hurricanedanger.cpp

#include<bits/stdc++.h>
using namespace std;

#define INF 1e9
#define EPS 1e-9
#define PI acos(-1.0) // important constant; alternative #define PI (2.0 * acos(0.0))

double DEG_to_RAD(double d) { return d * PI / 180.0; }

double RAD_to_DEG(double r) { return r * 180.0 / PI; }

// struct point_i { int x, y; };    // basic raw form, minimalist mode
struct point_i { int x, y;     // whenever possible, work with point_i
  point_i() { x = y = 0; }                      // default constructor
  point_i(int _x, int _y) : x(_x), y(_y) {} };         // user-defined

struct point { double x, y;   // only used if more precision is needed
  point() { x = y = 0.0; }                      // default constructor
  point(double _x, double _y) : x(_x), y(_y) {}        // user-defined
  bool operator < (point other) const { // override less than operator
	if (fabs(x - other.x) > EPS)                 // useful for sorting
	  return x < other.x;          // first criteria , by x-coordinate
	return y < other.y; }          // second criteria, by y-coordinate
  // use EPS (1e-9) when testing equality of two floating points
	bool operator == (point other) const {
		return (fabs(x - other.x) < EPS && (fabs(y - other.y) < EPS)); } };

double dist(point p1, point p2) {                // Euclidean distance
					  // hypot(dx, dy) returns sqrt(dx * dx + dy * dy)
  return hypot(p1.x - p2.x, p1.y - p2.y); }           // return double

// rotate p by theta degrees CCW w.r.t origin (0, 0)
  point rotate(point p, double theta) {
  double rad = DEG_to_RAD(theta);    // multiply theta with PI / 180.0
  return point(p.x * cos(rad) - p.y * sin(rad),
  	p.x * sin(rad) + p.y * cos(rad)); }

struct line { double a, b, c; };          // a way to represent a line

// the answer is stored in the third parameter (pass by reference)
void pointsToLine(point p1, point p2, line &l) {
  if (fabs(p1.x - p2.x) < EPS) {              // vertical line is fine
	l.a = 1.0;   l.b = 0.0;   l.c = -p1.x;           // default values
} else {
	l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x);
	l.b = 1.0;              // IMPORTANT: we fix the value of b to 1.0
	l.c = -(double)(l.a * p1.x) - p1.y;
} }

// not needed since we will use the more robust form: ax + by + c = 0 (see above)
struct line2 { double m, c; };      // another way to represent a line

int pointsToLine2(point p1, point p2, line2 &l) {
 if (abs(p1.x - p2.x) < EPS) {          // special case: vertical line
   l.m = INF;                    // l contains m = INF and c = x_value
   l.c = p1.x;                  // to denote vertical line x = x_value
   return 0;   // we need this return variable to differentiate result
}
else {
	l.m = (double)(p1.y - p2.y) / (p1.x - p2.x);
	l.c = p1.y - l.m * p1.x;
   return 1;     // l contains m and c of the line equation y = mx + c
} }

bool areParallel(line l1, line l2) {       // check coefficients a & b
	return (fabs(l1.a-l2.a) < EPS) && (fabs(l1.b-l2.b) < EPS); }

bool areSame(line l1, line l2) {           // also check coefficient c
	return areParallel(l1 ,l2) && (fabs(l1.c - l2.c) < EPS); }

// returns true (+ intersection point) if two lines are intersect
	bool areIntersect(line l1, line l2, point &p) {
  if (areParallel(l1, l2)) return false;            // no intersection
  // solve system of 2 linear algebraic equations with 2 unknowns
  p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);
  // special case: test for vertical line to avoid division by zero
  if (fabs(l1.b) > EPS) p.y = -(l1.a * p.x + l1.c);
  else                  p.y = -(l2.a * p.x + l2.c);
  return true; }

struct vec { double x, y;  // name: `vec' is different from STL vector
vec(double _x, double _y) : x(_x), y(_y) {} };

vec toVec(point a, point b) {       // convert 2 points to vector a->b
	return vec(b.x - a.x, b.y - a.y); }

vec scale(vec v, double s) {        // nonnegative s = [<1 .. 1 .. >1]
  return vec(v.x * s, v.y * s); }               // shorter.same.longer

point translate(point p, vec v) {        // translate p according to v
	return point(p.x + v.x , p.y + v.y); }

