QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#683184 | #9520. Concave Hull | F0giveners | AC ✓ | 73ms | 11816kb | C++20 | 15.4kb | 2024-10-27 19:18:33 | 2024-10-30 01:33:37 |
Judging History
This is the latest submission verdict.
- [2024-10-30 01:29:57]
- hack成功,自动添加数据
- (/hack/1083)
- [2024-10-27 19:18:33]
- Submitted
answer
#include <bits/stdc++.h>
using namespace std;
using ui = unsigned int;
using ull = unsigned long long;
using ll = long long;
#define endl '\n'
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int maxn = 2e5 + 10;
const int mod = 1000000007;
#include <bits/stdc++.h>
using namespace std;
#define int ll
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;
// 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 abs(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
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
// func 为更新答案的函数,可以根据题目调整位置
template <typename F>
void rotcaliper(const F &func) const
{
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);
func(p[i], p[nxti], p[j]);
while (area(p[this->nxt(j)], p[i], p[nxti]) >= area(p[j], p[i], p[nxti]))
{
j = this->nxt(j);
func(p[i], p[nxti], p[j]);
}
}
}
// 凸多边形的直径的平方
T diameter2() const
{
const auto &p = this->p;
if (p.size() == 1)
return 0;
if (p.size() == 2)
return p[0].dis2(p[1]);
T ans = 0;
auto func = [&](const point<T> &u, const point<T> &v, const point<T> &w)
{ ans = max({ans, w.dis2(u), w.dis2(v)}); };
rotcaliper(func);
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 &u, const Point &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 &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};
if (p.size() == 1)
return Convex{p};
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};
}
bool _output = 1;
void solve()
{
int n;
cin >> n;
vector<Point> a(n);
for (int i = 0; i < n; i++)
{
cin >> a[i].x >> a[i].y;
}
sort(a.begin(), a.end());
auto p1 = convexhull(a);
auto c1 = p1.p;
if (c1.size() == n)
{
cout << -1 << endl;
return;
}
set<Point> st;
for (int i = 0; i < c1.size(); i++)
{
st.insert(c1[i]);
}
// cout << "! ";
// for (auto x : st)
// {
// cout << x.x << " " << x.y << endl;
// }
int st_area = p1.area();
vector<Point> b;
for (int i = 0; i < n; i++)
{
if (!st.count(a[i]))
b.push_back(a[i]);
}
auto p2 = convexhull(b);
auto c2 = p2.p;
// cout << c2.size() << endl;
int sz = c1.size();
int pos = 0;
auto make = [&](Point p1, Point p2, Point p3)
{
return (ll)abs((p2 - p1) ^ (p3 - p1));
};
ll ans = 0;
for (int i = 0; i < c1.size(); i++)
{
auto p1 = c1[i];
auto p2 = c1[(i + 1) % sz];
auto p3 = c2[pos];
auto p4 = c2[(pos + 1) % c2.size()];
while (make(p1, p2, p3) > make(p1, p2, p4))
{
pos = (pos + 1) % c2.size();
p3 = c2[pos];
p4 = c2[(pos + 1) % c2.size()];
}
ans = max(ans, st_area - make(p1, p2, p3));
}
cout << ans << endl;
}
signed main()
{
ios::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
int _ = 1;
if (_output)
cin >> _;
while (_--)
solve();
return 0;
}
这程序好像有点Bug,我给组数据试试?
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 1ms
memory: 3844kb
input:
2 6 -2 0 1 -2 5 2 0 4 1 2 3 1 4 0 0 1 0 0 1 1 1
output:
40 -1
result:
ok 2 lines
Test #2:
score: 0
Accepted
time: 1ms
memory: 3700kb
input:
10 243 -494423502 -591557038 -493438474 -648991734 -493289308 -656152126 -491185085 -661710614 -489063449 -666925265 -464265894 -709944049 -447472922 -737242534 -415977509 -773788538 -394263365 -797285016 -382728841 -807396819 -373481975 -814685302 -368242265 -818267002 -344482838 -833805545 -279398...
output:
2178418010787347715 1826413114144932145 1651687576234220014 1883871859778998985 2119126281997959892 894016174881844630 2271191316922158910 1998643358049669416 1740474221286618711 1168195646932543192
result:
ok 10 lines
Test #3:
score: 0
Accepted
time: 25ms
memory: 3780kb
input:
1000 125 64661186 -13143076 302828013 -185438065 -418713797 -191594241 430218126 -397441626 354327250 -836704374 149668812 -598584998 311305970 66790541 199720625 -592356787 468137 -584752683 258775829 96211747 -358669612 -134890109 -129221188 -998432368 -277309896 -140056561 356901185 420557649 -51...
