結果

問題 No.2075 GCD Subsequence
ユーザー YFuka86YFuka86
提出日時 2022-09-17 05:14:48
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 331 ms / 4,000 ms
コード長 17,467 bytes
コンパイル時間 3,509 ms
コンパイル使用メモリ 248,200 KB
実行使用メモリ 25,308 KB
最終ジャッジ日時 2024-06-01 14:51:13
合計ジャッジ時間 9,705 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 8 ms
11,588 KB
testcase_01 AC 8 ms
11,588 KB
testcase_02 AC 9 ms
11,456 KB
testcase_03 AC 8 ms
11,584 KB
testcase_04 AC 8 ms
11,588 KB
testcase_05 AC 9 ms
11,592 KB
testcase_06 AC 8 ms
11,584 KB
testcase_07 AC 8 ms
11,716 KB
testcase_08 AC 97 ms
24,552 KB
testcase_09 AC 134 ms
25,184 KB
testcase_10 AC 93 ms
24,524 KB
testcase_11 AC 120 ms
25,172 KB
testcase_12 AC 106 ms
24,828 KB
testcase_13 AC 85 ms
24,548 KB
testcase_14 AC 120 ms
24,788 KB
testcase_15 AC 96 ms
24,436 KB
testcase_16 AC 111 ms
24,584 KB
testcase_17 AC 165 ms
25,256 KB
testcase_18 AC 323 ms
25,200 KB
testcase_19 AC 323 ms
25,240 KB
testcase_20 AC 319 ms
25,200 KB
testcase_21 AC 314 ms
25,200 KB
testcase_22 AC 325 ms
25,124 KB
testcase_23 AC 322 ms
25,252 KB
testcase_24 AC 323 ms
25,216 KB
testcase_25 AC 324 ms
25,196 KB
testcase_26 AC 320 ms
25,308 KB
testcase_27 AC 322 ms
25,212 KB
testcase_28 AC 331 ms
21,872 KB
testcase_29 AC 8 ms
11,592 KB
testcase_30 AC 9 ms
11,588 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
using namespace std;
using ll = long long; using ull = unsigned long long; using ld = long double; using i128 = __int128_t;
using P = pair<int, int>; using LP = pair<ll, ll>; using LT = tuple<ll, ll, ll>; using LT4 =  tuple<ll, ll, ll, ll>;
typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<ll> vl; typedef vector<vl> vvl; typedef vector<vvl> v3l; typedef vector<v3l> v4l; typedef vector<v4l> v5l;
typedef vector<LP> vlp; typedef vector<vlp> vvlp; typedef vector<LT> vlt; typedef vector<vlt> vvlt; typedef vector<LT4> vlt4; typedef vector<string> vs; typedef vector<vs> vvs;
typedef vector<ld> vd; typedef vector<vd> vvd; typedef vector<bool> vb; typedef vector<vb> vvb;
template<typename T> using pq = priority_queue<T>; template<typename T> using mpq = priority_queue<T, vector<T>, greater<T>>;
template<typename T> class infinity{ public: static constexpr T MAX=numeric_limits<T>::max(); static constexpr T MIN=numeric_limits<T>::min(); static constexpr T val=numeric_limits<T>::max()/2-1e6; static constexpr T mval=numeric_limits<T>::min()/2+1e6; };
const int INF = infinity<int>::val; const ll LINF = infinity<ll>::val; const ld DINF = infinity<ld>::val;
#define _overload5(a, b, c, d, e, name, ...) name
#define _overload4(a, b, c, d, name, ...) name
#define _overload3(a, b, c, name, ...) name
#define _rep0(n) for(ll i = 0; (ll)(i) < n; ++i)
#define _rep1(i, n) for(ll i = 0; i < (ll)(n); ++i)
#define _rep2(i, a, b) for(ll i = (ll)(a); i < (ll)(b); ++i)
#define _rep3(i, a, b, c) for(ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) _overload4(__VA_ARGS__, _rep3, _rep2, _rep1, _rep0)(__VA_ARGS__)
#define _per0(n) for(ll i = 0; i < (ll)(n); ++i)
#define _per1(i, n) for(ll i = (ll)(n)-1; i >= 0; --i)
#define _per2(i, a, b) for(ll i = (ll)(a)-1; i >= (ll)(b); --i)
#define _per3(i, a, b, c) for(ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c))
#define rep_r(...) _overload4(__VA_ARGS__, _per3, _per2, _per1, _per0)(__VA_ARGS__)
#define _fore0(a) rep(a.size())
#define _fore1(i, a) for(auto &&i : a)
#define _fore2(a, b, v) for(auto &&[a, b] : v)
#define _fore3(a, b, c, v) for(auto &&[a, b, c] : v)
#define _fore4(a, b, c, d, v) for(auto &&[a, b, c, d] : v)
#define fore(...) _overload5(__VA_ARGS__, _fore4, _fore3, _fore2, _fore1, _fore0)(__VA_ARGS__)
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define rng(v, l, r) (v).begin() + l, (v).begin() + r
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define v3(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define v4(type, name, a, b, c, ...) vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

