oj.uz

Submission #466812

# Submission time Handle Problem Language Result Execution time Memory
466812 2021-08-20T17:48:54 Z palilo None (KOI16_dist) C++17
100 / 100
 296 ms 2500 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

/**
 * @link    https://codeforces.com/blog/entry/48868
 * @return  points of the hull in ccw order
 * @warning points on the edge of the hull will be ignored
 */
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);
    int s = 0, t = 0;
    for (int it = 2; it--; 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) {
    T diameter = 0;
    int n = hull.size();
    for (int i = 0, j = n > 1; i < j; ++i) {
        for (;; j = j == n - 1 ? 0 : j + 1) {
            chmax(diameter, (hull[i] - hull[j]).dist2());
            if ((hull[(j + 1) % n] - 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), 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;
        return geo::distance2::hull_diameter(hull);
        // int64_t ret = 0;
        // for (size_t i = 0, j = 1, j2; i < j; ++i) {
        //     for (;; j = j2) {
        //         j2 = j == n - 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 0 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 0 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 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 3 ms 328 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 5 ms 388 KB Output is correct
20 Correct 7 ms 332 KB Output is correct

Subtask #3
39.0 / 39.0

# Verdict Execution time Memory Grader output
1 Correct 58 ms 1692 KB Output is correct
2 Correct 53 ms 1740 KB Output is correct
3 Correct 55 ms 1612 KB Output is correct
4 Correct 61 ms 1704 KB Output is correct
5 Correct 48 ms 1740 KB Output is correct
6 Correct 54 ms 1724 KB Output is correct
7 Correct 23 ms 1744 KB Output is correct
8 Correct 23 ms 1740 KB Output is correct
9 Correct 52 ms 1692 KB Output is correct
10 Correct 52 ms 1736 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 0 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 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 3 ms 328 KB Output is correct
18 Correct 3 ms 332 KB Output is correct
19 Correct 5 ms 388 KB Output is correct
20 Correct 7 ms 332 KB Output is correct
21 Correct 58 ms 1692 KB Output is correct
22 Correct 53 ms 1740 KB Output is correct
23 Correct 55 ms 1612 KB Output is correct
24 Correct 61 ms 1704 KB Output is correct
25 Correct 48 ms 1740 KB Output is correct
26 Correct 54 ms 1724 KB Output is correct
27 Correct 23 ms 1744 KB Output is correct
28 Correct 23 ms 1740 KB Output is correct
29 Correct 52 ms 1692 KB Output is correct
30 Correct 52 ms 1736 KB Output is correct
31 Correct 263 ms 2408 KB Output is correct
32 Correct 257 ms 2260 KB Output is correct
33 Correct 247 ms 2256 KB Output is correct
34 Correct 267 ms 2380 KB Output is correct
35 Correct 208 ms 2380 KB Output is correct
36 Correct 296 ms 2252 KB Output is correct
37 Correct 96 ms 2500 KB Output is correct
38 Correct 102 ms 2440 KB Output is correct
39 Correct 179 ms 2316 KB Output is correct
40 Correct 252 ms 2252 KB Output is correct
41 Correct 263 ms 2356 KB Output is correct
42 Correct 241 ms 2324 KB Output is correct