首页 > 代码库 > UVa 10256 The Great Divide,判断两个凸包是否相离
UVa 10256 The Great Divide,判断两个凸包是否相离
先从给出的两个点集中分别计算出两个凸包,
然后判断两个凸包是否相离。
#include<cstdio> #include<vector> #include<cmath> #include<algorithm> using namespace std; const double eps = 1e-10; double 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 - (const Point& A, const Point& B) { return Vector(A.x-B.x, A.y-B.y); } double Cross(const Vector& A, const Vector& B) { return A.x*B.y - A.y*B.x; } double Dot(const Vector& A, const Vector& B) { return A.x*B.x + A.y*B.y; } bool operator < (const Point& p1, const Point& p2) { return p1.x < p2.x || (p1.x == p2.x && p1.y < p2.y); } bool operator == (const Point& p1, const Point& p2) { return p1.x == p2.x && p1.y == p2.y; } bool SegmentProperIntersection(const Point& a1, const Point& a2, const Point& b1, const Point& b2) { double c1 = Cross(a2-a1,b1-a1), c2 = Cross(a2-a1,b2-a1), 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(const Point& p, const Point& a1, const Point& a2) { return dcmp(Cross(a1-p, a2-p)) == 0 && dcmp(Dot(a1-p, a2-p)) < 0; } // 点集凸包 // 如果不希望在凸包的边上有输入点,把两个 <= 改成 < // 如果不介意点集被修改,可以改成传递引用 vector<Point> ConvexHull(vector<Point> p) { // 预处理,删除重复点 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; } int IsPointInPolygon(const Point& p, const vector<Point>& poly) { int wn = 0; int n = poly.size(); for(int i=0; i<n; ++i) { const Point& p1 = poly[i]; const Point& p2 = poly[(i+1)%n]; if(p1 == p || p2 == p || OnSegment(p, p1, p2)) return -1;//在边界上 int k = dcmp(Cross(p2-p1, p-p1)); int d1 = dcmp(p1.y - p.y); int d2 = dcmp(p2.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; } bool ConvexPolygonDisjoint(const vector<Point> ch1, const vector<Point> ch2) { int c1 = ch1.size(); int c2 = ch2.size(); for(int i=0; i<c1; ++i) if(IsPointInPolygon(ch1[i], ch2) != 0) return false; for(int i=0; i<c2; ++i) if(IsPointInPolygon(ch2[i], ch1) != 0) return false; for(int i=0; i<c1; ++i) for(int j=0; j<c2; ++j) if(SegmentProperIntersection(ch1[i], ch1[(i+1)%c1], ch2[j], ch2[(j+1)%c2])) return false; return true; } int main() { int n, m; while(scanf("%d%d", &n, &m) == 2 && n > 0 && m > 0) { vector<Point> P1, P2; double x, y; 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)); } if(ConvexPolygonDisjoint(ConvexHull(P1), ConvexHull(P2))) printf("Yes\n"); else printf("No\n"); } return 0; }
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