struct RandGen {
  using ud = uniform_int_distribution<ll>; mt19937 mt; RandGen() : mt(chrono::steady_clock::now().time_since_epoch().count()) {}
  ll l(ll a, ll b) { ud d(a, b - 1); return d(mt); }
  LP lp(ll a, ll b, bool rng = true) { ll x = l(a, b - 1), y = l(rng ? x + 1 : a, b - 1); return {x, y}; }
  vl vecl(ll n, ll a, ll b) { ud d(a, b - 1); vl ret(n); rep(i, n) ret[i] = d(mt); return ret; }
  vl vecperm(ll n, ll from = 0) { vl perm(n); iota(all(perm), from); shuffle(perm); return perm; }
  string str(ll n, string op) { vl fig = vecl(n, 0, op.size()); string s; rep(i, n) s.pb(op[fig[i]]); return s; }
  string straz(ll n, ll a = 0, ll z = 26) { vl az = vecl(n, a, z); string s; rep(i, n) s.pb('a' + az[i]); return s; }
  string strnum(ll n, ll zero = 0, ll ten = 10) { vl zt = vecl(n, zero, ten); string s; rep(i, n) s.pb('0' + zt[i]); return s; }
  template<typename T> void shuffle(vector<T> &a) { std::shuffle(all(a), mt); }
};
// デバッグ系
#define dout cout
template<typename T, typename=void> struct is_specialize:false_type{};
template<typename T> struct is_specialize<T, typename conditional<false,typename T::iterator, void>::type>:true_type{};
template<typename T> struct is_specialize<T, typename conditional<false,decltype(T::first), void>::type>:true_type{};
template<typename T> struct is_specialize<T, enable_if_t<is_integral<T>::value, void>>:true_type{};
void dump(const char &t) { dout<<t; } void dump(const string &t) { dout<<t; } void dump(const bool &t) { dout<<(t ? "true" : "false"); }
template<typename T, enable_if_t<!is_specialize<T>::value, nullptr_t> =nullptr> void dump(const T&t) { dout << t; }
template<typename T> void dump(const T&t, enable_if_t<is_integral<T>::value>* =nullptr) { string tmp;if(t==infinity<T>::val||t==infinity<T>::MAX)tmp="inf";if(is_signed<T>::value&&(t==infinity<T>::mval||t==infinity<T>::MIN))tmp="-inf";if(tmp.empty())tmp=to_string(t);dout<<tmp; }
template<typename T, typename U, typename V> void dump(const tuple<T, U, V>&t) { dout<<"("; dump(get<0>(t)); dout<<" "; dump(get<1>(t)); dout << " "; dump(get<2>(t)); dout << ")"; }
template<typename T,typename U> void dump(const pair<T,U>&);
template<typename T> void dump(const T&t, enable_if_t<!is_void<typename T::iterator>::value>* =nullptr) { dout << "{ "; for(auto it=t.begin();it!=t.end();){ dump(*it); dout << (++it==t.end() ? "" : " "); } dout<<" }"; }
template<typename T,typename U> void dump(const pair<T,U>&t) { dout<<"("; dump(t.first); dout<<" "; dump(t.second); dout << ")"; }
void trace() { dout << "\n"; } template<typename Head, typename... Tail> void trace(Head&&head, Tail&&... tail) { dump(head); if(sizeof...(tail)) dout<<", "; trace(forward<Tail>(tail)...); }
#ifdef ONLINE_JUDGE
#define debug(...) (void(0))
#else
#define debug(...) do {dout<<#__VA_ARGS__<<" = ";trace(__VA_ARGS__); } while(0)
#endif
// 入出力系
#define LL(...) ll __VA_ARGS__; IN(__VA_ARGS__)
#define STR(...) string __VA_ARGS__; IN(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__; IN(__VA_ARGS__)
#define _vl(name, size) vl name(size); IN(name)
#define _vl2(name, size, off) vl name(size); IN(name); rep(i, size) name[i]-=off
#define VL(...) _overload3(__VA_ARGS__, _vl2, _vl)(__VA_ARGS__)
#define VEC(type, name, size) vector<type> name(size); IN(name)
#define VEC2(type, name1, name2, size) vector<type> name1(size), name2(size); for(int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size) vector<type> name1(size), name2(size), name3(size); for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size) vector<type> name1(size), name2(size), name3(size), name4(size); for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, h, w) vector<vector<type>> name(h, vector<type>(w)); IN(name)
void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &a) { for(auto &i : a) scan(i); } template <class T> void scan(T &a) { cin >> a; }
void IN() {} template <class Head, class... Tail> void IN(Head &head, Tail &...tail) { scan(head); IN(tail...); }
#define OUTRET(...) { { OUT(__VA_ARGS__); return; } }
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) { return os << p.first << " " << p.second; }
