import java.io.PrintWriter; import java.text.DecimalFormat; import java.util.ArrayList; import java.util.Arrays; import java.util.Collections; import java.util.Scanner; import java.util.TreeSet; public class ZeroCrossingsCh1 { static double globalX = 0; static void solve(Scanner fs, PrintWriter out, int tt) { int nHulls = fs.nextInt(); Hull[] hulls = new Hull[nHulls + 1]; for (int i = 0; i < nHulls; i++) { hulls[i] = new Hull(fs); } hulls[nHulls] = new Hull(); for (int i = 0; i <= nHulls; i++) { hulls[i].id = i; } ArrayList < Event > events = new ArrayList<>(); for (Hull h: hulls) { events.addAll(h.getEvents()); } int nQ = fs.nextInt(); Query[] queries = new Query[nQ]; for (int qq = 0; qq < nQ; qq++) { queries[qq] = new Query(fs); events.addAll(queries[qq].getEvents()); } Collections.sort(events); TreeSet set = new TreeSet<>((a, b) -> { double ay = a.evalAt(globalX), by = b.evalAt(globalX); return Double.compare(ay, by); }); for (Event e: events) { globalX = e.x; if (e.qp != null) { Vec position = e.qp.position; Seg hSeg = new Seg(position, position.add(new Vec(1, 0))); Seg higher = set.higher(hSeg); e.qp.node = parent(higher, hulls[nHulls]); } else { if (e.isEval) { Seg higher = set.higher(e.s); e.s.hull.parent = parent(higher, hulls[nHulls]); e.s.hull.parent.children.add(e.s.hull); } else if (e.isStart) { set.add(e.s); } else { set.remove(e.s); } } } hulls[nHulls].calcSubtreeHash(); hulls[nHulls].calcAllHash(new HarmeyerHash(), new HarmeyerHash()); int ans = 0; for (Query qq: queries) { Hull node1 = qq.qp1.node, node2 = qq.qp2.node; boolean possible = node1.allHash.equals(node2.allHash); if (possible) ans++; } out.println("Case #" + tt + ": " + ans); } static Hull parent(Seg higher, Hull rootHull) { if (higher == null) { return rootHull; } else if (higher.isUpper) { //father return higher.hull; } else { //brother return higher.hull.parent; } } // at a particular x: // query points (-0.3) // removals (-0.1) // additions(+0.1) // evals(+0.3) static class Event implements Comparable < Event > { double x, y; boolean isStart; boolean isEval; Seg s; QueryPoint qp; public Event(boolean isStart, Seg s, QueryPoint qp, boolean isEval) { this.isStart = isStart; this.isEval = isEval; this.s = s; this.qp = qp; if (this.s == null) { x = qp.position.x - 0.3; } else { if (isStart) { x = s.from.x + 0.1; } else if (isEval) { x = s.from.x + 0.3; y = s.from.y; } else { x = s.to.x - 0.1; } } } public int compareTo(Event o) { if (x != o.x) return Double.compare(x, o.x); //process higher y first, since we look upwards return Double.compare(o.y, y); } } static class Hull implements Comparable < Hull > { int nPoints; Vec[] points; Vec[] upperHull, lowerHull; Seg[] upperHullSegs, lowerHullSegs; int id; Hull parent; ArrayList < Hull > children = new ArrayList<>(); HarmeyerHash subtreeHash; HarmeyerHash allHash; //root hull public Hull() {} public Hull(Scanner fs) { nPoints = fs.nextInt(); points = new Vec[nPoints]; for (int i = 0; i < nPoints; i++) { points[i] = new Vec(fs.nextInt(), fs.nextInt()); } if (area() < 0) { Vec[] newPoints = new Vec[nPoints]; for (int i = 0; i < nPoints; i++) newPoints[i] = points[nPoints - 1 - i]; points = newPoints; } Vec[] sorted = points.clone(); Arrays.sort(sorted, (a, b) -> { if (a.x != b.x) return Double.compare(a.x, b.x); return Double.compare(a.y, b.y); }); int leftInd = 0, rightInd = 0; for (int i = 0; i < nPoints; i++) if (points[i] == sorted[0]) leftInd = i; for (int i = 0; i < nPoints; i++) if (points[i] == sorted[nPoints - 1]) rightInd = i; if (rightInd < leftInd) rightInd += nPoints; lowerHull = new Vec[rightInd - leftInd + 1]; for (int i = leftInd; i <= rightInd; i++) lowerHull[i - leftInd] = points[i % nPoints]; while (leftInd < rightInd) leftInd += nPoints; upperHull = new Vec[leftInd - rightInd + 1]; for (int i = rightInd; i <= leftInd; i++) upperHull[leftInd - i] = points[i % nPoints]; upperHullSegs = new Seg[upperHull.length - 1]; for (int i = 0; i + 1 < upperHull.length; i++) upperHullSegs[i] = new Seg(upperHull[i], upperHull[i + 1]); lowerHullSegs = new Seg[lowerHull.length - 1]; for (int i = 0; i + 1 < lowerHull.length; i++) lowerHullSegs[i] = new Seg(lowerHull[i], lowerHull[i + 1]); for (Seg s: upperHullSegs) { s.isUpper = true; s.hull = this; } for (Seg s: lowerHullSegs) { s.isUpper = false; s.hull = this; } } double area() { double area = 0; for (int i = 0; i < points.length; i++) { area += points[i].cross(points[(i + 1) % nPoints]); } return area / 2; } // Add events for all lines which aren't vertical. ArrayList < Event > getEvents() { if (nPoints == 0) { // Root query. return new ArrayList<>(); } ArrayList < Event > res = new ArrayList<>(); Seg firstUpper = null; for (Seg s: upperHullSegs) { if (s.isVertical()) continue; if (firstUpper == null) firstUpper = s; res.add(new Event(true, s, null, false)); res.add(new Event(false, s, null, false)); } for (Seg s: lowerHullSegs) { if (s.isVertical()) continue; res.add(new Event(true, s, null, false)); res.add(new Event(false, s, null, false)); } res.add(new Event(false, firstUpper, null, true)); return res; } void calcSubtreeHash() { for (Hull hh: children) { hh.calcSubtreeHash(); } Collections.sort(children); HarmeyerHash me = new HarmeyerHash(); me.add('('); for (Hull hh: children) { me.append(hh.subtreeHash); } me.add(')'); this.subtreeHash = me; } void calcAllHash(HarmeyerHash prefix, HarmeyerHash suffix) { prefix = prefix.clone(); suffix = suffix.clone(); allHash = new HarmeyerHash(); allHash.add('s'); allHash.append(prefix); allHash.add('S'); allHash.append(subtreeHash); allHash.add('e'); allHash.append(suffix); allHash.add('E'); // Now we need to calculate this for our kids prefix.add('('); { HarmeyerHash temp = new HarmeyerHash(); temp.add(')'); temp.append(suffix); suffix = temp; } HarmeyerHash[] subtreesCS = new HarmeyerHash[children.size() + 1]; subtreesCS[0] = new HarmeyerHash(); for (int i = 1; i <= children.size(); i++) { subtreesCS[i] = subtreesCS[i - 1].clone(); subtreesCS[i].append(children.get(i - 1).subtreeHash); } for (int at = 0; at < children.size(); at++) { int countIdentical = 1; while (at + countIdentical < children.size() && children.get(at + countIdentical).subtreeHash.equals( children.get(at).subtreeHash)) { countIdentical++; } HarmeyerHash beforeGroup = subtreesCS[at]; HarmeyerHash afterMe = subtreesCS[children.size()].clone(); afterMe.subHash(subtreesCS[at + 1]); HarmeyerHash groupPrefix = prefix.clone(); groupPrefix.append(beforeGroup); HarmeyerHash groupSuffix = afterMe.clone(); groupSuffix.append(suffix); for (int inGroup = 0; inGroup < countIdentical; inGroup++) { children.get(at + inGroup).calcAllHash(groupPrefix, groupSuffix); } at += countIdentical - 1; } } public int compareTo(Hull o) { return subtreeHash.compareTo(o.subtreeHash); } } static class QueryPoint { Query q; Vec position; Hull node; public QueryPoint(Query q, Vec p) { this.q = q; this.position = p; } Event getEvent() { return new Event(false, null, this, false); } } static class Query { QueryPoint qp1, qp2; public Query(Scanner fs) { Vec p1 = new Vec(fs.nextInt(), fs.nextInt()); Vec p2 = new Vec(fs.nextInt(), fs.nextInt()); qp1 = new QueryPoint(this, p1); qp2 = new QueryPoint(this, p2); } ArrayList < Event > getEvents() { ArrayList < Event > res = new ArrayList<>(); res.add(qp1.getEvent()); res.add(qp2.getEvent()); return res; } } static class VecL implements Comparable < VecL > { long x, y; public VecL(long x, long y) { this.x = x; this.y = y; } public VecL add(VecL o) { return new VecL(x + o.x, y + o.y); } public VecL sub(VecL o) { return new VecL(x - o.x, y - o.y); } public VecL scale(long s) { return