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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#600259#9434. Italian Cuisineucup-team2010WA 0ms3856kbC++2018.2kb2024-09-29 15:31:502024-09-29 15:31:51

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你现在查看的是最新测评结果

  • [2024-09-29 15:31:51]
  • 评测
  • 测评结果:WA
  • 用时:0ms
  • 内存:3856kb
  • [2024-09-29 15:31:50]
  • 提交

answer

#include<bits/extc++.h>
using namespace __gnu_pbds;
using namespace std;
using ll = long long;
#define LNF 0x3f3f3f3f3f3f3f3f
#define W(...) cerr<<"LINE:" << __LINE__ << " "; debug(#__VA_ARGS__, __VA_ARGS__)
void debug(const char* names) {cerr << endl;} template<typename T, typename... Args>void debug(const char* names, T value, Args... args) {const char* comma = strchr(names, ','); if (comma) {cerr.write(names, comma - names) << "=" << value << ", "; debug(comma + 1, args...);} else {cerr << names << " = " << value << endl; }}
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<class T, class... U>void chmax(T &a, const U &... b) {for (const auto& val : {b...})if (a < val) {a = val;}}
template<class T, class... U>void chmin(T &a, const U &... b) {for (const auto& val : {b...})if (a > val) {a = val;}}
#define pb push_back
#include <bits/stdc++.h>
using namespace std;

using point_t = long long;
// using point_t=long double;  //全局数据类型

constexpr point_t eps = 1e-8;
constexpr point_t INF = numeric_limits<point_t>::max();
constexpr long double PI = 3.1415926535897932384l;

// 点与向量
template<typename T> struct point
{
    T x, y;

    bool operator==(const point &a) const {return (abs(x - a.x) <= eps && abs(y - a.y) <= eps);}
    bool operator<(const point &a) const {if (abs(x - a.x) <= eps) return y < a.y - eps; return x < a.x - eps;}
    bool operator>(const point &a) const {return !(*this < a || *this == a);}
    point operator+(const point &a) const {return {x + a.x, y + a.y};}
    point operator-(const point &a) const {return {x - a.x, y - a.y};}
    point operator-() const {return { -x, -y};}
    point operator*(const T k) const {return {k * x, k * y};}
    point operator/(const T k) const {return {x / k, y / k};}
    T operator*(const point &a) const {return x * a.x + y * a.y;} // 点积
    T operator^(const point &a) const {return x * a.y - y * a.x;} // 叉积,注意优先级
    int toleft(const point &a) const {const auto t = (*this)^a; return (t > eps) - (t < -eps);} // to-left 测试
    T len2() const {return (*this) * (*this);} // 向量长度的平方
    T dis2(const point &a) const {return (a - (*this)).len2();} // 两点距离的平方

    // 涉及浮点数
    long double len() const {return sqrtl(len2());}  // 向量长度
    long double dis(const point &a) const {return sqrtl(dis2(a));}  // 两点距离
    long double ang(const point &a) const {return acosl(max(-1.0l, min(1.0l, ((*this) * a) / (len() * a.len()))));} // 向量夹角
    point rot(const long double rad) const {return {x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad)};} // 逆时针旋转(给定角度)
    point rot(const long double cosr, const long double sinr) const {return {x*cosr - y * sinr, x*sinr + y * cosr};} // 逆时针旋转(给定角度的正弦与余弦)
};

using Point = point<point_t>;

// 极角排序
struct argcmp
{
    bool operator()(const Point &a, const Point &b) const
    {
        const auto quad = [](const Point & a)
        {
            if (a.y < -eps) return 1;
            if (a.y > eps) return 4;
            if (a.x < -eps) return 5;
            if (a.x > eps) return 3;
            return 2;
        };
        const int qa = quad(a), qb = quad(b);
        if (qa != qb) return qa < qb;
        const auto t = a ^ b;
        // if (abs(t)<=eps) return a*a<b*b-eps;  // 不同长度的向量需要分开
        return t > eps;
    }
};

// 直线
template<typename T> struct line
{
    point<T> p, v; // p 为直线上一点,v 为方向向量

    bool operator==(const line &a) const {return v.toleft(a.v) == 0 && v.toleft(p - a.p) == 0;}
    int toleft(const point<T> &a) const {return v.toleft(a - p);} // to-left 测试
    bool operator<(const line &a) const  // 半平面交算法定义的排序
    {
        if (abs(v ^ a.v) <= eps && v * a.v >= -eps) return toleft(a.p) == -1;
        return argcmp()(v, a.v);
    }