output:
1986320445246155278 1900093336073022078 1612088392301142476 2012259136539173407 1819942017252118749 1772230185841892196 1164835025329039520 1527446155241140517 1807368432185303666 1236918659444944569 1306839249967484778 1984123720246784099 1868728080720036006 667458140583450322 2127932992585026491 4...
result:
ok 1000 lines
Test #4:
score: 0
Accepted
time: 41ms
memory: 3612kb
input:
10000 9 484630042 51929469 -40468396 -517784096 98214104 -103353239 629244333 -475172587 106398764 153884485 49211709 -44865749 1 10 166321833 -247717657 406208245 668933360 13 548702216 -631976459 37150086 -292461024 707804811 -486185860 239775286 -903166050 10096571 -541890068 686103484 558731937 ...
output:
950319193795831919 1661025342421008544 1285164852091455548 1159924751776806668 1206071151805176722 794021230296144371 699991678992587791 1133990718508584290 1486311831172661605 984875884297072200 1327767982175057345 758247019006396699 1355381234262206155 1139262078529131471 1613462877860621700 12392...
result:
ok 10000 lines
Test #5:
score: 0
Accepted
time: 64ms
memory: 4448kb
input:
100 439 471536154 -312612104 155692036 -937312180 -461624056 -357636609 236656684 -911414873 -288656914 -74788431 -465779694 -381475149 -334197401 -903065737 491513067 -447615916 337664889 -852236281 -281689379 -53519178 -159101704 -920779200 -326159514 -95396204 21868593 -994282736 488425383 -41046...
output:
1973162724053130487 2054612790507830954 1726805687754843724 1699420177872986528 2129388571309147631 2198295137903288810 1697185883164440272 1219697450095721478 2027023581922285255 1674691247127206655 1673105966817209954 2179188692918747442 2146544318743443141 2230356305133660648 1676850321902993764 ...
result:
ok 100 lines
Test #6:
score: 0
Accepted
time: 54ms
memory: 4420kb
input:
100 1362 -467257672 -466669 -467054869 -478108 -466973270 -481776 -466556983 -499770 -466329414 -508693 -466248017 -511805 -466158865 -513786 -466101273 -515035 -465927700 -518748 -465717624 -522106 -465303448 -528127 -465124548 -530726 -464649746 -536693 -464554872 -537799 -464478196 -538680 -46416...
output:
1666097696993497 1791366071767866 1806187278469532 1683419854733713 1685891971828916 1730190225081651 1787048201197565 1850308098208660 1710694884375502 1826363113637639 1816375352374659 2047431269497691 1549806516003854 1829438662895747 1678707854135065 1687423392883819 2121960009997761 16687219538...
result:
ok 100 lines
Test #7:
score: 0
Accepted
time: 30ms
memory: 8168kb
input:
2 62666 -486101704 -505730259 -486101698 -506082699 -486101689 -506111362 -486101682 -506126031 -486101528 -506293759 -486101259 -506556385 -486101196 -506613483 -486101154 -506648604 -486100935 -506831392 -486100631 -507083675 -486100470 -507199151 -486100233 -507368923 -486100193 -507397039 -48609...
output:
2178736946152219010 1825181940245096152
result:
ok 2 lines
Test #8:
score: 0
Accepted
time: 71ms
memory: 10884kb
input:
2 100000 301945097 76373292 467957663 -286424714 8245445 -597212507 -474204621 -708828667 184159460 105942538 443435905 -429212625 490658771 -382198656 82512047 -612522436 -228221388 -965890088 394789011 -145801151 -106120174 -528202395 428939626 -194437311 497429477 -527407728 365739746 -114818962 ...
output:
2502889432701099511 2267250485735988121
result:
ok 2 lines
Test #9:
score: 0
Accepted
time: 73ms
memory: 11816kb
input:
2 100000 221128057 -975244780 -618765360 -785575858 422567455 -906331476 -988680318 -150037424 -929870145 367887908 -757813541 -652471177 291995621 -956419655 -785381507 619012026 468864522 -883270094 -588416522 808557973 859345881 511394814 988105866 153775152 216931298 -976186873 467050734 8842305...
output:
6283183114882825575 6283183188903854361
result:
ok 2 lines
Test #10:
score: 0
Accepted
time: 0ms
memory: 3844kb
input:
7 5 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 1 0 -1 0 5 1000000000 1000000000 -1000000000 -1000000000 -2 0 -1 0 1 -1 6 1000000000 1000000000 -1000000000 -1000000000 -3 0 -1 0 0 -1 1 -1 4 -1000000000 -1000000000 1000000000 -1000000000 1000000000 1000000000 -1000000000 1000...
output:
4000000000000000000 7000000000 9000000001 -1 6000000002000000000 7999999998000000000 -1
result:
ok 7 lines
Extra Test:
score: 0
Extra Test Passed