void OUT() { cout << '\n'; } template <typename Head, typename... Tail> void OUT(const Head &head, const Tail &...tail) { cout << head; if(sizeof...(tail)) cout << ' '; OUT(tail...); }
template<typename T> void OUTARRAY(vector<T>& v, int offset = 0, string sep = " ") { rep(i, v.size()) { if (i > 0) cout << sep; if (offset) cout << v[i] + offset; else cout << v[i]; } cout << "\n"; }
template<typename T> void OUTMAT(vector<vector<T>>& v, int offset = 0) { rep(i, v.size()) { coutarray(v[i], offset); } }
template<typename T> void OUTBIN(T &a, int d) { for (int i = d - 1; i >= 0; i--) cout << ((a >> i) & (T)1); cout << "\n"; }
template<typename Q, typename A> void IQUERY(initializer_list<Q> q, A &a, string str = "? ") { cout << str; vector<Q> v(q); coutarray(v); cout.flush(); cin >> a; }
// template<typename Q, typename A> void IQUERY(initializer_list<Q> q, A &a, string str = "? ") { vector<Q> query(q); RandGen rg;
//   a = query[0] ? A() : A();
// }
template<typename A> void IANSWER(A a, string str = "! ") { cout << str << a << "\n"; cout.flush(); }
// 数値系
int ceil_pow2(ll n) { int x = 0; while ((1ULL << x) < (ull)(n)) x++; return x; }
int floor_pow2(ll n) { int x = 0; while ((1ULL << (x + 1)) <= (ull)(n)) x++; return x; }
ll POW(__uint128_t x, int n) { assert(n >= 0); ll res = 1; for(; n; n >>= 1, x *= x) if(n & 1) res *= x; return res; }
ll sqrt_ceil(ll x) { ll l = -1, r = x; while (r - l > 1) { ll m = (l + r) / 2; if (m * m >= x) r = m; else l = m; } return r; }
vl divisor(ll n) { vl ret; for (ll i = 1; i * i <= n; i++) { if (n % i == 0) { ret.pb(i); if (i * i != n) ret.pb(n / i); } } sort(all(ret)); return ret; }
template<typename T> vl digits(T n) { assert(n >= 0); vl ret; while(n > 0) { ret.pb(n % 10); n /= 10; } return ret; }
template<typename T, typename S> T ceil(T x, S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); }
template<typename T, typename S> T floor(T x, S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : (x - y + 1) / y)); }
template<typename T = ll> T sum_of(const vector<T> &v, int l = 0, int r = INF) { return accumulate(rng(v, l, min(r, (int)v.size())), T(0)); }
ll max(int x, ll y) { return max((ll)x, y); } ll max(ll x, int y) { return max(x, (ll)y); }
ll min(int x, ll y) { return min((ll)x, y); } ll min(ll x, int y) { return min(x, (ll)y); }
ll mex(vl& v) { ll n = v.size(); vb S(n + 1); for (auto a: v) if (a <= n) S[a] = 1; ll ret = 0; while (S[ret]) ret++; return ret; }
// 操作系
template<typename T> void uniq(vector<T>&a) { sort(all(a)); a.erase(unique(all(a)), a.end()); }
template<typename T> void comp(vector<T>&a) { vector<T> b = a; uniq(b); rep(i, a.size()) a[i] = lower_bound(all(b), a[i]) - b.begin(); }
template<class T, class U> bool chmin(T &a, const U &b) { if (b < a) { a = b; return 1;} return 0; }
template<class T, class U> bool chmax(T &a, const U &b) { if (b > a) { a = b; return 1;} return 0; }
template<class T> int lbs(vector<T> &a, const T &b) { return lower_bound(all(a), b) - a.begin(); };
template<class T> int ubs(vector<T> &a, const T &b) { return upper_bound(all(a), b) - a.begin(); };
ll binary_search(function<bool(ll)> check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; if (check(x)) ok = x; else ng = x; } return ok; }
template<class T> vector<T> csum(vector<T> &a) { vl ret(a.size() + 1, 0); rep(i, a.size()) ret[i + 1] = ret[i] + a[i]; return ret; }
template<class S> vector<pair<S, int>> RLE(const vector<S> &v) { vector<pair<S, int>> res; for(auto &e : v) if(res.empty() or res.back().first != e) res.emplace_back(e, 1); else res.back().second++; return res; }
vector<pair<char, int>> RLE(const string &v) { vector<pair<char, int>> res; for(auto &e : v) if(res.empty() or res.back().first != e) res.emplace_back(e, 1); else res.back().second++; return res; }
template <class T, class S> bool incl(const T &x, const S &l, const S &r) { return l <= x and x < r; }
bool is_palindrome(string s) { rep(i, (s.size() + 1) / 2) if (s[i] != s[s.size() - 1 - i]) { return false; } return true; }
const string drul = "DRUL"; vl dx = {1, 0, -1, 0}; vl dy = {0, 1, 0, -1};

