結果
問題 | No.3106 Simple Math Problem 3 |
ユーザー |
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提出日時 | 2025-04-11 23:00:55 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 281 ms / 2,000 ms |
コード長 | 6,386 bytes |
コンパイル時間 | 4,315 ms |
コンパイル使用メモリ | 220,060 KB |
実行使用メモリ | 18,960 KB |
最終ジャッジ日時 | 2025-04-11 23:01:08 |
合計ジャッジ時間 | 12,098 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 42 |
ソースコード
#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include <iostream> #include <vector> #include <algorithm> #include <cmath> #include <string> #include <queue> #include <stack> #include <set> #include <map> #include <array> #include <iomanip> #include <utility> #include <tuple> #include <functional> #include <bitset> #include <cassert> #include <complex> #include <stdio.h> #include <time.h> #include <numeric> #include <random> #include <unordered_set> #include <unordered_map> #define all(a) (a).begin(), (a).end() #define rep(i, n) for (ll i = 0; i < (n); i++) #define req(i, a, b) for (ll i = (a); i < (b); i++) #define pb push_back #define debug(x) cerr << __LINE__ << ' ' << #x << ':' << (x) << '\n' #define debug2(x, y) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << '\n' #define debug3(x, y, z) cerr << __LINE__ << ' ' << #x << ':' << (x) << ',' << #y << ':' << (y) << ',' << #z << ':' << (z) << '\n' using namespace std; typedef long long ll; typedef unsigned int uint; typedef unsigned long long ull; typedef long double ld; template<class T> using P = pair<T, T>; template<class T> using pri_l = priority_queue<T>; template<class T> using pri_s = priority_queue<T, vector<T>, greater<T>>; constexpr int inf = 1000000010; constexpr int inf2 = 2000000010; constexpr ll INF = 1000000000000000010; constexpr ll INF4 = 4000000000000000010; constexpr int mod1e9 = 1000000007; constexpr int mod998 = 998244353; constexpr ld eps = 1e-12; constexpr ld pi = 3.141592653589793238; constexpr ll ten(int n) { return n ? 10 * ten(n - 1) : 1; }; int dx[] = { 1,0,-1,0,1,1,-1,-1,0 }; int dy[] = { 0,1,0,-1,1,-1,1,-1,0 }; ll mul(ll a, ll b) { return (b != 0 && a > INF / b ? INF : a * b); } void fail() { cout << "-1\n"; exit(0); } void no() { cout << "No\n"; exit(0); } template<class T> void er(T a) { cout << a << '\n'; exit(0); } template<class T, class U> inline bool chmax(T& a, const U& b) { if (a < b) { a = b; return true; } return false; } template<class T, class U> inline bool chmin(T& a, const U& b) { if (a > b) { a = b; return true; } return false; } template<class T> istream& operator >>(istream& s, vector<T>& v) { for (auto& e : v) s >> e; return s; } template<class T> ostream& operator <<(ostream& s, const vector<T>& v) { for (auto& e : v) s << e << ' '; return s; } template<class T, class U> ostream& operator << (ostream& s, const pair<T, U>& p) { s << p.first << ' ' << p.second; return s; } struct fastio { fastio() { cin.tie(0); cout.