QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#697668 | #9520. Concave Hull | Nephrenn | AC ✓ | 118ms | 15624kb | C++20 | 9.3kb | 2024-11-01 15:16:59 | 2024-11-01 15:17:00 |
Judging History
answer
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> PII;
typedef pair<ll, ll> PLL;
const int MAXN = 2e5 + 10;
const int INF = 0x3f3f3f3f;
const ll INFLL = 0x3f3f3f3f3f3f3f3f;
namespace Geometry {
using T = ll;
constexpr T eps = 1e-8;
bool eq(const T &x, const T &y) { return abs(x - y) <= eps; }
inline constexpr int type(T x, T y) {
if(x == 0 and y == 0) return 0;
if(y < 0 or (y == 0 and x > 0)) return -1;
return 1;
}
struct Point {
T x, y;
constexpr Point(T _x = 0, T _y = 0) : x(_x), y(_y) {}
constexpr Point operator+() const noexcept { return *this; }
constexpr Point operator-() const noexcept { return Point(-x, -y); }
constexpr Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); }
constexpr Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); }
constexpr Point &operator+=(const Point &p) { return x += p.x, y += p.y, *this; }
constexpr Point &operator-=(const Point &p) { return x -= p.x, y -= p.y, *this; }
constexpr T operator*(const Point &p) const { return x * p.x + y * p.y; }
constexpr Point &operator*=(const T &k) { return x *= k, y *= k, *this; }
constexpr Point operator*(const T &k) { return Point(x * k, y * k); }
constexpr bool operator==(const Point &r) const noexcept { return r.x == x and r.y == y; }
constexpr T cross(const Point &r) const { return x * r.y - y * r.x; }
constexpr bool operator<(const Point &r) const { return pair(x, y) < pair(r.x, r.y); }
// 1 : left, 0 : same, -1 : right
constexpr int toleft(const Point &r) const {
auto t = cross(r);
return t > eps ? 1 : t < -eps ? -1 : 0;
}
constexpr bool arg_cmp(const Point &r) const {
int L = type(x, y), R = type(r.x, r.y);
if(L != R) return L < R;
T X = x * r.y, Y = r.x * y;
if(X != Y) return X > Y;
return x < r.x;
}
};
bool arg_cmp(const Point &l, const Point &r) { return l.arg_cmp(r); }
ostream &operator<<(ostream &os, const Point &p) { return os << p.x << " " << p.y; }
istream &operator>>(istream &is, Point &p) {
is >> p.x >> p.y;
return is;
}
struct Line {
Point a, b;
Line() = default;
Line(Point a, Point b) : a(a), b(b) {}
// ax + by = c
Line(T A, T B, T C) {
if(A == 0) {
a = Point(0, C / B), b = Point(1, C / B);
} else if(B == 0) {
a = Point(C / A, 0), b = Point(C / A, 1);
} else {
a = Point(0, C / B), b = Point(C / A, 0);
}
}
// 1 : left, 0 : same, -1 : right
constexpr int toleft(const Point &r) const {
auto t = (b - a).cross(r - a);
return t > eps ? 1 : t < -eps ? -1 : 0;
}
friend std::ostream &operator<<(std::ostream &os, Line &ls) {
return os << "{"
<< "(" << ls.a.x << ", " << ls.a.y << "), (" << ls.b.x << ", " << ls.b.y << ")}";
}
};
istream &operator>>(istream &is, Line &p) { return is >> p.a >> p.b; }
struct Segment : Line {
Segment() = default;
Segment(Point a, Point b) : Line(a, b) {}
};
ostream &operator<<(ostream &os, Segment &p) { return os << p.a << " to " << p.b; }
istream &operator>>(istream &is, Segment &p) {
is >> p.a >> p.b;
return is;
}
struct Circle {
Point p;
T r;
Circle() = default;
Circle(Point p, T r) : p(p), r(r) {}
};
using pt = Point;
using Points = vector<pt>;
using Polygon = Points;
T cross(const pt &x, const pt &y) { return x.x * y.y - x.y * y.x; }
T dot(const pt &x, const pt &y) { return x.x * y.x + x.y * y.y; }
T abs2(const pt &x) { return dot(x, x); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_1_C
// 点の回転方向
int ccw(const Point &a, Point b, Point c) {
b = b - a, c = c - a;
if(cross(b, c) > 0) return +1; // "COUNTER_CLOCKWISE"
if(cross(b, c) < 0) return -1; // "CLOCKWISE"
if(dot(b, c) < 0) return +2; // "ONLINE_BACK"
if(abs2(b) < abs2(c)) return -2; // "ONLINE_FRONT"
return 0; // "ON_SEGMENT"
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 平行判定
bool parallel(const Line &a, const Line &b) { return (cross(a.b - a.a, b.b - b.a) == 0); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_A
// 垂直判定
bool orthogonal(const Line &a, const Line &b) { return (dot(a.a - a.b, b.a - b.b) == 0); }
bool intersect(const Line &l, const Point &p) { return abs(ccw(l.a, l.b, p)) != 1; }
bool intersect(const Line &l, const Line &m) { return !parallel(l, m); }
bool intersect(const Segment &s, const Point &p) { return ccw(s.a, s.b, p) == 0; }
