#include <bits/stdc++.h> using namespace std; int n, m; double x, y; const double eps = 1e-10; int dcmp(double x) { if (fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; } struct Point { double x, y; Point(double x = 0, double y = 0): x(x), y(y) {} }; typedef Point Vector; Vector operator-(Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); } Vector operator+(Vector A, Vector B) { return Vector(A.x + B.x, A.y + B.y); } bool operator == (const Point&a, const Point &b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; } double Dot(Vector A, Vector B) { return A.x * B.x + A.y * B.y; } double Cross(Vector A, Vector B) { return A.x * B.y - A.y * B.x; } bool operator<(const Point&a, const Point &b) { return a.x < b.x || (a.x == b.x && a.y < b.y); } bool SegmentProperIntersection(Point a1, Point a2, Point b1, Point b2) { double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1); double c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1); return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0; } bool OnSegment(Point p, Point a1, Point a2) { return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0; } typedef vector<Point> Polygon; int isPointInPolygon(Point p, Polygon poly) { int wn = 0; int n = poly.size(); for (int i = 0; i < n; i++) { if ( poly[i] == p || poly[(i + 1) % n] == p || OnSegment(p, poly[i], poly[(i + 1) % n])) return -1; int k = dcmp(Cross(poly[(i + 1) % n] - poly[i], p - poly[i])); int d1 = dcmp(poly[i].y - p.y); int d2 = dcmp(poly[(i + 1) % n].y - p.y); if (k > 0 && d1 <= 0 && d2 > 0) wn++; if (k < 0 && d2 <= 0 && d1 > 0) wn--; } if (wn != 0) return 1; return 0; } vector<Point>ConvexHull(vector<Point>p) { sort(p.begin(), p.end()); p.erase(unique(p.begin(), p.end()), p.end()); int n = p.size(); int m = 0; vector<Point>ch(n + 1); for (int i = 0; i < n; i++) { while (m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m--; ch[m++] = p[i]; } int k = m; for (int i = n - 2; i >= 0; i--) { while (m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) m--; ch[m++] = p[i]; } if (n > 1) m--; ch.resize(m); return ch; } bool ConvexPolygonDisjoint(const Polygon p1, const Polygon p2) { int c1 = p1.size(); int c2 = p2.size(); for (int i = 0; i < c1; i++) if (isPointInPolygon(p1[i], p2)) return false; for (int i = 0; i < c2; i++) if (isPointInPolygon(p2[i], p1)) return false; for (int i = 0; i < c1; i++) for (int j = 0; j < c2; j++) if (SegmentProperIntersection(p1[i], p1[(i + 1) % c1], p2[j], p2[(j + 1) % c2])) return false; return true; } int main(int argc, char const *argv[]) { while (scanf("%d%d", &n, &m) != EOF) { if (n == 0 && m == 0) break; std::vector<Point> p1, p2; for (int i = 0; i < n; i++) { scanf("%lf%lf", &x, &y); p1.push_back(Point(x, y)); } for (int i = 0; i < m; i++) { scanf("%lf%lf", &x, &y); p2.push_back(Point(x, y)); } printf("%s\n", (ConvexPolygonDisjoint(ConvexHull(p1), ConvexHull(p2)) ? "Yes" : "No")); } return 0; }
求出两凸包,暴力判断是否相交,
退化为点或线段的情况一样处理,只要碰到另一个就是NO。