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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#612765 | #9434. Italian Cuisine | ucup-team2010 | WA | 0ms | 3880kb | C++23 | 18.2kb | 2024-10-05 12:51:24 | 2024-10-05 12:51:25 |
Judging History
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;
}
詳細信息
Test #1:
score: 100
Accepted
time: 0ms
memory: 3724kb
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: 3880kb
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'