結果

問題 No.2075 GCD Subsequence
ユーザー Kude
提出日時 2022-09-16 22:13:04
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 308 ms / 4,000 ms
コード長 2,955 bytes
コンパイル時間 2,079 ms
コンパイル使用メモリ 222,760 KB
最終ジャッジ日時 2025-02-07 09:47:07
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 28
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘std::pair<std::vector<int>, std::vector<int> > {anonymous}::primes_lpf(int)’:
main.cpp:34:48: warning: result of ‘2^4’ is 6; did you mean ‘1 << 4’ (16)? [-Wxor-used-as-pow]
   34 |   for (; x <= n5; x += add_next, add_next ^= 2 ^ 4) {
      |                                                ^
      |                                              -
      |                                              1 <<
main.cpp:34:46: note: you can silence this warning by using a hexadecimal constant (0x2 rather than 2)
   34 |   for (; x <= n5; x += add_next, add_next ^= 2 ^ 4) {
      |                                              ^
      |                                              0x2
main.cpp:48:47: warning: result of ‘2^4’ is 6; did you mean ‘1 << 4’ (16)? [-Wxor-used-as-pow]
   48 |   for (; x <= n; x += add_next, add_next ^= 2 ^ 4) {
      |                                               ^
      |                                             -
      |                                             1 <<
main.cpp:48:45: note: you can silence this warning by using a hexadecimal constant (0x2 rather than 2)
   48 |   for (; x <= n; x += add_next, add_next ^= 2 ^ 4) {
      |                                             ^
      |                                             0x2

ソースコード

diff # 

#include<bits/stdc++.h>
namespace {
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wunused-function"
#include<atcoder/all>
#pragma GCC diagnostic pop
using namespace std;
using namespace atcoder;
#define rep(i,n) for(int i = 0; i < (int)(n); i++)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--)
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
template<class T> bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; }
template<class T> bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; }
using ll = long long;
using P = pair<int,int>;
using VI = vector<int>;
using VVI = vector<VI>;
using VL = vector<ll>;
using VVL = vector<VL>;
using mint = modint998244353;

pair<vector<int>, vector<int>> primes_lpf(const int n) {
  vector<int> primes; primes.reserve(n / 10);
  vector<int> lpf(n + 1);
  for (int i = 2; i <= n; i += 2) lpf[i] = 2;
  for (int i = 3; i <= n; i += 6) lpf[i] = 3;
  if (2 <= n) primes.push_back(2);
  if (3 <= n) primes.push_back(3);
  // 5 * x <= n, x <= floor(n / 5)
  const int n5 = n / 5;
  int x = 5;
  char add_next = 2;
  for (; x <= n5; x += add_next, add_next ^= 2 ^ 4) {
    int px = lpf[x];
    if (px == 0) {
      lpf[x] = px = x;
      primes.push_back(x);
    }
    for (int i = 2;; ++i) {
      int q = primes[i];
      int y = q * x;
      if (y > n) break;
      lpf[y] = q;
      if (q == px) break;
    }
  }
  for (; x <= n; x += add_next, add_next ^= 2 ^ 4) {
    if (lpf[x] == 0) {
      lpf[x] = x;
      primes.push_back(x);
    }
  }
  return {move(primes), move(lpf)};
}

constexpr int PSIZE = 1000000;
auto [primes, lpf] = primes_lpf(PSIZE);

VI factorize(int x) {
  int ps[10], cs[10];
  int sz = 0;
  while (x != 1) {
    int p = lpf[x], c = 0;
    do {x /= p; c++;} while (x % p == 0);
    ps[sz] = p; cs[sz] = c; sz++;
  }
  VI fs(ps, ps + sz);
  // for (int i = 0; i < sz; i++) fs.emplace_back(ps[i], cs[i]);
  return fs;
}

vector<signed char> build_mu_table(const int n) {
  assert(n < (int)lpf.size());
  vector<signed char> res(n + 1);
  for(int p: primes) {
    if (p > n) break;
    res[p] = 1;
  }
  for(int x = 2; x <= n; x++) {
    if (!res[x]) continue;
    int px = lpf[x];
    for(int q: primes) {
      if (q == px) break;
      int y = q * x;
      if (y > n) break;
      res[y] = -res[x];
    }
  }
  return res;
}

auto mu = build_mu_table(1000000);

} int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<mint> dp(1000000);
  mint ans;
  rep(_, n) {
    int x;
    cin >> x;
    auto ps = factorize(x);
    int sz = ps.size();
    mint tot;
    rep(s, 1 << sz) if (s) {
      int t = 1;
      rep(k, sz) if (s >> k & 1) t *= ps[k];
      tot += dp[t] * mu[t];
    }
    tot++;
    ans += tot;
    rep(s, 1 << sz) if (s) {
      int t = 1;
      rep(k, sz) if (s >> k & 1) t *= ps[k];
      dp[t] += tot;
    }
  }
  cout << ans.val() << '\n';
}
0