    // 涉及浮点数
    point<T> inter(const line &a) const {return p + v * ((a.v ^ (p - a.p)) / (v ^ a.v));} // 直线交点
    long double dis(const point<T> &a) const {return abs(v ^ (a - p)) / v.len();} // 点到直线距离
    point<T> proj(const point<T> &a) const {return p + v * ((v * (a - p)) / (v * v));} // 点在直线上的投影
};

using Line = line<point_t>;

//线段
template<typename T> struct segment
{
    point<T> a, b;

    bool operator<(const segment &s) const {return make_pair(a, b) < make_pair(s.a, s.b);}

    // 判定性函数建议在整数域使用

    // 判断点是否在线段上
    // -1 点在线段端点 | 0 点不在线段上 | 1 点严格在线段上
    int is_on(const point<T> &p) const
    {
        if (p == a || p == b) return -1;
        return (p - a).toleft(p - b) == 0 && (p - a) * (p - b) < -eps;
    }

    // 判断线段直线是否相交
    // -1 直线经过线段端点 | 0 线段和直线不相交 | 1 线段和直线严格相交
    int is_inter(const line<T> &l) const
    {
        if (l.toleft(a) == 0 || l.toleft(b) == 0) return -1;
        return l.toleft(a) != l.toleft(b);
    }

    // 判断两线段是否相交
    // -1 在某一线段端点处相交 | 0 两线段不相交 | 1 两线段严格相交
    int is_inter(const segment<T> &s) const
    {
        if (is_on(s.a) || is_on(s.b) || s.is_on(a) || s.is_on(b)) return -1;
        const line<T> l{a, b - a}, ls{s.a, s.b - s.a};
        return l.toleft(s.a) * l.toleft(s.b) == -1 && ls.toleft(a) * ls.toleft(b) == -1;
    }

    // 点到线段距离
    long double dis(const point<T> &p) const
    {
        if ((p - a) * (b - a) < -eps || (p - b) * (a - b) < -eps) return min(p.dis(a), p.dis(b));
        const line<T> l{a, b - a};
        return l.dis(p);
    }

    // 两线段间距离
    long double dis(const segment<T> &s) const
    {
        if (is_inter(s)) return 0;
        return min({dis(s.a), dis(s.b), s.dis(a), s.dis(b)});
    }
};

using Segment = segment<point_t>;

// 多边形
template<typename T> struct polygon
{
    vector<point<T>> p;  // 以逆时针顺序存储

    size_t nxt(const size_t i) const {return i == p.size() - 1 ? 0 : i + 1;}
    size_t pre(const size_t i) const {return i == 0 ? p.size() - 1 : i - 1;}

    // 回转数
    // 返回值第一项表示点是否在多边形边上
    // 对于狭义多边形,回转数为 0 表示点在多边形外,否则点在多边形内
    pair<bool, int> winding(const point<T> &a) const
    {
        int cnt = 0;
        for (size_t i = 0; i < p.size(); i++)
        {
            const point<T> u = p[i], v = p[nxt(i)];
            if (abs((a - u) ^ (a - v)) <= eps && (a - u) * (a - v) <= eps) return {true, 0};
            if (abs(u.y - v.y) <= eps) continue;
            const Line uv = {u, v - u};
            if (u.y < v.y - eps && uv.toleft(a) <= 0) continue;
            if (u.y > v.y + eps && uv.toleft(a) >= 0) continue;
            if (u.y < a.y - eps && v.y >= a.y - eps) cnt++;
            if (u.y >= a.y - eps && v.y < a.y - eps) cnt--;
        }
        return {false, cnt};
    }

    // 多边形面积的两倍
    // 可用于判断点的存储顺序是顺时针或逆时针
    T area() const
    {
        T sum = 0;
        for (size_t i = 0; i < p.size(); i++) sum += p[i] ^ p[nxt(i)];
        return sum;
    }

