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#include <geometry/sortAround.cpp>
namespace details {
// Liegt p auf der Strecke a-b?
bool pointInLineSegment(pt a, pt b, pt p) {
if (cross(a, b, p) != 0) return false;
auto dist = norm(a - b);
return norm(a - p) < dist && norm(b - p) < dist;
}
// Test auf Streckenschnitt zwischen a-b und c-d.
// (nur intern)
bool lineSegmentIntersection(pt a, pt b, pt c, pt d) {
if (cross(a, b, c) == 0 && cross(a, b, d) == 0) {
return pointInLineSegment(a,b,c) ||
pointInLineSegment(a,b,d) ||
pointInLineSegment(c,d,a) ||
pointInLineSegment(c,d,b);
}
return ccw(a, b, c) * ccw(a, b, d) < 0 &&
ccw(c, d, a) * ccw(c, d, b) < 0;
}
}
namespace Random {
vector<ll> partition(ll n, std::size_t k){//min = 0;
n += k;
vector<ll> res = Random::distinct<ll>(k-1, 1, n);
sort(all(res));
res.emplace_back(n);
ll last = 0;
for (std::size_t i = 0; i < k; i++) {
res[i] -= last;
last += res[i];
res[i]--;
}
return res;
}
vector<pt> convex(int n, ll dim) {
binomial_distribution<int> binomial(n - 2, 0.5);
while (true) {
int left = 1 + binomial(Random::rng);
int down = 1 + binomial(Random::rng);
auto x = Random::partition(2 * dim - 2, left);
auto y = Random::partition(2 * dim - 2, down);
for (auto& z : x) z = -z;
for (auto& z : y) z = -z;
for (auto z : Random::partition(2 * dim - 2, n - left)) x.push_back(z);
for (auto z : Random::partition(2 * dim - 2, n - down)) y.push_back(z);
auto itX = std::partition(x.begin(), x.end(), [](ll z){return z == 0;});
auto itY = std::partition(y.begin(), y.end(), [](ll z){return z != 0;});
if (distance(x.begin(), itX) + distance(itY, y.end()) > n) continue;
shuffle(itX, x.end(), Random::rng);
if (itX != x.begin()) shuffle(y.begin(), itY, Random::rng);
vector<pt> dirs(n);
for (size_t i = 0; i < dirs.size(); i++) {
dirs[i] = pt(x[i], y[i]);
}
sortAround(0, dirs);
vector<pt> res = {{0, 0}};
ll maxX = 0;
ll maxY = 0;
for (auto dir : dirs) {
pt tmp(real(res.back()) + real(dir),
imag(res.back()) + imag(dir));
maxX = std::max<ll>(maxX, real(tmp));
maxY = std::max<ll>(maxY, imag(tmp));
res.emplace_back(tmp);
}
res.pop_back();
for (auto& point : res) {
point = pt(real(point) + dim - 1 - maxX,
imag(point) + dim - 1 - maxY);
}
bool strict = true;
for (int i = 0; i < n; i++) strict &= cross(res[i], res[(i + 1) % n], res[(i + 2) % n]) != 0;
if (strict) return res;
}
}
vector<pt> polygon(int n, ll dim) {
while (true) {
vector<pt> ps = points<pt::value_type>(n, -dim, dim);
bool coolinear = false;
for (int i = 0; i < n; i++) {
for (int j = 0; j < i; j++) {
for (int k = 0; k < j; k++) {
coolinear |= cross(ps[i], ps[j], ps[k]) == 0;
}
}
}
if (coolinear) continue;
bool changed;
do {
changed = false;
for (int i = 0; i < n && !changed; i++) {
for (int j = i + 1; j < n && !changed; j++) {
if (details::lineSegmentIntersection(ps[i], ps[(i+1) % n], ps[j], ps[(j+1) % n])) {
reverse(ps.begin() + i + 1, ps.begin() + j + 1);
changed = true;
}
}
}
} while (changed);
return ps;
}
}
pt integerPoint(ll range) {
return pt(integer<ll>(-range, range),
integer<ll>(-range, range));
}
vector<pt> integerPoints(std::size_t n, ll range) {
vector<pt> res(n);
for (auto& p : res) p = integerPoint(range);
return res;
}
array<pt, 2> line(ll range) {
pt a = integerPoint(range);
pt b = a;
while (b == a) b = integerPoint(range);
return {a, b};
}
array<pt, 3> triangle(ll range) {
pt a = integerPoint(range);
pt b = a;
while (b == a) b = integerPoint(range);
pt c = a;
while (ccw(a, b, c) == 0) c = integerPoint(range);
return {a, b, c};
}
}
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