oj.uz

Submission #466813

# Submission time Handle Problem Language Result Execution time Memory
466813 2021-08-20T17:50:18 Z palilo None (KOI16_dist) C++17
100 / 100
 272 ms 1744 KB 
#include <bits/stdc++.h>
using namespace std;

template <class T>
bool chmin(T& _old, T _new) { return _old > _new && (_old = _new, true); }
template <class T>
bool chmax(T& _old, T _new) { return _old < _new && (_old = _new, true); }

/* basics */
namespace geo {
#define EPS 1e-8
template <typename T, enable_if_t<is_integral<T>::value, bool> = true>
int sign(T x) { return (x > 0) - (x < 0); }
template <typename T, enable_if_t<is_floating_point<T>::value, bool> = true>
int sign(T x) { return (x > EPS) - (x < -EPS); }
}; // namespace geo

/* point2D */
namespace geo {
template <typename T>
struct point2D {
    T x, y;
    point2D() = default;
    point2D(T _x, T _y) : x(_x), y(_y) {}
    template <typename U>
    explicit point2D(const point2D<U>& p) : x(p.x), y(p.y) {}

    using P = point2D;

    bool operator<(const P& p) const { return tie(x, y) < tie(p.x, p.y); }
    bool operator==(const P& p) const { return tie(x, y) == tie(p.x, p.y); }
    bool operator!=(const P& p) const { return tie(x, y) != tie(p.x, p.y); }

    friend P operator+(const P& a, const P& b) { return P(a.x + b.x, a.y + b.y); }
    friend P operator-(const P& a, const P& b) { return P(a.x - b.x, a.y - b.y); }
    friend P operator*(const P& a, const T& scalar) { return P(a.x * scalar, a.y * scalar); }
    friend P operator*(const T& scalar, const P& a) { return P(scalar * a.x, scalar * a.y); }
    friend P operator/(const P& a, const T& scalar) { return P(a.x / scalar, a.y / scalar); }

    friend ostream& operator<<(ostream& o, const P& p) { return o << '(' << p.x << ", " << p.y << ')'; }
    friend istream& operator>>(istream& i, P& p) { return i >> p.x >> p.y; }

    T dot(const P& p) const { return x * p.x + y * p.y; }
    T cross(const P& p) const { return x * p.y - y * p.x; }
    T cross(const P& a, const P& b) const { return (a - *this).cross(b - *this); }

    T dist2() const { return x * x + y * y; }
    double dist() const { return sqrt(dist2()); }

    P perp_cw() const { return P(y, -x); }
    P perp_ccw() const { return P(-y, x); }

    P unit() const { return *this / dist(); }
    P normal() const { return perp_ccw().unit(); }

    P unit_int() const { return x || y ? *this / gcd(x, y) : *this; }
    P normal_int() const { return perp_ccw().unit_int(); }

    bool same_dir(const P& p) const { return cross(p) == 0 && dot(p) > 0; }
    int side_of(const P& s, const P& e) const {
        if constexpr (is_integral_v<T>) {
            return sign(s.cross(e, *this));
        } else {
            auto res = (e - s).cross(*this - s);
            double l = (e - s).dist() * EPS;
            return (res > l) - (res < -l);
        }
    }

    double angle() const { return atan2(y, x); }
    P rotate(double radian) const {
        return P(x * cos(radian) - y * sin(radian), x * sin(radian) + y * cos(radian));
    }
};
}; // namespace geo

struct star_t {
    int x, y, dx, dy;
};

