Submission #898989

#	Time	Username	Problem	Language	Result	Execution time	Memory
898989		WLZ	Mobile (BOI12_mobile)	C++17	0 / 100	377 ms	104644 KiB

mobile

#include <bits/stdc++.h>
using namespace std;

#ifdef DEBUG
#include "debug.hpp"
#else
#define debug(...)
#endif

using ld = long double;
constexpr ld inf = numeric_limits<long double>::infinity();
constexpr ld eps = 1e-9;

// https://github.com/kth-competitive-programming/kactl/blob/main/content/geometry/Point.h
template<class T>
struct Point {
    typedef Point P;
    T x, y;
    explicit Point(T _x = 0, T _y = 0) : x(_x), y(_y) {}
    P operator+(P p) const { return P(x + p.x, y + p.y); }
    P operator-(P p) const { return P(x - p.x, y - p.y); }
    P operator/(T d) const { return P(x / d, y / d); }
    T dist2() const { return x*x + y*y; }
    ld dist() const { return sqrt((ld) dist2()); }
    P perp() const { return P(-y, x); }
};

// #include "lib/geodeb.h"

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    // GD_INIT("geodeb.html");

    int n; ld l; cin >> n >> l;
    vector< Point<ld> > p(n);
    for (int i = 0; i < n; i++) {
        cin >> p[i].x >> p[i].y;
        p[i].y = abs(p[i].y);
        // GD_POINT(p[i].x, p[i].y, "black bold");
    }

    vector<ld> ends = {-inf};
    vector< Point<ld> > st = {p[0]};

    for (int i = 1; i < n; i++) {
        // GD_LAYER();
        // GD_POINT(p[i].x, p[i].y, "red bold");
        if (abs(p[i].x - p[i - 1].x) < eps) continue;

        while (true) {
            // GD_LAYER();
            auto q = st.back();
            // GD_SEGMENT(p[i].x, p[i].y, q.x, q.y, "red bold");
            auto m = (p[i] + q) / 2;
            // auto tmp = (q - p[i]).perp() + m;
            // GD_LINE(m.x, m.y, tmp.x, tmp.y, "black");
            ld k = -m.y / (q.x - p[i].x);
            ld x = m.x - k * (q.y - p[i].y);
            // GD_POINT(x, 0, "red bold");
            if (x < ends.back()) {
                st.pop_back(); ends.pop_back();
            } else {
                st.push_back(p[i]); ends.push_back(x);
                break;
            }
        }
    }
    ends.push_back(inf);
    ld ans = 0.0;
    for (int i = 0; i < (int) st.size(); i++) {
        ans = max(ans, (Point<ld>(clamp(ends[i], 0.0l, l), 0) - st[i]).dist());
        ans = max(ans, (Point<ld>(clamp(ends[i + 1], 0.0l, l), 0) - st[i]).dist());
    }
    cout << fixed << setprecision(10) << ans << '\n';

    return 0;
}

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