> void view(const tuple<T1, T2, T3, T4>& a) { cerr << "("; view(get<0>(a)); cerr << ", "; view(get<1>(a)); cerr << ", "; view(get<2>(a)); cerr << ", "; view(get<3>(a)); cerr << ")"; }
    template<class T> void view(const vector<T>& v){ cerr << "["; for (int i = 0; i < (int)v.size(); i++) { if (i) { cerr << ", "; } view(v[i]); } cerr << "]"; }
    template<class T> void view(const vector<vector<T>>& vv){ cerr << "["; for (int i = 0; i < (int)vv.size(); i++) { if (i) { cerr << ", "; } view(vv[i]); } cerr << "]"; }
    template<class K, class V> void view(const map<K, V>& mp){ cerr << "["; for (auto it = mp.begin(); it != mp.end(); it++) { if (it != mp.begin()) { cerr << ", "; } cerr << "("; view(it->first); cerr << ", "; view(it->second); cerr << ")"; } cerr << "]"; }
    template<class K, class V> void view(const multimap<K, V>& mmp){ cerr << "["; for (auto it = mmp.begin(); it != mmp.end(); it++) { if (it != mmp.begin()) { cerr << ", "; } cerr << "("; view(it->first); cerr << ", "; view(it->second); cerr << ")"; } cerr << "]"; }
    template<class T> void view(const set<T>& s){ cerr << "["; for (auto it = s.begin(); it != s.end(); it++) { if (it != s.begin()) { cerr << ", "; } view(*it); } cerr << "]"; }
    template<class T> void view(const multiset<T>& ms){ cerr << "["; for (auto it = ms.begin(); it != ms.end(); it++) { if (it != ms.begin()) { cerr << ", "; } view(*it); } cerr << "]"; }
    template<class T> void view(const deque<T>& d){ cerr << "(front)<-["; for (auto it = d.begin(); it != d.end(); it++) { if (it != d.begin()) { cerr << ", "; } view(*it); } cerr << "]"; }
    template<class T> void view(stack<T> s){ vector<T> v; while (not s.empty()) { v.push_back(s.top()); s.pop(); } reverse(v.begin(), v.end()); view(v); cerr << "->(top)"; }
    template<class T> void view(queue<T> q){ vector<T> v; while (not q.empty()) { v.push_back(q.front()); q.pop(); } cerr << "(front)<-"; view(v); }
    template<class T> void view(PQ_max<T> pq){ vector<T> v; while (not pq.empty()) { v.push_back(pq.top()); pq.pop(); } cerr << "(top)<-"; view(v); }
    template<class T> void view(PQ_min<T> pq){ vector<T> v; while (not pq.empty()) { v.push_back(pq.top()); pq.pop(); } cerr << "(top)<-"; view(v); }
    template<class T> void view2d(const vector<vector<T>>& vv){ for (int i = 0; i < (int)vv.size(); i++) { cerr << "    "; view(vv[i]); cerr << ",\n"; } }
    template<class T> void view3d(const vector<vector<vector<T>>>& vvv) { for (int i = 0; i < (int)vvv.size(); i++) { for (int j = 0; j < (int)vvv[i].size(); j++) { cerr << "    " << " ["[j == 0]; view(vvv[i][j]); if (j == (int)vvv[i].size() - 1) { cerr << "]"; } cerr << ",\n"; } if (i < (int)vvv.size() - 1) { cerr << "\n"; } } }
    template<class T, class... Ts> void view(const T& a, const Ts&... b) { view(a); cerr << ", "; view(b...); }
#else
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(...)
    #define debug2(vv)
    #define debug3(vvv)
#endif
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> T SUM(const vector<T>& A) { return accumulate(ALL(A), T(0)); }
template<class T> vector<T> cumsum(const vector<T>& A, bool offset = false) { int N = A.size(); vector<T> S(N+1, 0); for (int i = 0; i < N; i++) { S[i+1] = S[i] + A[i]; } if (not offset) { S.erase(S.begin()); } return S; }
template<class T> string to_binary(T x, int B) { string s; while (x) { s += ('0' + (x & 1)); x >>= 1; } while ((int)s.size() < B) { s += '0'; } reverse(s.begin(), s.end()); return s; }
ll mod(ll x, ll m) { assert(m != 0); return (x % m + m) % m; }
ll ceil(ll a, ll b) { if (b < 0) { return ceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll floor(ll a, ll b) { if (b < 0) { return floor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll powint(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = powint(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
pair<ll,ll> divmod(ll a, ll b) { assert(b != 0); ll q = floor(a, b); return make_pair(q, a - q * b); }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digit_len(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll digit_sum(ll n) { assert(n >= 0); ll sum = 0; while (n > 0) { sum += n % 10; n /= 10; } return sum; }
ll digit_prod(ll n) { assert(n >= 0); if (n == 0) { return 0; } ll prod = 1; while (n > 0) { prod *= n % 10; n /= 10; } return prod; }
ll xor_sum(ll x) { assert(0 <= x); switch (x % 4) { case 0: return x; case 1: return 1; case 2: return x ^ 1; case 3: return 0; } assert(false); }
string toupper(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = toupper(T[i]); } return T; }
string tolower(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = tolower(T[i]); } return T; }
int a2i(const char& c) { assert(islower(c)); return (c - 'a'); }
int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); }
int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); }
char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); }
char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); }
char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); }
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VLD = vector<ld>;
using VVLD = vector<VLD>;
using VVVLD = vector<VVLD>;
const ld EPS = 1e-10;
const ld PI  = acosl(-1.0);
// --------------------------------------------------------
// #include <atcoder/all>
// using namespace atcoder;