    // 多边形的周长
    long double circ() const
    {
        long double sum = 0;
        for (size_t i = 0; i < p.size(); i++) sum += p[i].dis(p[nxt(i)]);
        return sum;
    }
};

using Polygon = polygon<point_t>;
struct Circle
{
    Point c;
    long double r;

    bool operator==(const Circle &a) const {return c == a.c && abs(r - a.r) <= eps;}
    long double circ() const {return 2 * PI * r;} // 周长
    long double area() const {return PI * r * r;} // 面积

    // 点与圆的关系
    // -1 圆上 | 0 圆外 | 1 圆内
    int is_in(const Point &p) const {const long double d = p.dis(c); return abs(d - r) <= eps ? -1 : d < r - eps;}

    // 直线与圆关系
    // 0 相离 | 1 相切 | 2 相交
    int relation(const Line &l) const
    {
        const long double d = l.dis(c);
        if (d > r + eps) return 0;
        long double ss=std::abs(d-r);
        if (std::abs(d - r) <= eps) return 1;
        return 2;
    }

    // 圆与圆关系
    // -1 相同 | 0 相离 | 1 外切 | 2 相交 | 3 内切 | 4 内含
    int relation(const Circle &a) const
    {
        if (*this == a) return -1;
        const long double d = c.dis(a.c);
        if (d > r + a.r + eps) return 0;
        if (abs(d - r - a.r) <= eps) return 1;
        if (abs(d - abs(r - a.r)) <= eps) return 3;
        if (d < abs(r - a.r) - eps) return 4;
        return 2;
    }

    // 直线与圆的交点
    vector<Point> inter(const Line &l) const
    {
        const long double d = l.dis(c);
        const Point p = l.proj(c);
        const int t = relation(l);
        if (t == 0) return vector<Point>();
        if (t == 1) return vector<Point> {p};
        const long double k = sqrt(r * r - d * d);
        return vector<Point> {p - (l.v / l.v.len())*k, p + (l.v / l.v.len())*k};
    }

    // 圆与圆交点
    vector<Point> inter(const Circle &a) const
    {
        const long double d = c.dis(a.c);
        const int t = relation(a);
        if (t == -1 || t == 0 || t == 4) return vector<Point>();
        Point e = a.c - c; e = e / e.len() * r;
        if (t == 1 || t == 3)
        {
            if (r * r + d * d - a.r * a.r >= -eps) return vector<Point> {c + e};
            return vector<Point> {c - e};
        }
        const long double costh = (r * r + d * d - a.r * a.r) / (2 * r * d), sinth = sqrt(1 - costh * costh);
        return vector<Point> {c + e.rot(costh, -sinth), c + e.rot(costh, sinth)};
    }

    // 圆与圆交面积
    long double inter_area(const Circle &a) const
    {
        const long double d = c.dis(a.c);
        const int t = relation(a);
        if (t == -1) return area();
        if (t < 2) return 0;
        if (t > 2) return min(area(), a.area());
        const long double costh1 = (r * r + d * d - a.r * a.r) / (2 * r * d), costh2 = (a.r * a.r + d * d - r * r) / (2 * a.r * d);
        const long double sinth1 = sqrt(1 - costh1 * costh1), sinth2 = sqrt(1 - costh2 * costh2);
        const long double th1 = acos(costh1), th2 = acos(costh2);
        return r * r * (th1 - costh1 * sinth1) + a.r * a.r * (th2 - costh2 * sinth2);
    }

    // 过圆外一点圆的切线
    vector<Line> tangent(const Point &a) const
    {
        const int t = is_in(a);
        if (t == 1) return vector<Line>();
        if (t == -1)
        {
            const Point v = { -(a - c).y, (a - c).x};
            return vector<Line> {{a, v}};
        }
        Point e = a - c; e = e / e.len() * r;
        const long double costh = r / c.dis(a), sinth = sqrt(1 - costh * costh);
        const Point t1 = c + e.rot(costh, -sinth), t2 = c + e.rot(costh, sinth);
        return vector<Line> {{a, t1 - a}, {a, t2 - a}};
    }

