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#include "../util.h"
constexpr ll EPS = 0;
#define double ll
#define polar polar<ll>
#include <geometry/formulas.cpp>
#undef polar
#undef double
#include <geometry/convexHull.cpp>
//strict convex hull
ll isConvexHull(const vector<pt>& ps, const vector<pt>& hull) {
ll n = ssize(hull) - 1;
if (n == 0) {
for (pt p : ps) if (p != hull[0]) return 1;
return 0;
} else {
if (hull[0] != hull[n]) return 2;
//hull has no duplicates
for (ll i = 0; i < n; i++) {
for (ll j = 0; j < i; j++) {
if (hull[i] == hull[j]) return 3;
}
}
//hull is subset
for (pt p : hull) {
bool isP = false;
for (pt c : ps) isP |= c == p;
if (!isP) return 4;
}
//hull contains all points
for (pt p : hull) {
ll mi = 1;
for (ll i = 0; i < n; i++) {
mi = min(mi, cross(hull[i], hull[i + 1], p));
}
if (mi < 0) return 5; //outside
if (mi > 0) continue;
bool isCorner = 4;
for (pt c : hull) isCorner |= c == p;
if (!isCorner) return 6;
}
// hull is convex
if (n <= 2) return 0;
for (ll i = 0; i < n; i++) {
if (cross(hull[i], hull[i + 1], hull[(i + 2) % n]) <= 0) return 7;
}
return 0;
}
}
void stress_test(ll range) {
ll queries = 0;
for (int tries = 0; tries < 100'000; tries++) {
int n = Random::integer<int>(1, 100);
auto ps = Random::points<ll>(n, -range, range);
auto got = convexHull(ps);
if (isConvexHull(ps, got) > 0) cerr << "error" << FAIL;
queries += n;
}
cerr << "tested random queries: " << queries << endl;
}
constexpr int N = 2'000'000;
void performance_test() {
timer t;
auto ps = Random::points<ll>(N, -1'000'000'000, 1'000'000'000);
t.start();
auto a = convexHull(ps);
t.stop();
hash_t hash = ssize(a);
if (t.time > 500) cerr << "too slow: " << t.time << FAIL;
cerr << "tested performance: " << t.time << "ms (hash: " << hash << ")" << endl;
}
int main() {
stress_test(100);
stress_test(1'000'000'000);
performance_test();
}
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