#include <atcoder/modint>
using namespace atcoder;

// constexpr ll MOD = 1000003;
// using mint = modint;
// mint::set_mod(MOD);  // main() 内に書く

// using mint = modint1000000007;
using mint = modint998244353;

using VM = vector<mint>;
using VVM = vector<VM>;
using VVVM = vector<VVM>;
using VVVVM = vector<VVVM>;

template<int M> istream &operator>>(istream &is, static_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> istream &operator>>(istream &is, dynamic_modint<M> &m) { ll v; is >> v; m = v; return is; }
template<int M> ostream &operator<<(ostream &os, const static_modint<M> &m) { return os << m.val(); }
template<int M> ostream &operator<<(ostream &os, const dynamic_modint<M> &m) { return os << m.val(); }




// エラトステネスの篩
struct eratosthenes {
  public:
    // 前計算
    //   - O(N log log N)
    eratosthenes(int N) : N(N) {
        D.resize(N+1);
        iota(D.begin(), D.end(), 0);
        for (int p : {2, 3, 5}) {
            for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
        }
        vector<int> inc = {4, 2, 4, 2, 4, 6, 2, 6};
        int p = 7, idx = 0;
        int root = floor(sqrt(N) + 0.5);
        while (p <= root) {
            if (D[p] == p) {
                for (int i = p*p; i <= N; i += p) { if (D[i] == i) { D[i] = p; } }
            }
            p += inc[idx++];
            if (idx == 8) { idx = 0; }
        }
    }

    // 素数判定
    //   - O(1)
    bool is_prime(int x) const {
        assert(1 <= x && x <= N);
        if (x == 1) { return false; }
        return D[x] == x;
    }

    // 素因数分解
    //   - O(log x), 厳密には O(Σi ei)
    vector<pair<int,int>> factorize(int x) const {
        assert(1 <= x && x <= N);
        vector<pair<int,int>> F;
        while (x != 1) {
            int p = D[x];
            int e = 0;
            while (x % p == 0) { x /= p; e++; }
            F.emplace_back(p, e);
        }
        return F;
    }

    // 約数列挙
    //   - O(Πi(1+ei))
    //   - ソートされていないことに注意
    vector<int> calc_divisors(int x) const {
        assert(1 <= x && x <= N);

        int n = 1;  // 約数の個数
        vector<pair<int,int>> F;
        while (x != 1) {
            int p = D[x];
            int e = 0;
            while (x % p == 0) { x /= p; e++; }
            F.emplace_back(p, e);
            n *= (1 + e);
        }

        vector<int> divisors(n,1);
        int sz = 1;  // 現在の約数の個数
        for (const auto& [p, e] : F) {
            for (int i = 0; i < sz * e; i++) {
                divisors[sz + i] = divisors[i] * p;
            }
            sz *= (1 + e);
        }
        return divisors;
    }

    // 最小素因数 (least prime factor)
    //   - O(1)
    int lpf(int x) const { assert(1 <= x && x <= N); return D[x]; }

    /** TODO: Verify **/
    // オイラーの φ 関数
    // 1 から x までの整数のうち x と互いに素なものの個数 φ(x)
    //   - O(log x), 厳密には O(Σi ei)
    int euler_phi(int x) const {
        assert(1 <= x && x <= N);
        int res = x;
        while (x != 1) {
            int p = D[x];
            res -= res / p;
            while (x % p == 0) { x /= p; }
        }
        return res;
    }

    // メビウス関数のテーブルを計算する
    //   - O(N)
    vector<int> calc_moebius() const {
        vector<int> moebius(N+1, 0);
        moebius[1] = 1;
        for (int x = 2; x <= N; x++) {
            int y = x / D[x];
            if (D[x] != D[y]) { moebius[x] = -moebius[y]; }
        }
        return moebius;
    }

  private:
    int N;
    vector<int> D;  // 最小素因数 (least prime factor)
};


int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    ll N; input(N);
    VLL A(N); REP(i,N) { input(A[i]); }

    int M = 1e6;
    eratosthenes era(M);

    VM dp(M+1);
    mint ans = 0;
    for (const auto& a : A) {
        if (a == 1) { ans++; continue; }
        auto F = era.factorize(a);
        int n = F.size();

        mint sum = 1;
        FOR(S,1,1<<n) {
            ll prod = 1;
            REP(i,n) if (BIT(S,i)) prod *= F[i].first;
            int k = (PCNT(S) % 2 == 1 ? 1 : -1);
            sum += mint(k) * dp[prod];
        }
        ans += sum;

        FOR(S,1,1<<n) {
            ll prod = 1;
            REP(i,n) if (BIT(S,i)) prod *= F[i].first;
            if (a % prod == 0) dp[prod] += sum;
        }
    }
    print(ans);

    return 0;
}
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