#757298 (C++17) No.1918 Simple Math ?

提出ソース

結果

問題	No.1918 Simple Math ?
ユーザー	heno239
提出日時	2022-04-30 00:09:32
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	241 ms / 2,000 ms
コード長	5,601 bytes
コンパイル時間	1,882 ms
コンパイル使用メモリ	146,700 KB
実行使用メモリ	11,648 KB
最終ジャッジ日時	2024-06-29 05:58:26
合計ジャッジ時間	6,005 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

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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	24 ms 11,648 KB
testcase_01	AC	23 ms 11,520 KB
testcase_02	AC	23 ms 11,520 KB
testcase_03	AC	23 ms 11,520 KB
testcase_04	AC	22 ms 11,520 KB
testcase_05	AC	23 ms 11,520 KB
testcase_06	AC	27 ms 11,648 KB
testcase_07	AC	26 ms 11,648 KB
testcase_08	AC	24 ms 11,520 KB
testcase_09	AC	26 ms 11,648 KB
testcase_10	AC	32 ms 11,648 KB
testcase_11	AC	23 ms 11,520 KB
testcase_12	AC	27 ms 11,520 KB
testcase_13	AC	41 ms 11,648 KB
testcase_14	AC	24 ms 11,648 KB
testcase_15	AC	25 ms 11,520 KB
testcase_16	AC	117 ms 11,648 KB
testcase_17	AC	125 ms 11,520 KB
testcase_18	AC	159 ms 11,520 KB
testcase_19	AC	171 ms 11,648 KB
testcase_20	AC	141 ms 11,648 KB
testcase_21	AC	231 ms 11,648 KB
testcase_22	AC	223 ms 11,648 KB
testcase_23	AC	225 ms 11,520 KB
testcase_24	AC	224 ms 11,648 KB
testcase_25	AC	222 ms 11,520 KB
testcase_26	AC	241 ms 11,520 KB
testcase_27	AC	240 ms 11,520 KB
testcase_28	AC	23 ms 11,648 KB
testcase_29	AC	23 ms 11,648 KB
testcase_30	AC	23 ms 11,520 KB
testcase_31	AC	240 ms 11,520 KB
testcase_32	AC	23 ms 11,520 KB
testcase_33	AC	22 ms 11,520 KB

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ソースコード

raw source code

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 100005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;

const string drul = "DRUL";
//DRUL
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------

ll calclen(ll x, ll d,ll a) {
	//x,x+d,x+2*d-2,x+3*d-2-4,...
	//x+md-m(m+1)<0 and x+md-m(m+1)<a
	if (d > 0) {
		ll m = (d + 1) / 2;
		ll val = x + m * d - m * (m + 1);
		if (val >= a)return 1;
	}
	ll l = 0, r = 100000001;
	while (r - l > 1) {
		ll m = (l + r) / 2;
		if (x + m * d - m * (m - 1) < 0)r = m;
		else l = m;
	}
	return l;
}

void solve() {
	ll a, n; cin >> a >> n;
	if (n <= 1000000) {
		ll x = 1;
		modint ans = 0;
		for (ll i = 1; i <= n; i++) {
			while ((x + 1) * (x + 1) <= a * i)x++;
			ans += x;
		}
		cout << ans << "\n";
		return;
	}
	ll x = sqrt(a * n);
	while (x * x <= a * n)x++;
	while (x * x > a * n)x--;
	modint ans = 0;
	ll cl = (x * x + a - 1) / a;
	ans += (modint)(n - cl + 1) * (modint)x;
	x--;
	ans += (modint)x * (modint)(((x + 1) * (x + 1) - 1) / a);
	modint sum = 0;
	sum += (modint)x * (modint)(x + 1) * (modint)(2 * x + 1) / (modint)6;
	sum -= x;
	rep(i, a) {
		//[0,x-1]
		if (i > x)continue;
		int cnt = 1 + (x - 1-i) / a;
		int r = ((ll)(i + 1) * (i + 1) - 1) % a;
		sum -= (modint)r * (modint)cnt;
	}
	sum /= a;
	ans -= sum;
	cout << ans << "\n";
}

signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//init();
	//while(true)
	//expr();
	int t; cin >> t; rep(i, t)
		solve();
	return 0;
}

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結果

テストケース

ソースコード