QOJ.ac
QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#762064 | #9520. Concave Hull | Fr1nGeLove | WA | 1ms | 3624kb | C++23 | 14.1kb | 2024-11-19 13:14:34 | 2024-11-19 13:14:35 |
Judging History
answer
#include <bits/stdc++.h>
using i64 = long long;
template<class T>
struct Point {
T x;
T y;
Point(const T &x_ = 0, const T &y_ = 0) : x(x_), y(y_) {}
template<class U>
operator Point<U>() {
return Point<U>(U(x), U(y));
}
Point &operator+=(const Point &p) & {
x += p.x;
y += p.y;
return *this;
}
Point &operator-=(const Point &p) & {
x -= p.x;
y -= p.y;
return *this;
}
Point &operator*=(const T &v) & {
x *= v;
y *= v;
return *this;
}
Point &operator/=(const T &v) & {
x /= v;
y /= v;
return *this;
}
Point operator-() const {
return Point(-x, -y);
}
friend Point operator+(Point a, const Point &b) {
return a += b;
}
friend Point operator-(Point a, const Point &b) {
return a -= b;
}
friend Point operator*(Point a, const T &b) {
return a *= b;
}
friend Point operator/(Point a, const T &b) {
return a /= b;
}
friend Point operator*(const T &a, Point b) {
return b *= a;
}
friend bool operator==(const Point &a, const Point &b) {
return a.x == b.x && a.y == b.y;
}
friend std::istream &operator>>(std::istream &is, Point &p) {
return is >> p.x >> p.y;
}
friend std::ostream &operator<<(std::ostream &os, const Point &p) {
return os << "(" << p.x << ", " << p.y << ")";
}
};
template<class T>
struct Line {
Point<T> a;
Point<T> b;
Line(const Point<T> &a_ = Point<T>(), const Point<T> &b_ = Point<T>()) : a(a_), b(b_) {}
};
template<class T>
T dot(const Point<T> &a, const Point<T> &b) {
return a.x * b.x + a.y * b.y;
}
template<class T>
T cross(const Point<T> &a, const Point<T> &b) {
return a.x * b.y - a.y * b.x;
}
template<class T>
T square(const Point<T> &p) {
return dot(p, p);
}
template<class T>
double length(const Point<T> &p) {
return std::sqrt(square(p));
}
template<class T>
double length(const Line<T> &l) {
return length(l.a - l.b);
}
template<class T>
Point<T> normalize(const Point<T> &p) {
return p / length(p);
}
template<class T>
bool parallel(const Line<T> &l1, const Line<T> &l2) {
return cross(l1.b - l1.a, l2.b - l2.a) == 0;
}
template<class T>
double distance(const Point<T> &a, const Point<T> &b) {
return length(a - b);
}
template<class T>
double distancePL(const Point<T> &p, const Line<T> &l) {
return std::abs(cross(l.a - l.b, l.a - p)) / length(l);
}
template<class T>
double distancePS(const Point<T> &p, const Line<T> &l) {
if (dot(p - l.a, l.b - l.a) < 0) {
return distance(p, l.a);
}
if (dot(p - l.b, l.a - l.b) < 0) {
return distance(p, l.b);
}
return distancePL(p, l);
}
template<class T>
Point<T> rotate(const Point<T> &a) {
return Point(-a.y, a.x);
}
template<class T>
Point<T> rotate(const Point<T> &a, double theta) {
return Point(a.x * std::cos(theta) - a.y * std::sin(theta), a.x * std::sin(theta) + a.y * std::cos(theta));
}
template<class T>
int sgn(const Point<T> &a) {
return a.y > 0 || (a.y == 0 && a.x > 0) ? 1 : -1;
}
template<class T>
bool pointOnLineLeft(const Point<T> &p, const Line<T> &l) {
return cross(l.b - l.a, p - l.a) > 0;
}
template<class T>
Point<T> lineIntersection(const Line<T> &l1, const 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));
}
template<class T>
bool pointOnSegment(const Point<T> &p, const Line<T> &l) {
return cross(p - l.a, l.b - l.a) == 0 && std::min(l.a.x, l.b.x) <= p.x && p.x <= std::max(l.a.x, l.b.x)
&& std::min(l.a.y, l.b.y) <= p.y && p.y <= std::max(l.a.y, l.b.y);
}
template<class T>
std::pair<int, Point<T>> SegmentLineIntersection(const Line<T> &seg, const Line<T> &line) {
int ok = cross(seg.a - line.a, line.b - line.a) * cross(seg.b - line.a, line.b - line.a) <= 0;
return std::make_pair(ok, ok ? lineIntersection(seg, line) : Point<T>());
