結果

問題 No.3106 Simple Math Problem 3
ユーザー cn_449
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
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 42
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("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';
}
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