    // 两圆的公切线
    vector<Line> tangent(const Circle &a) const
    {
        const int t = relation(a);
        vector<Line> lines;
        if (t == -1 || t == 4) return lines;
        if (t == 1 || t == 3)
        {
            const Point p = inter(a)[0], v = { -(a.c - c).y, (a.c - c).x};
            lines.push_back({p, v});
        }
        const long double d = c.dis(a.c);
        const Point e = (a.c - c) / (a.c - c).len();
        if (t <= 2)
        {
            const long double costh = (r - a.r) / d, sinth = sqrt(1 - costh * costh);
            const Point d1 = e.rot(costh, -sinth), d2 = e.rot(costh, sinth);
            const Point u1 = c + d1 * r, u2 = c + d2 * r, v1 = a.c + d1 * a.r, v2 = a.c + d2 * a.r;
            lines.push_back({u1, v1 - u1}); lines.push_back({u2, v2 - u2});
        }
        if (t == 0)
        {
            const long double costh = (r + a.r) / d, sinth = sqrt(1 - costh * costh);
            const Point d1 = e.rot(costh, -sinth), d2 = e.rot(costh, sinth);
            const Point u1 = c + d1 * r, u2 = c + d2 * r, v1 = a.c - d1 * a.r, v2 = a.c - d2 * a.r;
            lines.push_back({u1, v1 - u1}); lines.push_back({u2, v2 - u2});
        }
        return lines;
    }

};
Circle cir;
//凸多边形
template<typename T> struct convex: polygon<T>
{
    // 闵可夫斯基和
    convex operator+(const convex &c) const
    {
        const auto &p = this->p;
        vector<Segment> e1(p.size()), e2(c.p.size()), edge(p.size() + c.p.size());
        vector<point<T>> res; res.reserve(p.size() + c.p.size());
        const auto cmp = [](const Segment & u, const Segment & v) {return argcmp()(u.b - u.a, v.b - v.a);};
        for (size_t i = 0; i < p.size(); i++) e1[i] = {p[i], p[this->nxt(i)]};
        for (size_t i = 0; i < c.p.size(); i++) e2[i] = {c.p[i], c.p[c.nxt(i)]};
        rotate(e1.begin(), min_element(e1.begin(), e1.end(), cmp), e1.end());
        rotate(e2.begin(), min_element(e2.begin(), e2.end(), cmp), e2.end());
        merge(e1.begin(), e1.end(), e2.begin(), e2.end(), edge.begin(), cmp);
        const auto check = [](const vector<point<T>> &res, const point<T> &u)
        {
            const auto back1 = res.back(), back2 = *prev(res.end(), 2);
            return (back1 - back2).toleft(u - back1) == 0 && (back1 - back2) * (u - back1) >= -eps;
        };
        auto u = e1[0].a + e2[0].a;
        for (const auto &v : edge)
        {
            while (res.size() > 1 && check(res, u)) res.pop_back();
            res.push_back(u);
            u = u + v.b - v.a;
        }
        if (res.size() > 1 && check(res, res[0])) res.pop_back();
        return {res};
    }

    // 旋转卡壳
    // 例:凸多边形的直径的平方
    T rotcaliper() const
    {
        const auto &p = this->p;
        T ans = 0;
        T sum = (p[0]^p[1]);
        for (size_t i = 0, j = 1; i < p.size(); i++)
        {
            while (1) {
                auto nxtj = this->nxt(j);
                auto w = (p[nxtj] - p[i]) ^ (cir.c - p[i]);
                if (w <= 0)break;
                if (cir.relation(Line(p[i], p[i] - p[nxtj]))==2)break;
                sum += (p[j] ^ p[nxtj]);
                j = nxtj;
            }
            ans = max(ans, sum + (p[j] ^ p[i]));
            sum -= (p[i] ^ p[this->nxt(i)]);
        }
        return ans;
    }

    // 判断点是否在凸多边形内
    // 复杂度 O(logn)
    // -1 点在多边形边上 | 0 点在多边形外 | 1 点在多边形内
    int is_in(const point<T> &a) const
    {
        const auto &p = this->p;
        if (p.size() == 1) return a == p[0] ? -1 : 0;
        if (p.size() == 2) return segment<T> {p[0], p[1]} .is_on(a) ? -1 : 0;
        if (a == p[0]) return -1;
        if ((p[1] - p[0]).toleft(a - p[0]) == -1 || (p.back() - p[0]).toleft(a - p[0]) == 1) return 0;
        const auto cmp = [&](const point<T> &u, const point<T> &v) {return (u - p[0]).toleft(v - p[0]) == 1;};
        const size_t i = lower_bound(p.begin() + 1, p.end(), a, cmp) - p.begin();
        if (i == 1) return segment<T> {p[0], p[i]} .is_on(a) ? -1 : 0;
        if (i == p.size() - 1 && segment<T> {p[0], p[i]} .is_on(a)) return -1;
        if (segment<T> {p[i - 1], p[i]} .is_on(a)) return -1;
        return (p[i] - p[i - 1]).toleft(a - p[i - 1]) > 0;
    }

