oj.uz

Submission #466816

# Submission time Handle Problem Language Result Execution time Memory
466816 2021-08-20T18:00:14 Z palilo None (KOI16_dist) C++17
100 / 100
 298 ms 2220 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); }

namespace geo {
/* basics */
#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); }

/* point2D */
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

namespace geo {
template <typename T>
vector<point2D<T>> convex_hull(vector<point2D<T>>& pts) {
    if (pts.size() <= 1) return pts;
    sort(pts.begin(), pts.end());
    vector<point2D<T>> hull(pts.size() + 1);
    size_t s = 0, t = 0;
    for (const auto& p : pts) {
        while (t >= s + 2 && hull[t - 2].cross(hull[t - 1], p) <= 0) --t;
        hull[t++] = p;
    }
    s = --t;
    reverse(pts.begin(), pts.end());
    for (const auto& p : pts) {
        while (t >= s + 2 && hull[t - 2].cross(hull[t - 1], p) <= 0) t--;
        hull[t++] = p;
    }
    return {hull.begin(), hull.begin() + t - (t == 2 && hull[0] == hull[1])};
}
}; // namespace geo

namespace geo::distance2 {
template <typename T>
T hull_diameter(const vector<point2D<T>>& hull) {
    if (hull.size() < 2) return 0;
    T diameter = 0;
    const size_t n = hull.size();
    for (size_t i = 0, j = 1, j2; i < j; ++i) {
        for (;; j = j2) {
            j2 = j == n - 1 ? 0 : j + 1;
            chmax(diameter, (hull[i] - hull[j]).dist2());
            if ((hull[j2] - hull[j]).cross(hull[i + 1] - hull[i]) >= 0) {
                break;
            }
        }
    }
    return diameter;
}
}; // namespace geo::distance2

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);
    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);
        });
        return geo::distance2::hull_diameter(geo::convex_hull(star));
    };
    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 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 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 0 ms 204 KB Output is correct
9 Correct 1 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 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 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 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 7 ms 332 KB Output is correct
12 Correct 6 ms 332 KB Output is correct
13 Correct 5 ms 332 KB Output is correct
14 Correct 7 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 5 ms 332 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 5 ms 332 KB Output is correct
20 Correct 8 ms 364 KB Output is correct

Subtask #3
39.0 / 39.0

# Verdict Execution time Memory Grader output
1 Correct 55 ms 1652 KB Output is correct
2 Correct 53 ms 1716 KB Output is correct
3 Correct 52 ms 1700 KB Output is correct
4 Correct 55 ms 2172 KB Output is correct
5 Correct 47 ms 1716 KB Output is correct
6 Correct 58 ms 2204 KB Output is correct
7 Correct 24 ms 1652 KB Output is correct
8 Correct 23 ms 1740 KB Output is correct
9 Correct 53 ms 2180 KB Output is correct
10 Correct 54 ms 1652 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 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 1 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 0 ms 204 KB Output is correct
9 Correct 1 ms 204 KB Output is correct
10 Correct 0 ms 204 KB Output is correct
11 Correct 7 ms 332 KB Output is correct
12 Correct 6 ms 332 KB Output is correct
13 Correct 5 ms 332 KB Output is correct
14 Correct 7 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 5 ms 332 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 5 ms 332 KB Output is correct
20 Correct 8 ms 364 KB Output is correct
21 Correct 55 ms 1652 KB Output is correct
22 Correct 53 ms 1716 KB Output is correct
23 Correct 52 ms 1700 KB Output is correct
24 Correct 55 ms 2172 KB Output is correct
25 Correct 47 ms 1716 KB Output is correct
26 Correct 58 ms 2204 KB Output is correct
27 Correct 24 ms 1652 KB Output is correct
28 Correct 23 ms 1740 KB Output is correct
29 Correct 53 ms 2180 KB Output is correct
30 Correct 54 ms 1652 KB Output is correct
31 Correct 253 ms 1732 KB Output is correct
32 Correct 250 ms 1740 KB Output is correct
33 Correct 247 ms 1720 KB Output is correct
34 Correct 273 ms 1732 KB Output is correct
35 Correct 209 ms 1740 KB Output is correct
36 Correct 266 ms 2220 KB Output is correct
37 Correct 108 ms 1728 KB Output is correct
38 Correct 84 ms 1652 KB Output is correct
39 Correct 180 ms 1732 KB Output is correct
40 Correct 258 ms 1720 KB Output is correct
41 Correct 298 ms 2176 KB Output is correct
42 Correct 246 ms 2124 KB Output is correct