update geo templates + others

Implementations/content/geometry (13)/Polygons/HalfPlaneSet.h

@@ -0,0 +1,85 @@
+/**
+ * Description: Online Half-Plane Intersection
+ * Source: retrograd
+ * Verification:
+   * https://infoarena.ro/job_detail/2700262?action=view-source
+   * https://open.kattis.com/problems/bigbrother
+ */
+
+using T = int;
+using T2 = long long;
+using T4 = __int128_t;
+const T2 INF = 2e9;
+
+struct Line {
+	T a, b;
+	T2 c;
+};
+
+bool operator<(Line m, Line n) {
+	auto half = [&](Line m) { return m.b < 0 || m.b == 0 && m.a < 0; };
+	return make_tuple(half(m), (T2)m.b * n.a) <
+		   make_tuple(half(n), (T2)m.a * n.b);
+}
+tuple<T4, T4, T2> LineIntersection(Line m, Line n) {
+	T2 d = (T2)m.a * n.b - (T2)m.b * n.a; // assert(d);
+	T4 x = (T4)m.c * n.b - (T4)m.b * n.c;
+	T4 y = (T4)m.a * n.c - (T4)m.c * n.a;
+	return {x, y, d};
+}
+Line LineFromPoints(T x1, T y1, T x2, T y2) {
+	// everything to the right of ray {x1, y1} -> {x2, y2}
+	T a = y1 - y2, b = x2 - x1;
+	T2 c = (T2)a * x1 + (T2)b * y1;
+	return {a, b, c}; // ax + by <= c
+}
+ostream &operator<<(ostream &out, Line l) {
+	out << "Line " << l.a << " " << l.b << " " << -l.c;
+	// out << "(" << l.a << " * x + " << l.b << " * y <= " << l.c << ")";
+	return out;
+}
+
+struct HalfplaneSet : multiset<Line> {
+	HalfplaneSet() {
+		insert({+1, 0, INF});
+		insert({0, +1, INF});
+		insert({-1, 0, INF});
+		insert({0, -1, INF});
+	};
+	auto adv(auto it, int z) { // z = {-1, +1}
+		return (z == -1 ? --(it == begin() ? end() : it)
+						: (++it == end() ? begin() : it));
+	}
+	bool chk(auto it) {
+		Line l = *it, pl = *adv(it, -1), nl = *adv(it, +1);
+		auto [x, y, d] = LineIntersection(pl, nl);
+		T4 sat = l.a * x + l.b * y - (T4)l.c * d;
+		if (d < 0 && sat < 0) return clear(), 0; // unsat
+		if ((d > 0 && sat <= 0) || (d == 0 && sat < 0)) return erase(it), 1;
+		return 0;
+	}
+	void Cut(Line l) { // add ax + by <= c
+		if (empty()) return;
+		auto it = insert(l);
+		if (chk(it)) return;
+		for (int z : {-1, +1})
+			while (size() && chk(adv(it, z)))
+				;
+	}
+	double Maximize(T a, T b) { // max ax + by (UNTESTED)
+		if (empty()) return -1 / 0.;
+		auto it = lower_bound({a, b});
+		if (it == end()) it = begin();
+		auto [x, y, d] = LineIntersection(*adv(it, -1), *it);
+		return (1.0 * a * x + 1.0 * b * y) / d;
+	}
+	double Area() {
+		double total = 0.;
+		for (auto it = begin(); it != end(); ++it) {
+			auto [x1, y1, d1] = LineIntersection(*adv(it, -1), *it);
+			auto [x2, y2, d2] = LineIntersection(*it, *adv(it, +1));
+			total += (1.0 * x1 * y2 - 1.0 * x2 * y1) / d1 / d2;
+		}
+		return total * 0.5;
+	}
+};

Implementations/content/geometry (13)/Polygons/HullDiameter.h

@@ -1,17 +1,18 @@
 /**
- * Description: rotating caliphers, gives greatest distance between two points in $P$
+ * Description: Rotating caliphers. Returns square of greatest distance 
+   * between two points in $P$.
  * Time: $O(N)$ given convex hull
  * Source: KACTL
  * Verification: https://open.kattis.com/problems/roberthood
  */
 
 #include "ConvexHull (13.2).h"
 
-db diameter(vP P) {
+db diameter2(vP P) {
 	P = hull(P);
-	int n = sz(P), ind = 1; db ans = 0;
+	int n = sz(P), ind = 1; T ans = 0;
 	if (n > 1) F0R(i,n) for (int j = (i+1)%n;;ind = (ind+1)%n) {
-		ckmax(ans,abs(P[i]-P[ind]));
+		ckmax(ans, norm(P[i]-P[ind]));
 		if (cross(P[j]-P[i],P[(ind+1)%n]-P[ind]) <= 0) break;
 	}
 	return ans;