// convert point and gradient/slope to line
	void pointSlopeToLine(point p, double m, line &l) {
  l.a = -m;                                               // always -m
  l.b = 1;                                                 // always 1
  l.c = -((l.a * p.x) + (l.b * p.y)); }                // compute this

  void closestPoint(line l, point p, point &ans) {
  line perpendicular;         // perpendicular to l and pass through p
  if (fabs(l.b) < EPS) {              // special case 1: vertical line
  	ans.x = -(l.c);   ans.y = p.y;      return; }

  if (fabs(l.a) < EPS) {            // special case 2: horizontal line
  	ans.x = p.x;      ans.y = -(l.c);   return; }

  pointSlopeToLine(p, 1 / l.a, perpendicular);          // normal line
  // intersect line l with this perpendicular line
  // the intersection point is the closest point
  areIntersect(l, perpendicular, ans); }

// returns the reflection of point on a line
  void reflectionPoint(line l, point p, point &ans) {
  	point b;
  closestPoint(l, p, b);                     // similar to distToLine
  vec v = toVec(p, b);                             // create a vector
  ans = translate(translate(p, v), v); }         // translate p twice

  double dot(vec a, vec b) { return (a.x * b.x + a.y * b.y); }

  double norm_sq(vec v) { return v.x * v.x + v.y * v.y; }

// returns the distance from p to the line defined by
// two points a and b (a and b must be different)
// the closest point is stored in the 4th parameter (byref)
  double distToLine(point p, point a, point b, point &c) {
  // formula: c = a + u * ab
  	vec ap = toVec(a, p), ab = toVec(a, b);
  	double u = dot(ap, ab) / norm_sq(ab);
  c = translate(a, scale(ab, u));                  // translate a to c
  return dist(p, c); }           // Euclidean distance between p and c

// returns the distance from p to the line segment ab defined by
// two points a and b (still OK if a == b)
// the closest point is stored in the 4th parameter (byref)
  double distToLineSegment(point p, point a, point b, point &c) {
  	vec ap = toVec(a, p), ab = toVec(a, b);
  	double u = dot(ap, ab) / norm_sq(ab);
  if (u < 0.0) { c = point(a.x, a.y);                   // closer to a
	return dist(p, a); }         // Euclidean distance between p and a
  if (u > 1.0) { c = point(b.x, b.y);                   // closer to b
	return dist(p, b); }         // Euclidean distance between p and b
  return distToLine(p, a, b, c); }          // run distToLine as above

double angle(point a, point o, point b) {  // returns angle aob in rad
	vec oa = toVec(o, a), ob = toVec(o, b);
	return acos(dot(oa, ob) / sqrt(norm_sq(oa) * norm_sq(ob))); }

	double cross(vec a, vec b) { return a.x * b.y - a.y * b.x; }

//// another variant
//int area2(point p, point q, point r) { // returns 'twice' the area of this triangle A-B-c
//  return p.x * q.y - p.y * q.x +
//         q.x * r.y - q.y * r.x +
//         r.x * p.y - r.y * p.x;
//}

// note: to accept collinear points, we have to change the `> 0'
// returns true if point r is on the left side of line pq
	bool ccw(point p, point q, point r) {
		return cross(toVec(p, q), toVec(p, r)) > 0; }

// returns true if point r is on the same line as the line pq
		bool collinear(point p, point q, point r) {
			return fabs(cross(toVec(p, q), toVec(p, r))) < EPS; }

int main() {
	int t; cin >> t;
	while(t--) {
		double x1, y1, x2, y2;
		cin >> x1 >> y1 >> x2 >> y2;
		// ++x1;++x2;++y1;++y2;
		point p1(x1, y1), p2(x2, y2), p3;
		int n; cin >> n;
		double minDist = INF;
		vector<string> cities(n);
		vector<double> dists(n);
		for(int i = 0; i < n; i++) {
			cin >> cities[i];
			double cx, cy; cin >> cx >> cy;
			// ++cx;++cy;
			point pc(cx, cy);
			double dist = distToLine(pc, p1, p2, p3);
			dists[i] = dist;
			if(dist <= minDist - EPS)
				minDist = dist;
		}
		for(int i = 0; i < n; i++) {
			if(abs(dists[i] - minDist) < EPS)
				cout << cities[i] << ' ';
		}
		cout << endl;
	}
}