結果

問題 No.2262 Fractions
ユーザー fuppy_kyoprofuppy_kyopro
提出日時 2023-04-08 00:00:31
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,138 ms / 2,000 ms
コード長 5,188 bytes
コンパイル時間 2,909 ms
コンパイル使用メモリ 226,412 KB
実行使用メモリ 9,704 KB
最終ジャッジ日時 2024-05-05 07:27:03
合計ジャッジ時間 34,953 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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 629 ms
6,752 KB
testcase_01 AC 264 ms
5,376 KB
testcase_02 AC 245 ms
5,376 KB
testcase_03 AC 201 ms
5,376 KB
testcase_04 AC 205 ms
5,376 KB
testcase_05 AC 178 ms
5,376 KB
testcase_06 AC 201 ms
5,376 KB
testcase_07 AC 186 ms
5,376 KB
testcase_08 AC 173 ms
5,376 KB
testcase_09 AC 185 ms
5,376 KB
testcase_10 AC 179 ms
5,376 KB
testcase_11 AC 371 ms
5,376 KB
testcase_12 AC 400 ms
5,376 KB
testcase_13 AC 394 ms
5,376 KB
testcase_14 AC 397 ms
5,376 KB
testcase_15 AC 381 ms
5,376 KB
testcase_16 AC 211 ms
5,376 KB
testcase_17 AC 188 ms
5,376 KB
testcase_18 AC 191 ms
5,376 KB
testcase_19 AC 785 ms
6,624 KB
testcase_20 AC 707 ms
6,496 KB
testcase_21 AC 776 ms
6,748 KB
testcase_22 AC 692 ms
6,492 KB
testcase_23 AC 588 ms
6,368 KB
testcase_24 AC 1,091 ms
9,696 KB
testcase_25 AC 1,133 ms
9,572 KB
testcase_26 AC 1,095 ms
9,572 KB
testcase_27 AC 1,077 ms
9,696 KB
testcase_28 AC 1,082 ms
9,444 KB
testcase_29 AC 1,133 ms
9,696 KB
testcase_30 AC 1,116 ms
9,596 KB
testcase_31 AC 1,136 ms
9,576 KB
testcase_32 AC 1,138 ms
9,700 KB
testcase_33 AC 1,126 ms
9,696 KB
testcase_34 AC 1,136 ms
9,568 KB
testcase_35 AC 1,108 ms
9,572 KB
testcase_36 AC 1,106 ms
9,704 KB
testcase_37 AC 15 ms
7,908 KB
testcase_38 AC 14 ms
7,908 KB
testcase_39 AC 902 ms
6,500 KB
testcase_40 AC 877 ms
6,496 KB
testcase_41 AC 892 ms
6,500 KB
testcase_42 AC 929 ms
6,372 KB
testcase_43 AC 865 ms
6,396 KB
testcase_44 AC 1,125 ms
9,576 KB
testcase_45 AC 1,121 ms
9,572 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 target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
//*/

// #include <atcoder/all>
#include <atcoder/maxflow>
#include <bits/stdc++.h>

using namespace std;
using namespace atcoder;

// #define _GLIBCXX_DEBUG

#define DEBUG(x) cerr << #x << ": " << x << endl;
#define DEBUG_VEC(v)                                        \
    cerr << #v << ":";                                      \
    for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \
        cerr << " " << v[iiiiiiii];                         \
    cerr << endl;
#define DEBUG_MAT(v)                                \
    cerr << #v << endl;                             \
    for (int iv = 0; iv < v.size(); iv++) {         \
        for (int jv = 0; jv < v[iv].size(); jv++) { \
            cerr << v[iv][jv] << " ";               \
        }                                           \
        cerr << endl;                               \
    }
typedef long long ll;
// #define int ll

#define vi vector<int>
#define vl vector<ll>
#define vii vector<vector<int>>
#define vll vector<vector<ll>>
#define vs vector<string>
#define pii pair<int, int>
#define pis pair<int, string>
#define psi pair<string, int>
#define pll pair<ll, ll>
template <class S, class T>
pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {
    return pair<S, T>(s.first + t.first, s.second + t.second);
}
template <class S, class T>
pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template <class S, class T>
ostream &operator<<(ostream &os, pair<S, T> p) {
    os << "(" << p.first << ", " << p.second << ")";
    return os;
}
#define X first
#define Y second
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)
#define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)
#define REP(i, a, b) for (int i = a; i < b; i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(), c.end()
void YES(bool t = true) {
    cout << (t ? "YES" : "NO") << endl;
}
void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }
void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }
void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }
void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }
void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }
template <class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
bool chmin(T &a, const T &b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
const long double pi = 3.1415926535897932384626433832795028841971L;
int popcount(ll t) { return __builtin_popcountll(t); }
// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};
vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};
struct Setup_io {
    Setup_io() {
        ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
        cout << fixed << setprecision(25);
    }
} setup_io;
// const ll MOD = 1000000007;
const ll MOD = 998244353;
// #define mp make_pair
//#define endl '\n'

ll gcd(ll a, ll b) {
    if (b > a) {
        swap(a, b);
    }
    if (b == 0) return a;
    ll r = a % b;
    while (r != 0) {
        a = b;
        b = r;
        r = a % b;
    }
    return b;
}

ll lcm(ll a, ll b) {
    return (a / gcd(a, b)) * b;
}

ll f(ll n, double x) {
    vl g(1, 0);
    rep1(bo, n) {
        ll ma = bo * x;
        chmin(ma, n);
        g.push_back(ma);
    }

    vl f = g;
    ll ret = 0;
    rep1(i, n) {
        for (int j = 2; i * j <= n; j++) {
            f[i * j] -= f[i];
        }
        ret += f[i];
    }

    return ret;
}

void solve(ll n, ll k) {
    ll m = f(n, 1.0);
    // DEBUG(m);
    if (m == k) {
        cout << "1/1" << endl;
        return;
    }

    bool flip = false;
    if (k > m) {
        k = 2 * m - k;
        if (k <= 0) {
            cout << -1 << endl;
            return;
        }
        flip = true;
    }

    double ng = 0, ok = 1.0;

    rep(_, 100) {
        double mid = (ng + ok) / 2;
        ll ret = f(n, mid);
        if (ret >= k) {
            ok = mid;
        } else {
            ng = mid;
        }
    }
    // cout << ok << endl;

    if (ok > n + 0.5) {
        cout << -1 << endl;
        return;
    }

    pair<double, int> mi(inf, inf);
    rep1(bo, n) {
        ll ma = round(bo * ok);
        chmin(ma, n);
        ll g = gcd(bo, ma);

        if (g != 1) {
            continue;
        }

        double d = (double)ma / bo;
        chmin(mi, {abs(d - ok), bo});
    }

    ll bo = mi.second;
    ll si = round(bo * ok);

    if (flip) {
        swap(bo, si);
    }
    cout << si << "/" << bo << endl;
}

signed main() {

    int t;
    cin >> t;

    while (t--) {
        ll n, k;
        cin >> n >> k;
        solve(n, k);
    }
}
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