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); cerr << fixed << setprecision(20); } }fastio_; namespace rdv { random_device seed_gen; mt19937_64 engine(seed_gen()); ll rnum(ll r) { return engine() % r; } // [0, r) ll rnum(ll l, ll r) { return rnum(r - l) + l; } // [l, r) ll rng(ll l, ll r) { return rnum(l, r + 1); } // [l, r] double rng01() { return engine() * pow(2, -64); } template<class T> void shuf(vector<T>& v) { shuffle(all(v), engine); } void shuf(string& s) { shuffle(all(s), engine); } } using namespace rdv; template<class T> vector<int> compress(vector<T> v) { int n = v.size(); vector<T> tmp = v; sort(tmp.begin(), tmp.end()); tmp.erase(unique(tmp.begin(), tmp.end()), tmp.end()); vector<int> res(n); for (int i = 0; i < n; i++) res[i] = lower_bound(tmp.begin(), tmp.end(), v[i]) - tmp.begin(); return res; } #include <atcoder/all> using namespace atcoder; constexpr ll mod = mod998; using mint = static_modint<mod>; istream& operator >>(istream& s, mint& m) { ll y; s >> y; m = y; return s; } ostream& operator <<(ostream& s, mint& m) { return s << m.val(); } ostream& operator <<(ostream& s, const vector<mint>& v) { for (auto& e : v) s << e.val() << ' '; return s; } vector<mint> fac, inv, facinv; void modcalc(int n) { fac.resize(n); inv.resize(n); facinv.resize(n); fac[0] = 1; fac[1] = 1; inv[1] = 1; facinv[0] = 1; facinv[1] = 1; for (ll i = 2; i < n; i++) { fac[i] = fac[i - 1] * i; inv[i] = -inv[mod % i] * (mod / i); facinv[i] = facinv[i - 1] * inv[i]; } } mint comb(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[k] * facinv[n - k]; } mint perm(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[n - k]; } mint hom(ll n, ll k) { if (n < 0 || k < 0 || n == 0 && k > 0) return 0; if (n == 0 && k == 0) return 1; return fac[n + k - 1] * facinv[k] * facinv[n - 1]; } vector<int> pf; // 最小素因数, pf[0] = pf[1] = 0 vector<int> prime; // 素数列 void sieve(int A) { pf.resize(A); for (int i = 2; i < A; i++) { if (pf[i] != 0) continue; prime.push_back(i); for (int j = i; j < A; j += i) if (pf[j] == 0) pf[j] = i; } } int op(int a, int b) { return a + b; } int e() { return 0; } int main() { auto sum = [](ll n) -> mint { // [1, n] の約数の個数の和 // sum_{i = 1}^{n} n/i mint res = 0; ll l = 1; while (l <= n) { ll r = n / (n / l) + 1; res += n / l * (r - l); l = r; } return res; }; ll n; cin >> n; mint ans = 0; ll sz = min(n, ll(sqrtl(n)) + 2); vector<ll> v(sz); // v[i] = n - i の約数の個数 vector<ll> small(sz); // small[i] = n - i の約数のうち i 未満のものの個数 ll mn = n - sz + 1; for (ll d = 1; d * d <= n; d++) { // 約数 d についてカウント for (ll i = (mn + d - 1) / d * d; i <= n; i += d) { if (i + d < n) small[n - i]++; // d の倍数を走査 if (i < d * d) continue; else if (i == d * d) v[n - i]++; else v[n - i] += 2; } } mint cur = sum(n); mint sq = 0; for (ll c = 1; c * c <= n; c++) { // c の個数をカウント mint cnt = 0; /*for (ll a = 1; a <= n - c; a++) { for (ll d = 1; d <= a; d++) { if (a % d == 0 && c < d && d <= a / c) cnt++; } }*/ /*for (ll a = c * (c + 1); a <= n - c; a++) { if (a % c == 0) cnt--; for (ll d = 1; d <= a; d++) { if (a % d == 0 && c <= d && d <= a / c) cnt++; } }*/ ll L = c * (c + 1), R = n - c; // [L, R] if (L > R) continue; // cnt += sum(R); // cnt -= sum(L - 1); cur -= v[c - 1]; // update sum(R) cnt += cur; cnt -= R / c; cnt += (L - 1) / c; /*for (ll i = 1; i < c; i++) { cnt -= R / i * 2; // cnt += (L - 1) / i * 2; }*/ if (c != 1) { sq += R / (c - 1) * 2; sq -= small[c - 1] * 2; } cnt -= sq; cnt += (c - 1) * (c - 1) - 1; ans += cnt * c; } cout << ans << '\n'; }