ll solve(ll n, vl a) {
  ll ans = n - a[0]; return ans;
}

ll naive(ll n, vl a) {
  ll ans = n + a[0]; return ans;
}

void compare(bool check = true) { RandGen rg; ll c = 0, loop = 10;
  while (++c) { if (c % loop == 0) cout << "reached " << c / loop << "loop" <<  "\n", cout.flush();
    ll n = 10;
    vl a = rg.vecl(n, 1, 1e2);
    auto so = solve(n, a); auto na = naive(n, a);
    if (!check || na != so) { cout << c << "times tried" << "\n";
      debug(n, a); debug(so); debug(na);
    if (check || (!check && c > loop)) break; }
  }
}


vector<ll> primes_below(const ll N) {
  vector<bool> is_prime(N + 1, true); for(ll i = 2; i * i <= N; i++) { if ((i > 2 && i % 2 == 0) || !is_prime[i]) continue; for(ll j = i * i; j <= N; j += i) is_prime[j] = false; }
  vector<ll> ret; for(ll i = 2; i <= N; i++) if (is_prime[i]) ret.emplace_back(i); return ret; }

const ll mod = 998244353;
//------------------------------------------------------------------------------
template< int mod > struct ModInt {
  int x; ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; }  ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; }
  ModInt &operator*=(const ModInt &p) { x = (int) (1LL * x * p.x % mod); return *this; }  ModInt &operator/=(const ModInt &p) { *this *= p.inv(); return *this; }
  ModInt operator-() const { return ModInt(-x); }
  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
  bool operator==(const ModInt &p) const { return x == p.x; }  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inv() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); }
  ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; }
  friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; }
  friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt< mod >(t); return (is); }
  static int get_mod() { return mod; }
};
using mint = ModInt< mod >; using vmi = vector<mint>; using vvmi = vector<vmi>; using v3mi = vector<vvmi>; using v4mi = vector<v3mi>;
//------------------------------------------------------------------------------
const int max_n = 1 << 20;
mint fact[max_n], factinv[max_n];
void init_f() { fact[0] = 1; for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * (i + 1); } factinv[max_n - 1] = mint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * (i + 1); } }
mint comb(int a, int b) { assert(fact[0] != 0); if (a < 0 || b < 0 || a < b) return 0; return fact[a] * factinv[b] * factinv[a - b]; }
mint combP(int a, int b) { assert(fact[0] != 0); if (a < 0 || b < 0 || a < b) return 0; return fact[a] * factinv[a - b]; }
//------------------------------------------------------------------------------