}
template<class T>
bool pointInPolygon(const Point<T> &a, const std::vector<Point<T>> &p) {
int n = p.size();
for (int i = 0; i < n; i++) {
if (pointOnSegment(a, Line(p[i], p[(i + 1) % n]))) {
return true;
}
}
int t = 0;
for (int i = 0; i < n; i++) {
auto u = p[i];
auto v = p[(i + 1) % n];
if (u.x < a.x && v.x >= a.x && pointOnLineLeft(a, Line(v, u))) {
t ^= 1;
}
if (u.x >= a.x && v.x < a.x && pointOnLineLeft(a, Line(u, v))) {
t ^= 1;
}
}
return t == 1;
}
// 0 : not intersect
// 1 : strictly intersect
// 2 : overlap
// 3 : intersect at endpoint
template<class T>
std::tuple<int, Point<T>, Point<T>> segmentIntersection(const Line<T> &l1, const Line<T> &l2) {
if (std::max(l1.a.x, l1.b.x) < std::min(l2.a.x, l2.b.x)) {
return {0, Point<T>(), Point<T>()};
}
if (std::min(l1.a.x, l1.b.x) > std::max(l2.a.x, l2.b.x)) {
return {0, Point<T>(), Point<T>()};
}
if (std::max(l1.a.y, l1.b.y) < std::min(l2.a.y, l2.b.y)) {
return {0, Point<T>(), Point<T>()};
}
if (std::min(l1.a.y, l1.b.y) > std::max(l2.a.y, l2.b.y)) {
return {0, Point<T>(), Point<T>()};
}
if (cross(l1.b - l1.a, l2.b - l2.a) == 0) {
if (cross(l1.b - l1.a, l2.a - l1.a) != 0) {
return {0, Point<T>(), Point<T>()};
} else {
auto maxx1 = std::max(l1.a.x, l1.b.x);
auto minx1 = std::min(l1.a.x, l1.b.x);
auto maxy1 = std::max(l1.a.y, l1.b.y);
auto miny1 = std::min(l1.a.y, l1.b.y);
auto maxx2 = std::max(l2.a.x, l2.b.x);
auto minx2 = std::min(l2.a.x, l2.b.x);
auto maxy2 = std::max(l2.a.y, l2.b.y);
auto miny2 = std::min(l2.a.y, l2.b.y);
Point<T> p1(std::max(minx1, minx2), std::max(miny1, miny2));
Point<T> p2(std::min(maxx1, maxx2), std::min(maxy1, maxy2));
if (!pointOnSegment(p1, l1)) {
std::swap(p1.y, p2.y);
}
if (p1 == p2) {
return {3, p1, p2};
} else {
return {2, p1, p2};
}
}
}
auto cp1 = cross(l2.a - l1.a, l2.b - l1.a);
auto cp2 = cross(l2.a - l1.b, l2.b - l1.b);
auto cp3 = cross(l1.a - l2.a, l1.b - l2.a);
auto cp4 = cross(l1.a - l2.b, l1.b - l2.b);
if ((cp1 > 0 && cp2 > 0) || (cp1 < 0 && cp2 < 0) || (cp3 > 0 && cp4 > 0) || (cp3 < 0 && cp4 < 0)) {
return {0, Point<T>(), Point<T>()};
}
Point p = lineIntersection(l1, l2);
if (cp1 != 0 && cp2 != 0 && cp3 != 0 && cp4 != 0) {
return {1, p, p};
} else {
return {3, p, p};
}
}
template<class T>
double distanceSS(const Line<T> &l1, const Line<T> &l2) {
if (std::get<0>(segmentIntersection(l1, l2)) != 0) {
return 0.0;
}
return std::min({distancePS(l1.a, l2), distancePS(l1.b, l2), distancePS(l2.a, l1), distancePS(l2.b, l1)});
}
template<class T>
bool segmentInPolygon(const Line<T> &l, const std::vector<Point<T>> &p) {
int n = p.size();
if (!pointInPolygon(l.a, p)) {
return false;
}
if (!pointInPolygon(l.b, p)) {
return false;
}
for (int i = 0; i < n; i++) {
auto u = p[i];
auto v = p[(i + 1) % n];
auto w = p[(i + 2) % n];
auto [t, p1, p2] = segmentIntersection(l, Line(u, v));
if (t == 1) {
return false;
}
if (t == 0) {
continue;
}
if (t == 2) {
if (pointOnSegment(v, l) && v != l.a && v != l.b) {
if (cross(v - u, w - v) > 0) {
return false;
}
}
} else {
if (p1 != u && p1 != v) {
if (pointOnLineLeft(l.a, Line(v, u))
|| pointOnLineLeft(l.b, Line(v, u))) {
return false;
}
} else if (p1 == v) {
if (l.a == v) {
if (pointOnLineLeft(u, l)) {
if (pointOnLineLeft(w, l)
&& pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, l)
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
} else if (l.b == v) {
if (pointOnLineLeft(u, Line(l.b, l.a))) {
if (pointOnLineLeft(w, Line(l.b, l.a))
&& pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, Line(l.b, l.a))
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
} else {
if (pointOnLineLeft(u, l)) {
if (pointOnLineLeft(w, Line(l.b, l.a))
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
} else {
