oj.uz

Submission #466729

# Submission time Handle Problem Language Result Execution time Memory
466729 2021-08-20T14:21:00 Z palilo None (KOI16_dist) C++17
100 / 100
 292 ms 3348 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

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;
    }
    auto cross2 = [&](const pair<int, int>& u, const pair<int, int>& v) {
        return int64_t(u.first) * v.second - int64_t(u.second) * v.first;
    };
    auto cross3 = [&](const pair<int, int>& o, const pair<int, int>& u, const pair<int, int>& v) {
        return int64_t(u.first - o.first) * (v.second - o.second) -
               int64_t(u.second - o.second) * (v.first - o.first);
    };
    auto dist = [&](const pair<int, int>& u, const pair<int, int>& v) {
        int64_t dx = u.first - v.first, dy = u.second - v.second;
        return dx * dx + dy * 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);
        });
        auto hull = geo::convex_hull(star);
        return geo::distance2::hull_diameter(hull);
    };
    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);
}

Compilation message

dist.cpp: In function 'int main()':
dist.cpp:125:10: warning: variable 'cross2' set but not used [-Wunused-but-set-variable]
  125 |     auto cross2 = [&](const pair<int, int>& u, const pair<int, int>& v) {
      |          ^~~~~~
dist.cpp:128:10: warning: variable 'cross3' set but not used [-Wunused-but-set-variable]
  128 |     auto cross3 = [&](const pair<int, int>& o, const pair<int, int>& u, const pair<int, int>& v) {
      |          ^~~~~~
dist.cpp:132:10: warning: variable 'dist' set but not used [-Wunused-but-set-variable]
  132 |     auto dist = [&](const pair<int, int>& u, const pair<int, int>& v) {
      |          ^~~~

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 1 ms 204 KB Output is correct
4 Correct 1 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 1 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 1 ms 204 KB Output is correct
4 Correct 1 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 1 ms 204 KB Output is correct
11 Correct 8 ms 332 KB Output is correct
12 Correct 7 ms 328 KB Output is correct
13 Correct 6 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 4 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 7 ms 404 KB Output is correct

Subtask #3
39.0 / 39.0

# Verdict Execution time Memory Grader output
1 Correct 56 ms 2204 KB Output is correct
2 Correct 55 ms 2736 KB Output is correct
3 Correct 54 ms 2728 KB Output is correct
4 Correct 58 ms 3296 KB Output is correct
5 Correct 51 ms 2892 KB Output is correct
6 Correct 61 ms 3220 KB Output is correct
7 Correct 28 ms 2636 KB Output is correct
8 Correct 29 ms 2564 KB Output is correct
9 Correct 57 ms 3248 KB Output is correct
10 Correct 57 ms 2812 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 1 ms 204 KB Output is correct
4 Correct 1 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 1 ms 204 KB Output is correct
11 Correct 8 ms 332 KB Output is correct
12 Correct 7 ms 328 KB Output is correct
13 Correct 6 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 4 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 7 ms 404 KB Output is correct
21 Correct 56 ms 2204 KB Output is correct
22 Correct 55 ms 2736 KB Output is correct
23 Correct 54 ms 2728 KB Output is correct
24 Correct 58 ms 3296 KB Output is correct
25 Correct 51 ms 2892 KB Output is correct
26 Correct 61 ms 3220 KB Output is correct
27 Correct 28 ms 2636 KB Output is correct
28 Correct 29 ms 2564 KB Output is correct
29 Correct 57 ms 3248 KB Output is correct
30 Correct 57 ms 2812 KB Output is correct
31 Correct 284 ms 2900 KB Output is correct
32 Correct 262 ms 2864 KB Output is correct
33 Correct 268 ms 2740 KB Output is correct
34 Correct 288 ms 2872 KB Output is correct
35 Correct 231 ms 2884 KB Output is correct
36 Correct 292 ms 3220 KB Output is correct
37 Correct 120 ms 2892 KB Output is correct
38 Correct 113 ms 2892 KB Output is correct
39 Correct 189 ms 2908 KB Output is correct
40 Correct 258 ms 2844 KB Output is correct
41 Correct 279 ms 3280 KB Output is correct
42 Correct 254 ms 3348 KB Output is correct