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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#616143 | #9434. Italian Cuisine | XiaoTie | WA | 21ms | 3752kb | C++20 | 10.3kb | 2024-10-05 22:47:42 | 2024-10-05 22:47:43 |
Judging History
answer
#include <bits/stdc++.h>
#define int long long
using namespace std;
using point_t = long long; // 全局数据类型,可修改为 long long 等
constexpr point_t eps = 1e-8;
constexpr long double PI = 3.1415926535897932384l;
point_t xc, yc, r;
// 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(-1l, min(1l, ((*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>;
Point o;
// 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>;
// 凸多边形
template <typename T>
struct convex : polygon<T> {
// 闵可夫斯基和
// 旋转卡壳
// func 为更新答案的函数,可以根据题目调整位置
void rotcaliper(T &ans, T &res) const
{
std::function<void(const point<T> &, const point<T> &, const point<T> &)> funcadd = [&](const point<T> &u, const point<T> &v, const point<T> &w) {
ans += abs((w - u) ^ (w - v));
};
std::function<void(const point<T> &, const point<T> &, const point<T> &)> funcsub = [&](const point<T> &u, const point<T> &v, const point<T> &w) {
ans -= abs((w - u) ^ (w - v));
};
std::function<void()> func = [&]() {
res = max(res, ans);
};
const auto &p = this->p;
const auto area = [](const point<T> &u, const point<T> &v, const point<T> &w) { return (w - u) ^ (w - v); };
for (size_t i = 0, j = 1; i < p.size(); i++) {
const auto nxti = this->nxt(i);
while (1) {
int nxtj = this->nxt(j);
point_t cross = ((p[nxtj] - p[i]) ^ (o - p[i]));
if (cross <= 0 || (__int128_t)cross * cross < (__int128_t)r * r * p[i].dis2(p[nxtj])) {
break;
}
funcadd(p[i], p[j], p[nxtj]);
j = nxtj;
}
func();
funcsub(p[i], p[nxti], p[j]);
}
}
// 题目要求的答案
T get_area() const
{
const auto &p = this->p;
T ans = 0;
T res = 0;
rotcaliper(ans, res);
return res;
}
};
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()
{
int n;
cin >> n;
cin >> o.x >> o.y >> r;
vector<Point> po(n);
for (int i = 0; i < n; i++)
cin >> po[i].x >> po[i].y;
Convex t1 = convexhull(po);
int ans = t1.get_area();
// for (auto i : t1.p) {
// cerr << i.x << " " << i.y << endl;
// }
// cerr << endl;
reverse(t1.p.begin(), t1.p.end());
ans = max(ans, (int)t1.get_area());
cout << ans << endl;
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
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: 3604kb
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: 0
Accepted
time: 0ms
memory: 3752kb
input:
1 6 0 0 499999993 197878055 -535013568 696616963 -535013568 696616963 40162440 696616963 499999993 -499999993 499999993 -499999993 -535013568
output:
0
result:
ok 1 number(s): "0"
Test #3:
score: -100
Wrong Answer
time: 21ms
memory: 3632kb
input:
6666 19 -142 -128 26 -172 -74 -188 -86 -199 -157 -200 -172 -199 -186 -195 -200 -175 -197 -161 -188 -144 -177 -127 -162 -107 -144 -90 -126 -87 -116 -86 -104 -89 -97 -108 -86 -125 -80 -142 -74 -162 -72 16 -161 -161 17 -165 -190 -157 -196 -154 -197 -144 -200 -132 -200 -128 -191 -120 -172 -123 -163 -138...
output:
5093 3086 2539 668 3535 7421 4883 5711 5624 1034 2479 3920 4372 2044 4996 4569 2251 4382 4175 1489 1154 3231 4038 1631 5086 14444 1692 6066 687 1512 4849 5456 2675 8341 8557 8235 1013 5203 10853 6042 6300 4480 2303 2728 1739 2187 3385 4266 6322 909 4334 1518 948 5036 1449 2376 3180 4810 1443 1786 46...
result:
wrong answer 16th numbers differ - expected: '5070', found: '4569'