bool intersect(const Line &l, const Segment &s) { return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) <= 0; }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_B
bool intersect(const Segment &s, const Segment &t) { return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 && ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0; }
bool intersect(const Polygon &ps, const Polygon &qs) {
int pl = ps.size(), ql = qs.size(), i = 0, j = 0;
while((i < pl or j < ql) and (i < 2 * pl) and (j < 2 * ql)) {
auto ps0 = ps[(i + pl - 1) % pl], ps1 = ps[i % pl];
auto qs0 = qs[(j + ql - 1) % ql], qs1 = qs[j % ql];
if(intersect(Segment(ps0, ps1), Segment(qs0, qs1))) return true;
Point a = ps1 - ps0;
Point b = qs1 - qs0;
T v = cross(a, b);
T va = cross(qs1 - qs0, ps1 - qs0);
T vb = cross(ps1 - ps0, qs1 - ps0);
if(!v and va < 0 and vb < 0) return false;
if(!v and !va and !vb) {
i += 1;
} else if(v >= 0) {
if(vb > 0)
i += 1;
else
j += 1;
} else {
if(va > 0)
j += 1;
else
i += 1;
}
}
return false;
}
T norm(const Point &p) { return p.x * p.x + p.y * p.y; }
Point projection(const Segment &l, const Point &p) {
T t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
return l.a + (l.a - l.b) * t;
}
Point crosspoint(const Line &l, const Line &m) {
T A = cross(l.b - l.a, m.b - m.a);
T B = cross(l.b - l.a, l.b - m.a);
if(A == 0 and B == 0) return m.a;
return m.a + (m.b - m.a) * (B / A);
}
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_2_C
Point crosspoint(const Segment &l, const Segment &m) { return crosspoint(Line(l), Line(m)); }
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_3_B
// 凸性判定
bool is_convex(const Points &p) {
int n = (int)p.size();
for(int i = 0; i < n; i++) {
if(ccw(p[(i + n - 1) % n], p[i], p[(i + 1) % n]) == -1) return false;
}
return true;
}
Points convex_hull(Points p) {
int n = p.size(), k = 0;
if(n <= 2) return p;
sort(begin(p), end(p), [](pt x, pt y) { return (x.x != y.x ? x.x < y.x : x.y < y.y); });
Points ch(2 * n);
for(int i = 0; i < n; ch[k++] = p[i++]) {
while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) <= 0) --k;
}
for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) <= 0) --k;
}
ch.resize(k - 1);
return ch;
}
// 面積の 2 倍
T area2(const Points &p) {
T res = 0;
for (int i = 0; i < p.size(); ++i) { res += cross(p[i], p[i == p.size() - 1 ? 0 : i + 1]); }
return res;
}
}
using namespace Geometry;
void solve () {
int n;
cin >> n;
Points a(n);
for (int i = 0; i < n; ++i) {
cin >> a[i];
}
auto c1 = convex_hull(a);
set<pt> tmp;
for (auto i : c1) tmp.insert(i);
Points b;
for (int i = 0; i < n; ++i) {
if (!tmp.count(a[i])) b.push_back(a[i]);
}
auto c2 = convex_hull(b);
if (c1.size() <= 2 || c2.empty()) {
cout << "-1\n";
return;
}
ll S1 = area2(c1);
if (c2.size() <= 2) {
ll res = 5e18;
for (int i = 0; i < c2.size(); ++i) {
for (int j = 0; j < c1.size(); ++j) {
int k = (j + 1) % c1.size();
res = min(res, abs(cross(c1[j] - c2[i], c1[k] - c2[i])));
}
}
cout << S1 - res << "\n";
} else {
int p = 0;
Line ini(c1[0], c1[1]);
for (int i = 0; i < c2.size(); ++i) {
if (abs(cross(c1[0] - c2[i], c1[1] - c2[i])) < abs(cross(c1[0] - c2[i], c1[1] - c2[i]))) p = i;
}
ll res = 5e18;
for (int i = 0; i < c1.size(); ++i) {
int j = (i + 1) % c1.size();
Line now(c1[i], c1[j]);
res = min(res, abs(cross(c1[i] - c2[p], c1[j] - c2[p])));
while (abs(cross(c1[i] - c2[(p + 1) % c2.size()], c1[j] - c2[(p + 1) % c2.size()])) < abs(cross(c1[i] - c2[p], c1[j] - c2[p]))) p = (p + 1) % c2.size();
res = min(res, abs(cross(c1[i] - c2[p], c1[j] - c2[p])));
}
cout << S1 - res << "\n";
}
}
int main () {
ios::sync_with_stdio(false);
cin.tie(nullptr);
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: 3816kb
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: 3660kb
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: 30ms
memory: 3736kb
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: 3700kb
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: 68ms
memory: 4336kb
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: 4444kb
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: 19ms
memory: 10572kb
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: 83ms
memory: 15624kb
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: 118ms
memory: 14956kb
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: 3644kb
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