    // 凸多边形关于某一方向的极点
    // 复杂度 O(logn)
    // 参考资料:https://codeforces.com/blog/entry/48868
    template<typename F> size_t extreme(const F &dir) const
    {
        const auto &p = this->p;
        const auto check = [&](const size_t i) {return dir(p[i]).toleft(p[this->nxt(i)] - p[i]) >= 0;};
        const auto dir0 = dir(p[0]); const auto check0 = check(0);
        if (!check0 && check(p.size() - 1)) return 0;
        const auto cmp = [&](const point<T> &v)
        {
            const size_t vi = &v - p.data();
            if (vi == 0) return 1;
            const auto checkv = check(vi);
            const auto t = dir0.toleft(v - p[0]);
            if (vi == 1 && checkv == check0 && t == 0) return 1;
            return checkv ^ (checkv == check0 && t <= 0);
        };
        return partition_point(p.begin(), p.end(), cmp) - p.begin();
    }

    // 过凸多边形外一点求凸多边形的切线,返回切点下标
    // 复杂度 O(logn)
    // 必须保证点在多边形外
    pair<size_t, size_t> tangent(const point<T> &a) const
    {
        const size_t i = extreme([&](const point<T> &u) {return u - a;});
        const size_t j = extreme([&](const point<T> &u) {return a - u;});
        return {i, j};
    }

    // 求平行于给定直线的凸多边形的切线,返回切点下标
    // 复杂度 O(logn)
    pair<size_t, size_t> tangent(const line<T> &a) const
    {
        const size_t i = extreme([&](...) {return a.v;});
        const size_t j = extreme([&](...) {return -a.v;});
        return {i, j};
    }
};

using Convex = convex<point_t>;


// 点集的凸包
// Andrew 算法,复杂度 O(nlogn)
Convex convexhull(vector<Point> p)
{
    vector<Point> st;
    if (p.empty()) return Convex{st};
    sort(p.begin(), p.end());
    const auto check = [](const vector<Point> &st, const Point & u)
    {
        const auto back1 = st.back(), back2 = *prev(st.end(), 2);
        return (back1 - back2).toleft(u - back1) <= 0;
    };
    for (const Point &u : p)
    {
        while (st.size() > 1 && check(st, u)) st.pop_back();
        st.push_back(u);
    }
    size_t k = st.size();
    p.pop_back(); reverse(p.begin(), p.end());
    for (const Point &u : p)
    {
        while (st.size() > k && check(st, u)) st.pop_back();
        st.push_back(u);
    }
    st.pop_back();
    return Convex{st};
}
void solve(void) {
    ll n;
    cin >> n;
    Convex con;
    cin >> cir.c.x >> cir.c.y >> cir.r;
    vector<Point>w;
    for (int i = 1; i <= n; i++) {
        Point pp;
        cin >> pp.x >> pp.y;
        con.p.pb(pp);
        w.pb(pp);
    }
    cout << con.rotcaliper() << "\n";
}
int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    int t = 1;
    cin >> t;
    while (t--)
        solve();
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3856kb

input:

3
5
1 1 1
0 0
1 0
5 0
3 3
0 5
6
2 4 1
2 0
4 0
6 3
4 6
2 6
0 3
4
3 3 1
3 0
6 3
3 6
0 3

output:

5
24
0

result:

ok 3 number(s): "5 24 0"

Test #2:

score: -100
Wrong Answer
time: 0ms
memory: 3640kb

input:

1
6
0 0 499999993
197878055 -535013568
696616963 -535013568
696616963 40162440
696616963 499999993
-499999993 499999993
-499999993 -535013568

output:

286862654137719264

result:

wrong answer 1st numbers differ - expected: '0', found: '286862654137719264'