UVA 10256 The Great Divide (判断凸包相交)
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题目链接:UVA 10256
题意
有n个红点和m个蓝点,问是否存在一条直线能够分开红点和蓝点。
题解
分别求出红点和蓝点的凸包,判断两个凸包是否相交。
凸包不相交的条件:
- 凸包上的任意点都在另一个凸包的外面
- 凸包的任意线段都与另一个凸包不相交
代码
#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
const double pi = acos(-1.0);
class Point
public:
double x, y;
Point(double x = 0, double y = 0) : x(x), y(y)
Point operator+(Point a)
return Point(a.x + x, a.y + y);
Point operator-(Point a)
return Point(x - a.x, y - a.y);
bool operator<(const Point &a) const
if (x == a.x)
return y < a.y;
return x < a.x;
bool operator==(const Point &a) const
if (fabs(x - a.x) < eps && fabs(y - a.y) < eps)
return 1;
return 0;
double length()
return sqrt(x * x + y * y);
;
typedef Point Vector;
double cross(Vector a, Vector b)
return a.x * b.y - a.y * b.x;
double dot(Vector a, Vector b)
return a.x * b.x + a.y * b.y;
bool isclock(Point p0, Point p1, Point p2)
Vector a = p1 - p0;
Vector b = p2 - p0;
if (cross(a, b) < -eps)
return true;
return false;
double getDistance(Point a, Point b)
return sqrt(pow(a.x - b.x, 2) + pow(a.y - b.y, 2));
typedef vector<Point> Polygon;
Polygon Andrew(Polygon s)
Polygon u, l;
if(s.size() < 3) return s;
sort(s.begin(), s.end());
u.push_back(s[0]);
u.push_back(s[1]);
l.push_back(s[s.size() - 1]);
l.push_back(s[s.size() - 2]);
for(int i = 2 ; i < s.size() ; ++i)
for(int n = u.size() ; n >= 2 && !isclock(u[n - 2], u[n - 1], s[i]); --n)
u.pop_back();
u.push_back(s[i]);
for(int i = s.size() - 3 ; i >= 0 ; --i)
for(int n = l.size() ; n >=2 && !isclock(l[n-2],l[n-1],s[i]); --n)
l.pop_back();
l.push_back(s[i]);
for(int i = 1 ; i < u.size() - 1 ; i++) l.push_back(u[i]);
return l;
int dcmp(double x)
if (fabs(x) <= eps)
return 0;
return x > 0 ? 1 : -1;
// 判断点在线段上
bool OnSegment(Point p, Point a1, Point a2)
return dcmp(cross(a1 - p, a2 - p)) == 0 && dcmp(dot(a1 - p, a2 - p)) < 0;
// 判断线段相交
bool Intersection(Point a1, Point a2, Point b1, 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;
// 判断点在凸包内
int isPointInPolygon(Point p, vector<Point> s)
int wn = 0, cc = s.size();
for (int i = 0; i < cc; i++)
Point p1 = s[i];
Point p2 = s[(i + 1) % cc];
if (p1 == p || p2 == p || OnSegment(p, p1, p2)) return -1;
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;
void solve(Polygon s1, Polygon s2)
int c1 = s1.size(), c2 = s2.size();
for(int i = 0; i < c1; ++i)
if(isPointInPolygon(s1[i], s2))
printf("No\n");
return;
for(int i = 0; i < c2; ++i)
if(isPointInPolygon(s2[i], s1))
printf("No\n");
return;
for (int i = 0; i < c1; i++)
for (int j = 0; j < c2; j++)
if (Intersection(s1[i], s1[(i + 1) % c1], s2[j], s2[(j + 1) % c2]))
printf("No\n");
return;
printf("Yes\n");
int main()
int n, m;
while (cin >> n >> m)
if(n == 0 && m == 0) break;
Polygon s1, s2;
for (int i = 0; i < n; ++i)
double x1, x2;
scanf("%lf%lf", &x1, &x2);
s1.push_back(Point(x1, x2));
for (int i = 0; i < m; ++i)
double x1, x2;
scanf("%lf%lf", &x1, &x2);
s2.push_back(Point(x1, x2));
if(s1.size()) s1 = Andrew(s1);
if(s2.size()) s2 = Andrew(s2);
solve(s1, s2);
return 0;
参考
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