int main() {
    cin.tie(nullptr)->sync_with_stdio(false);
#ifdef palilo
    freopen("in", "r", stdin);
    freopen("out", "w", stdout);
#endif
    int n, t;
    cin >> n >> t;
    vector<star_t> a(n);
    for (auto& [x, y, dx, dy] : a) {
        cin >> x >> y >> dx >> dy;
    }
    using point = geo::point2D<int64_t>;
    vector<point> star(n), hull(n + 1);
    auto f = [&](int dt) -> int64_t {
        transform(a.begin(), a.end(), star.begin(), [&](const auto& star) {
            return point(star.x + star.dx * dt, star.y + star.dy * dt);
        });
        sort(star.begin(), star.end());
        hull.clear();
        size_t st = 0;
        for (const auto& p : star) {
            while (hull.size() >= st + 2 && hull.end()[-2].cross(hull.end()[-1], p) <= 0) {
                hull.pop_back();
            }
            hull.emplace_back(p);
        }
        hull.pop_back();
        reverse(star.begin(), star.end());
        st = hull.size();
        for (const auto& p : star) {
            while (hull.size() >= st + 2 && hull.end()[-2].cross(hull.end()[-1], p) <= 0) {
                hull.pop_back();
            }
            hull.emplace_back(p);
        }
        if (hull.size() == 2 && hull[0] == hull[1]) return 0;
        int64_t ret = 0;
        for (size_t i = 0, j = 1, j2; i < j; ++i) {
            for (;; j = j2) {
                j2 = j == hull.size() - 1 ? 0 : j + 1;
                chmax(ret, (hull[i] - hull[j]).dist2());
                if ((hull[j2] - hull[j]).cross(hull[i + 1] - hull[i]) >= 0) {
                    break;
                }
            }
        }
        return ret;
    };
    int lo = 0, hi = t;
    while (lo != hi) {
        const auto ml = lo + (hi - lo) / 3;
        const auto mr = hi - (hi - lo) / 3;
        f(ml) <= f(mr) ? hi = mr - 1 : lo = ml + 1;
    }
    cout << lo << '\n';
    cout << f(lo);
}

Subtask #1
2.0 / 2.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct

Subtask #2
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 6 ms 332 KB Output is correct
12 Correct 6 ms 360 KB Output is correct
13 Correct 5 ms 364 KB Output is correct
14 Correct 6 ms 332 KB Output is correct
15 Correct 5 ms 332 KB Output is correct
16 Correct 6 ms 332 KB Output is correct
17 Correct 3 ms 332 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 6 ms 332 KB Output is correct
20 Correct 6 ms 332 KB Output is correct

Subtask #3
39.0 / 39.0

# Verdict Execution time Memory Grader output
1 Correct 54 ms 1720 KB Output is correct
2 Correct 53 ms 1732 KB Output is correct
3 Correct 52 ms 1728 KB Output is correct
4 Correct 51 ms 1684 KB Output is correct
5 Correct 46 ms 1692 KB Output is correct
6 Correct 54 ms 1720 KB Output is correct
7 Correct 23 ms 1744 KB Output is correct
8 Correct 23 ms 1688 KB Output is correct
9 Correct 51 ms 1692 KB Output is correct
10 Correct 53 ms 1612 KB Output is correct

Subtask #4
19.0 / 19.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 0 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 6 ms 332 KB Output is correct
12 Correct 6 ms 360 KB Output is correct
13 Correct 5 ms 364 KB Output is correct
14 Correct 6 ms 332 KB Output is correct
15 Correct 5 ms 332 KB Output is correct
16 Correct 6 ms 332 KB Output is correct
17 Correct 3 ms 332 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 6 ms 332 KB Output is correct
20 Correct 6 ms 332 KB Output is correct
21 Correct 54 ms 1720 KB Output is correct
22 Correct 53 ms 1732 KB Output is correct
23 Correct 52 ms 1728 KB Output is correct
24 Correct 51 ms 1684 KB Output is correct
25 Correct 46 ms 1692 KB Output is correct
26 Correct 54 ms 1720 KB Output is correct
27 Correct 23 ms 1744 KB Output is correct
28 Correct 23 ms 1688 KB Output is correct
29 Correct 51 ms 1692 KB Output is correct
30 Correct 53 ms 1612 KB Output is correct
31 Correct 246 ms 1736 KB Output is correct
32 Correct 249 ms 1732 KB Output is correct
33 Correct 243 ms 1720 KB Output is correct
34 Correct 272 ms 1736 KB Output is correct
35 Correct 203 ms 1692 KB Output is correct
36 Correct 255 ms 1612 KB Output is correct
37 Correct 93 ms 1740 KB Output is correct
38 Correct 86 ms 1612 KB Output is correct
39 Correct 180 ms 1720 KB Output is correct
40 Correct 246 ms 1732 KB Output is correct
41 Correct 235 ms 1732 KB Output is correct
42 Correct 241 ms 1740 KB Output is correct