http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=533&page=show_problem&problem=1197

暴力搞定。

如果用旋转卡壳的话应该可以做出来。

/*0.172s*/

#include<bits/stdc++.h>
using namespace std;
const double eps = 1e-10;

struct Point
{
    double x, y;
    Point(double x = 0, double y = 0): x(x), y(y) { }
};
typedef Point Vector;

double dcmp(double x)
{
    if (fabs(x) < eps) return 0;
    else return x < 0 ? -1 : 1;
}

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) return 1; /// 内部
 return 0; /// 外部
}

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++) ///判断红点是否在蓝凸包内部
     if (IsPointInPolygon(ch1[i], ch2)) return false; /// 内部或边界上
 for (int i = 0; i < c2; i++) ///判断蓝点是否在红凸包内部
     if (IsPointInPolygon(ch2[i], ch1)) return false; /// 内部或边界上
 for (int i = 0; i < c1; i++)
        for (int j = 0; j < c2; j++) ///测试线段相交
         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), n)
    {
        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;
}

Comments

comments powered by Disqus