new VecL(x * s, y * s); } public long dot(VecL o) { return x * o.x + y * o.y; } public long cross(VecL o) { return x * o.y - y * o.x; } public long mag2() { return dot(this); } public VecL rot90() { return new VecL(-y, x); } public VecL rot270() { return new VecL(y, -x); } public String toString() { return "(" + x + ", " + y + ")"; } public int hashCode() { return Long.hashCode(x << 13 ^ (y * 57)); } public boolean equals(Object oo) { VecL o = (VecL) oo; return x == o.x && y == o.y; } public int compareTo(VecL o) { if (x != o.x) return Long.compare(x, o.x); return Long.compare(y, o.y); } // origin->q1, axes-> quadrant in ccw direction public int quadrant() { if (x == 0 || y == 0) { if (y == 0) { return x >= 0 ? 1 : 3; } return y >= 0 ? 2 : 4; } if (x > 0) { return y > 0 ? 1 : 4; } return y > 0 ? 2 : 3; } public int radialCompare(VecL o) { if (quadrant() == o.quadrant()) { return -Long.signum(cross(o)); } return Integer.compare(quadrant(), o.quadrant()); } } static class Vec { static final double EPS = 1e-6; double x, y; public Vec(double x, double y) { this.x = x; this.y = y; } public Vec add(Vec o) { return new Vec(x + o.x, y + o.y); } public Vec sub(Vec o) { return new Vec(x - o.x, y - o.y); } public Vec scale(double s) { return new Vec(x * s, y * s); } public double dot(Vec o) { return x * o.x + y * o.y; } public double cross(Vec o) { return x * o.y - y * o.x; } public double mag2() { return dot(this); } public double mag() { return Math.sqrt(mag2()); } public Vec unit() { return scale(1 / mag()); } public Vec rot90() { return new Vec(-y, x); } public Vec rot270() { return new Vec(y, -x); } public Vec rotate(double theta) { double PI = Math.PI; double newX = x * Math.cos(theta) + y * Math.cos(PI / 2 + theta); double newY = x * Math.sin(theta) + y * Math.sin(PI / 2 + theta); return new Vec(newX, newY); } // Angle between 0 and 2PI public double angle() { return (Math.atan2(y, x) + 2 * Math.PI) % (2 * Math.PI); } public String toString() { DecimalFormat df = new DecimalFormat("#.##"); return "(" + df.format(x) + ", " + df.format(y) + ")"; } static boolean eq(double a, double b) { return Math.abs(a - b) < EPS; } static boolean leq(double a, double b) { return a - EPS < b; } static boolean geq(double a, double b) { return a + EPS > b; } public boolean equals(Object oo) { Vec o = (Vec) oo; return eq(x, o.x) && eq(y, o.y); } } static class Seg { Vec from, to, dir; Hull hull; boolean isUpper; double m, b; public Seg(Vec from, Vec to) { this.from = from; this.to = to; dir = to.sub(from); if (!isVertical()) { m = dir.y / dir.x; b = from.y - m * from.x; } } boolean isVertical() { return Math.abs(dir.x) < 0.5; } double evalAt(double x) { return m * x + b; } //line-line intersection public Vec lineIntersect(Seg o) { double det = o.dir.x * dir.y - dir.x * o.dir.y; if (Vec.eq(det, 0)) { return null; } double dist = (o.dir.x * (o.from.y - from.y) - o.dir.y * (o.from.x - from.x)) / det; return from.add(dir.scale(dist)); } public boolean containsPoint(Vec o) { double distFromLine = dir.unit().cross(o.sub(from)); if (!Vec.eq(distFromLine, 0)) { return false; } return Vec.eq(dir.mag(), from.sub(o).mag() + to.sub(o).mag()); } // seg-seg intersection public Vec segIntersection(Seg o) { Vec intersect = lineIntersect(o); if (intersect == null) { return null; } return containsPoint(intersect) && o.containsPoint(intersect) ? intersect : null; } // returns 1 if above, 0 if on, -1 if below public int side(Vec o) { Vec oDir = o.sub(from); double distFromLine = dir.unit().cross(oDir); if (Vec.eq(distFromLine, 0)) { return 0; } return (int)Math.signum(distFromLine); } public boolean intersects(Seg o) { return side(o.from) != side(o.to) && o.side(from) != o.side(to); } public Vec getClosestTo(Vec o) { double percentThere = o.sub(from).dot(dir) / dir.mag2(); return