ll mod_pow(ll x, ll n, const ll &p = mod) { ll ret = 1; while(n > 0) { if(n & 1) (ret *= x) %= p; (x *= x) %= p; n >>= 1; } return ret; }
ll mod_inv(ll x, ll m) { ll a = x, b = m, u = 1, v = 0, t; while(b) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } if (u < 0) u += m; return u % m; }
//------------------------------------------------------------------------------

//-------------------------------------------------------
// https://atcoder.jp/contests/abc238/submissions/29086825
// https://cp-algorithms.com/algebra/prime-sieve-linear.html
struct PrimeSieve {
  int n; vector<bool> is_prime; vector<int> pr, mu, pf;
  // pr := primes, mu := moebius, pf[i] := smallest prime p s.t. p | i
  PrimeSieve(int _n){
    n = ++_n; is_prime.assign(n, true); mu.assign(n, 0); pf.assign(n, 0);
    is_prime[0] = is_prime[1] = false; mu[1] = 1;
    for (int i = 2; i < n; i++) {
      if (is_prime[i]) { pr.emplace_back(i); pf[i] = i; mu[i] = -1; }
      for (int p : pr) {
        if (ll(i) * p >= n) break;
        is_prime[i * p] = false; mu[i * p] = -mu[i]; pf[i * p] = p;
        if (i % p == 0) { mu[i * p] = 0; break; }
      }
    }
  }
  vector<pair<int, int>> factorize(int x) { assert(x < n); vector<pair<int, int>> res;
    while (pf[x] > 1) { int d = pf[x], c = 0; while (x % d == 0) { x /= d; c++; } res.emplace_back(d, c); }
    if (x != 1) res.emplace_back(x, 1); return res;
  }
  // not sorted [1..x]
  vector<int> divisors(int x) { assert(x < n); auto f = factorize(x); vector<int> res = { 1 };
    for (auto [p, c] : f) {
      vector<int> powp; powp.emplace_back(p); rep(i, c - 1) powp.emplace_back(powp.back() * p);
      for (int i = res.size() - 1; i >= 0; --i) for (int j = 0; j < c; ++j) res.emplace_back(res[i] * powp[j]);
    }
    // res.erase(res.begin()); [2..x]
    return res;
  }
};

void solve() {
  LL(n);
  VL(a, n);
  ll MA = *max_element(all(a));
  PrimeSieve ps(MA);

  vmi dp(MA + 1, 0);
  mint ans = 0;

  rep(i, n) {
    auto f = ps.factorize(a[i]);
    ll sz = f.size();
    mint cnt = 1;
    vlp combi;
    rep(S, 1 << sz) {
      ll div = 1; rep(j, sz) if (S & 1 << j) div *= f[j].fi;
      combi.pb({div, __builtin_popcount(S)});
      if (S == 0) continue;
      cnt += dp[div];
    }
    fore(d, c, combi) {
      if (c == 0) continue;
      dp[d] += (c & 1 ? cnt : -cnt);
    }

    // debug(dp);
    ans += cnt;
  }
  OUT(ans);
}

signed main() {
  cin.tie(0)->sync_with_stdio(0); cout.tie(0); cout << fixed << setprecision(20);
  int t = 1; // cin >> t;
  while (t--) solve();
  // while (t--) compare();
}
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