QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#694978 | #9520. Concave Hull | answerend42 | AC ✓ | 72ms | 10696kb | C++17 | 5.8kb | 2024-10-31 19:03:55 | 2024-10-31 19:03:56 |
Judging History
answer
#include <bits/stdc++.h>
using namespace std;
using i64 = long long;
using f64 = double;
const double eps = 1e-9;
template <class T>
bool eq(T a, T b) { return abs(a - b) < eps; } // ==
template <class T>
bool gt(T a, T b) { return a - b > eps; } // >
template <class T>
bool lt(T a, T b) { return a - b < -eps; } // <
template <class T>
bool ge(T a, T b) { return a - b > -eps; } // >=
template <class T>
bool le(T a, T b) { return a - b < eps; } // <=
template <class T>
struct Point {
T x, y;
Point(T x_ = 0, T y_ = 0) : x(x_), y(y_) {}
template <class U>
operator Point<U>() { return Point<U>(U(x), U(y)); }
Point& operator+=(Point p) & { x += p.x, y += p.y;return *this; }
Point& operator-=(Point p) & { x -= p.x, y -= p.y;return *this; }
Point& operator*=(T v) & { x *= v, y *= v;return *this; }
Point operator-() const { return Point(-x, -y); }
friend Point operator+(Point a, Point b) { return a += b; }
friend Point operator-(Point a, Point b) { return a -= b; }
friend Point operator*(Point a, T b) { return a *= b; }
friend Point operator*(T a, Point b) { return b *= a; }
friend bool operator==(Point a, Point b) { return a.x == b.x && a.y == b.y; }
friend bool operator!=(Point a, Point b) { return !(a == b); }
friend bool operator<(Point a, Point b) {
if(eq(a.x, b.x)) return lt(a.y, b.y);
return lt(a.x, b.x);
}
friend istream &operator>>(istream &is, Point& p) { return is >> p.x >> p.y; }
friend ostream &operator<<(ostream &os, Point p) { return os << "(" << p.x << ", " << p.y << ")"; }
};
template <class T>
using Vec = Point<T>;
template <class T>
struct Line {
Point<T> a, b;
Line(Point<T> a_ = Point<T>(), Point<T> b_ = Point<T>()) : a(a_), b(b_) {}
};
template <class T>
using Seg = Line<T>;
// 点乘
template <class T>
T dot(Vec<T> a, Vec<T> b) { return a.x * b.x + a.y * b.y; }
// 模长平方
template <class T>
T square(Vec<T> p) { return dot(p, p); }
// 叉乘
template <class T>
T cross(Vec<T> a, Vec<T> b) { return a.x * b.y - a.y * b.x; }
// 向量长度
// square
template <class T>
double len(Vec<T> p) { return sqrt(double(square(p))); }
// 求凸包
template <class T>
vector<Point<T>> hull(vector<Point<T>> p) {
vector<Point<T>> h, l;
sort(p.begin(), p.end(), [&](auto a, auto b) {
if (a.x != b.x) {
return a.x < b.x;
} else {
return a.y < b.y;
}
});
p.erase(unique(p.begin(), p.end()), p.end());
if (p.size() <= 1) {
return p;
}
for (auto a : p) {
while (h.size() > 1 && le(cross(a - h.back(), a - h[h.size() - 2]), (T)0)) {
h.pop_back();
}
while (l.size() > 1 && ge(cross(a - l.back(), a - l[l.size() - 2]), (T)0)) {
l.pop_back();
}
l.push_back(a);
h.push_back(a);
}
l.pop_back();
reverse(h.begin(), h.end());
h.pop_back();
l.insert(l.end(), h.begin(), h.end());
return l;
}
// 直线相交
template <class T>
Point<T> inter(Line<T> l1, Line<T> l2) {
return l1.a + (l1.b - l1.a) * (cross(l2.b - l2.a, l1.a - l2.a) / cross(l2.b - l2.a, l1.a - l1.b));
}
// 点到线段最近点
template <class T>
Point<T> closet_seg(Point<T> p, Line<T> l) {
auto t = p;
t.x += l.a.y - l.b.y;
t.y += l.b.x - l.a.x;
if (gt(cross(l.a - p, t - p) * cross(l.b - p, t - p), (T)0)) {
return lt(dis(p, l.a), dis(p, l.b)) ? l.a : l.b;
}
return inter(Line<T>(p, t), l);
}
// 线段间最近距离
template <class T>
T dis_seg(Seg<T> s1, Seg<T> s2) {
return min(min(closet_seg(s1.a, s2), closet_seg(s1.b, s2),
min(closet_seg(s2.a, s1), closet_seg(s2.b, s1))));
}
template <class T>
i64 area_t(Point<T> p, Seg<T> s) {
return abs(cross(s.a - p, s.b - p));
};
template <class T>
i64 RotateCalipers(vector<Point<T>> P1, vector<Point<T>> P2) {
int n = P1.size(), m = P2.size();
int j = 0;
i64 res = LONG_LONG_MAX;
for(int i = 0; i < n; i++) {
auto u = P1[i], v = P1[(i + 1) % n];
while(abs(cross(u - P2[(j + 1) % m], v - P2[(j + 1) % m])) <
abs(cross(u - P2[j], v - P2[j]))) j = (j + 1) % m;
res = min(res, area_t(P2[j], {u, v}));
}
return res;
}
template <class T>
i64 calculateArea(const vector<Point<T>>& P) {
int n = P.size();
i64 area = 0;
for (int i = 0; i < n; i++) {
int j = (i + 1) % n;
area += cross(P[i], P[j]);
}
return area;
}
template<typename T>
struct std::hash<Point<T>> {
size_t operator()(const Point<T>& p) const noexcept { // 添加 noexcept
return std::hash<T>()(p.x) ^ (std::hash<T>()(p.y) << 1);
}
};
void solve() {
int n;
cin >> n;
vector<Point<i64>> P(n);
for(auto &i : P) cin >> i;
auto tu1 = hull(P);
vector<Point<i64>> left;
unordered_set<Point<i64>> tu1_set(tu1.begin(), tu1.end());
for(int i = 0; i < n; i++) {
if(tu1_set.find(P[i]) == tu1_set.end()) {
left.push_back(P[i]);
}
}
auto tu2 = hull(left);
i64 Area = abs(calculateArea(tu1));
if(tu2.size() == 0) {
cout << "-1\n";
return;
}
if(tu2.size() <= 2) {
i64 d = LONG_LONG_MAX;
for(int i = 0; i < tu2.size(); i++) {
for(int j = 0; j < tu1.size(); j++) {
d = min(area_t(tu2[i], {tu1[j], tu1[(j + 1) % tu1.size()]}), d);
}
}
cout << (i64)(Area - d) << '\n';
return;
}
i64 ans = RotateCalipers(tu1, tu2);
cout << (i64)(Area - ans) << '\n';
}
int main() {
ios::sync_with_stdio(false);
cin.tie(0), cout.tie(0);
int t = 1;
cin >> t;
while(t--) {
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: 0ms
memory: 3628kb
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: 3604kb
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: 29ms
memory: 3696kb
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: 43ms
memory: 3584kb
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: 62ms
memory: 4244kb
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: 48ms
memory: 3988kb
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: 25ms
memory: 7872kb
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: 72ms
memory: 10188kb
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: 66ms
memory: 10696kb
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: 3632kb
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