from.add(dir.scale(Math.max(0, Math.min(1, percentThere)))); } public Vec projectToLine(Vec o) { return dir.scale(o.sub(from).dot(dir) / dir.mag2()).add(from); } // toContain must be a point with positive x and y coordinates. // this method returns the shortest line segment from the x-axis to the // point to the y axis public static Seg getShortestSegFromAxesContainingQ1Point(Vec toContain) { double slope = -Math.pow(toContain.y / toContain.x, 1.0 / 3); double b = toContain.y - toContain.x * slope; double xInt = -b / slope; return new Seg(new Vec(0, b), new Vec(xInt, 0)); } public String toString() { return from + " -> " + to; } } public static void main(String[] args) throws InterruptedException { Thread t = new Thread(null, null, "", 1 << 29) { public void run() { A(null); } }; t.start(); t.join(); } public static void A(String[] args) { Scanner fs = new Scanner(System.in); PrintWriter out = new PrintWriter(System.out); long time = System.currentTimeMillis(); int T = fs.nextInt(); for (int tt = 0; tt < T; tt++) { solve(fs, out, tt + 1); } fs.close(); out.close(); } // Cannot use 0 as a character in the strings static class HarmeyerHash implements Comparable < HarmeyerHash > { static final long m1 = 8675309, m2 = 1_000_000_007, m3 = 1_000_000_009; long v1 = 0, v2 = 0, v3; int l = 0; static final long s1 = 257, s2 = 619, s3 = 10007; static long[] s1Pow, s2Pow, s3Pow; static boolean precomped = false; void add(char o) { v1 = (v1 * s1 + o) % m1; v2 = (v2 * s2 + o) % m2; v3 = (v3 * s3 + o) % m3; l++; } void subHash(HarmeyerHash smallerPrefix) { HarmeyerHash old = this; HarmeyerHash toSub = smallerPrefix; int diff = this.l - smallerPrefix.l; old.v1 = (old.v1 - (toSub.v1 * s1Pow[diff]) % m1 + m1) % m1; old.v2 = (old.v2 - (toSub.v2 * s2Pow[diff]) % m2 + m2) % m2; old.v3 = (old.v3 - (toSub.v3 * s3Pow[diff]) % m3 + m3) % m3; l = diff; } public int compareTo(HarmeyerHash o) { if (v1 != o.v1) { return Long.compare(v1, o.v1); } if (v2 != o.v2) { return Long.compare(v2, o.v2); } return Long.compare(v3, o.v3); } public boolean equals(Object o) { return compareTo((HarmeyerHash) o) == 0; } public int hashCode() { return (int)v1; } public HarmeyerHash clone() { HarmeyerHash toReturn = new HarmeyerHash(); toReturn.v1 = v1; toReturn.v2 = v2; toReturn.v3 = v3; toReturn.l = l; return toReturn; } static void precomp() { if (precomped) { return; } precomped = true; s1Pow = new long[10_000_000]; s2Pow = new long[10_000_000]; s3Pow = new long[10_000_000]; s1Pow[0] = s2Pow[0] = s3Pow[0] = 1; for (int i = 1; i < s1Pow.length; i++) { s1Pow[i] = (s1Pow[i - 1] * s1) % m1; } for (int i = 1; i < s2Pow.length; i++) { s2Pow[i] = (s2Pow[i - 1] * s2) % m2; } for (int i = 1; i < s3Pow.length; i++) { s3Pow[i] = (s3Pow[i - 1] * s3) % m3; } } //need fastPow if o can be longer than 10^6 void append(HarmeyerHash o) { precomp(); v1 = (v1 * s1Pow[o.l] + o.v1) % m1; v2 = (v2 * s2Pow[o.l] + o.v2) % m2; v3 = (v3 * s3Pow[o.l] + o.v3) % m3; l += o.l; } public static HarmeyerHash[] getPrefixHashes(char[] word) { precomp(); int n = word.length; HarmeyerHash[] toReturn = new HarmeyerHash[n + 1]; toReturn[0] = new HarmeyerHash(); for (int i = 1; i <= n; i++) { toReturn[i] = toReturn[i - 1].clone(); toReturn[i].add(word[i - 1]); } return toReturn; } //inclusive, exclusive public static HarmeyerHash substringHash(HarmeyerHash[] prefixHashes, int from, int to) { if (from == to) { return new HarmeyerHash(); } HarmeyerHash old = prefixHashes[to].clone(), toSub = prefixHashes[from]; int diff = to - from; old.v1 = (old.v1 - (toSub.v1 * s1Pow[diff]) % m1 + m1) % m1; old.v2 = (old.v2 - (toSub.v2 * s2Pow[diff]) % m2 + m2) % m2; old.v3 = (old.v3 - (toSub.v3 * s3Pow[diff]) % m3 + m3) % m3; old.l = to - from; return old; } public String toString() { return "[" + v1 + " " + v2 + " " + v3 + "]"; } } }