if (pointOnLineLeft(w, l)
|| pointOnLineLeft(w, Line(u, v))) {
return false;
}
}
}
}
}
}
return true;
}
template<class T>
std::vector<Point<T>> getConvex(std::vector<Point<T>> p) {
std::sort(p.begin(), p.end(),
[&](auto a, auto b) {
return a.x < b.x || (a.x == b.x && a.y < b.y);
});
std::vector<Point<T>> hi, lo;
for (auto p : p) {
while (hi.size() > 1 && cross(hi.back() - hi[hi.size() - 2], p - hi.back()) > 0) {
hi.pop_back();
}
while (!hi.empty() && hi.back().x == p.x) {
hi.pop_back();
}
hi.push_back(p);
while (lo.size() > 1 && cross(lo.back() - lo[lo.size() - 2], p - lo.back()) < 0) {
lo.pop_back();
}
if (lo.empty() || lo.back().x < p.x) {
lo.push_back(p);
}
}
std::vector<Point<T>> convex = lo;
if (!convex.empty() && lo.back() == hi.back()) {
convex.pop_back();
}
for (int i = hi.size() - 1; i >= 0; i--) {
convex.push_back(hi[i]);
}
if (!convex.empty() && convex.front() == convex.back()) {
convex.pop_back();
}
return convex;
}
template<class T>
std::vector<Point<T>> hp(std::vector<Line<T>> lines) {
std::sort(lines.begin(), lines.end(), [&](auto l1, auto l2) {
auto d1 = l1.b - l1.a;
auto d2 = l2.b - l2.a;
if (sgn(d1) != sgn(d2)) {
return sgn(d1) == 1;
}
return cross(d1, d2) > 0;
});
std::deque<Line<T>> ls;
std::deque<Point<T>> ps;
for (auto l : lines) {
if (ls.empty()) {
ls.push_back(l);
continue;
}
while (!ps.empty() && !pointOnLineLeft(ps.back(), l)) {
ps.pop_back();
ls.pop_back();
}
while (!ps.empty() && !pointOnLineLeft(ps[0], l)) {
ps.pop_front();
ls.pop_front();
}
if (cross(l.b - l.a, ls.back().b - ls.back().a) == 0) {
if (dot(l.b - l.a, ls.back().b - ls.back().a) > 0) {
if (!pointOnLineLeft(ls.back().a, l)) {
assert(ls.size() == 1);
ls[0] = l;
}
continue;
}
return {};
}
ps.push_back(lineIntersection(ls.back(), l));
ls.push_back(l);
}
while (!ps.empty() && !pointOnLineLeft(ps.back(), ls[0])) {
ps.pop_back();
ls.pop_back();
}
if (ls.size() <= 2) {
return {};
}
ps.push_back(lineIntersection(ls[0], ls.back()));
return std::vector(ps.begin(), ps.end());
}
using real = i64;
using P = Point<real>;
void solve() {
int n;
std::cin >> n;
std::vector<P> p(n);
std::set<std::pair<int, int>> s;
for (int i = 0; i < n; i++) {
std::cin >> p[i];
}
auto out = getConvex(p);
for (auto po : out) {
s.emplace(po.x, po.y);
}
std::vector<P> pp;
for (auto po : p) {
if (!s.contains(std::make_pair(po.x, po.y))) {
pp.push_back(po);
}
}
auto in = getConvex(pp);
// debug(out);
// debug(in);
Line<i64> line(out[0], out[1]);
double dis = 1E18;
int select = -1;
for (int i = 0; i < in.size(); i++) {
if (distancePL(in[i], line) < dis) {
select = i;
dis = distancePL(in[i], line);
}
}
if (select == -1) {
std::cout << "-1\n";
return;
}
double ans = 0;
double area = 0;
for (int i = 0; i < out.size(); i++) {
area += cross(out[i], out[(i + 1) % int(out.size())]);
}
for (int i = 0, j = select; i < out.size(); i++) {
line = {out[i], out[(i + 1) % int(out.size())]};
while (j < out.size() && distancePL(in[j], line) > distancePL(in[(j + 1) % int(in.size())], line)) {
j++;
}
ans = std::max(ans, area - length(line) * distancePL(in[j], line));
}
// ans *= 0.5;
std::cout << i64(ans) << "\n";
}
int main() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
// std::cout << std::fixed << std::setprecision(12);
int t;
std::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: 3624kb
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: -100
Wrong Answer
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:
2178418010787347456 1826413114144932608 1651687576234220032 1883871859778999040 2117861879018439936 894016174881844608 2271191316922159360 1998636064101411584 1740474221286618880 1168195646932543232
result:
wrong answer 1st lines differ - expected: '2178418010787347715', found: '2178418010787347456'