[UVA Live 12931 Common Area]扫描线

题意：判断两个多边形是否有面积大于0的公共部分

思路：扫描线基础。

#pragma comment(linker, "/STACK:10240000")
#include <bits/stdc++.h>
using namespace std;

#define X                   first
#define Y                   second
#define pb                  push_back
#define mp                  make_pair
#define all(a)              (a).begin(), (a).end()
#define fillchar(a, x)      memset(a, x, sizeof(a))

typedef long long ll;
typedef pair<int, int> pii;

namespace Debug {
void print(){cout<<endl;}template<typename T>
void print(const T t){cout<<t<<endl;}template<typename F,typename...R>
void print(const F f,const R...r){cout<<f<<" ";print(r...);}template<typename T>
void print(T*p, T*q){int d=p<q?1:-1;while(p!=q){cout<<*p<<", ";p+=d;}cout<<endl;}
}
template<typename T>bool umax(T&a, const T&b){return b<=a?false:(a=b,true);}
template<typename T>bool umin(T&a, const T&b){return b>=a?false:(a=b,true);}
/* -------------------------------------------------------------------------------- */


const double eps = 1e-10;/** 设置比较精度 **/
struct Real {
    double x;
    double get() { return x; }
    Real(const double &x) { this->x = x; }
    Real() {}

    Real operator + (const Real &that) const { return Real(x + that.x);}
    Real operator - (const Real &that) const { return Real(x - that.x);}
    Real operator * (const Real &that) const { return Real(x * that.x);}
    Real operator / (const Real &that) const { return Real(x / that.x);}

    Real operator += (const Real &that) { return Real(x += that.x); }
    Real operator -= (const Real &that) { return Real(x -= that.x); }
    Real operator *= (const Real &that) { return Real(x *= that.x); }
    Real operator /= (const Real &that) { return Real(x /= that.x); }

    bool operator < (const Real &that) const { return x - that.x <= -eps; }
    bool operator > (const Real &that) const { return x - that.x >= eps; }
    bool operator == (const Real &that) const { return x - that.x > -eps && x - that.x < eps; }
    bool operator <= (const Real &that) const { return x - that.x < eps; }
    bool operator >= (const Real &that) const { return x - that.x > -eps; }
};

struct Point {
    Real x, y;
    int read() { return scanf("%lf%lf", &x.x, &y.x); }
    Point(const Real &x, const Real &y) { this->x = x; this->y = y; }
    Point() {}
    Point operator + (const Point &that) const { return Point(this->x + that.x, this->y + that.y); }
    Point operator - (const Point &that) const { return Point(this->x - that.x, this->y - that.y); }
    Real operator * (const Point &that) const { return x * that.x + y * that.y; }
    Point operator * (const Real &that) const { return Point(x * that, y * that); }
    Point operator += (const Point &that)  { return Point(this->x += that.x, this->y += that.y); }
    Point operator -= (const Point &that)  { return Point(this->x -= that.x, this->y -= that.y); }
    Point operator *= (const Real &that)  { return Point(x *= that, y *= that); }
    Real cross(const Point &that) const { return x * that.y - y * that.x; }
};
typedef Point Vector;

struct Segment {
    Point a, b;
    Segment(const Point &a, const Point &b) { this->a = a; this->b = b; }
    Segment() {}
    bool intersect(const Segment &that) const {
        Point c = that.a, d = that.b;
        Vector ab = b - a, cd = d - c, ac = c - a, ad = d - a, ca = a - c, cb = b - c;
        return ab.cross(ac) * ab.cross(ad) < 0 && cd.cross(ca) * cd.cross(cb) < 0;
    }
    Point getLineIntersection(const Segment &that) const {
        Vector u = a - that.a, v = b - a, w = that.b - that.a;
        Real t = w.cross(u) / v.cross(w);
        return a + v * t;
    }
};

Point p1[123], p2[123];
Segment side1[123], side2[123];

bool cmp(const pair<Segment, int> &a, const pair<Segment, int> &b) {
    return a.X.a.x + a.X.b.x < b.X.a.x + b.X.b.x;
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("in.txt", "r", stdin);
    //freopen("out.txt", "w", stdout);
#endif // ONLINE_JUDGE
    int n, m, cas = 0;
    while (cin >> n) {
        for (int i = 0; i < n; i ++) {
            p1[i].read();
            if (i) side1[i - 1] = Segment(p1[i - 1], p1[i]);
        }
        side1[n - 1] = Segment(p1[n - 1], p1[0]);
        cin >> m;
        for (int i = 0; i < m; i ++) {
            p2[i].read();
            if (i) side2[i - 1] = Segment(p2[i - 1], p2[i]);
        }
        side2[m - 1] = Segment(p2[m - 1], p2[0]);
        /** 得到所有的扫描线并排序去重 **/
        vector<Real> Y;
        for (int i = 0; i < n; i ++) Y.pb(p1[i].y);
        for (int i = 0; i < m; i ++) Y.pb(p2[i].y);
        for (int i = 0; i < n; i ++) {
            for (int j = 0; j < m; j ++) {
                if (side1[i].intersect(side2[j])) {
                    Y.pb(side1[i].getLineIntersection(side2[j]).y);
                }
            }
        }
        sort(all(Y));
        Y.resize(unique(all(Y)) - Y.begin());
        //Debug::print("Y.size=", Y.size());
        Real area = 0;
        for (int i = 1; i < Y.size(); i ++) {
            vector<pair<Segment, int> > V;
            /** 得到扫描线之间的所有线段 **/
            for (int j = 0; j < n; j ++) {
                Real miny = side1[j].a.y, maxy = side1[j].b.y;
                if (miny > maxy) swap(miny, maxy);
                if (miny <= Y[i - 1] && maxy >= Y[i]) {
                    Point dot1 = side1[j].getLineIntersection(Segment(Point(0, Y[i - 1]), Point(1, Y[i - 1])));
                    Point dot2 = side1[j].getLineIntersection(Segment(Point(0, Y[i]), Point(1, Y[i])));
                    V.pb(mp(Segment(dot1, dot2), 0));
                }
            }
            for (int j = 0; j < m; j ++) {
                Real miny = side2[j].a.y, maxy = side2[j].b.y;
                if (miny > maxy) swap(miny, maxy);
                if (miny <= Y[i - 1] && maxy >= Y[i]) {
                    Point dot1 = side2[j].getLineIntersection(Segment(Point(0, Y[i - 1]), Point(1, Y[i - 1])));
                    Point dot2 = side2[j].getLineIntersection(Segment(Point(0, Y[i]), Point(1, Y[i])));
                    V.pb(mp(Segment(dot1, dot2), 1));
                }
            }
            sort(all(V), cmp);
            //Debug::print("V.size=", V.size());
            /** 从左至右统计 **/
            bool in1 = 0, in2 = 0;/** 当前延伸的区域是否在多边形内部 **/
            for (int i = 0; i < V.size(); i ++) {
                if (in1 && in2) area += V[i].X.a.x - V[i - 1].X.a.x + V[i].X.b.x - V[i - 1].X.b.x;
                if (V[i].Y) in2 ^= 1;
                else in1 ^= 1;
            }
        }
        printf("Case %d: %s
", ++ cas, area > 0? "Yes" : "No");
    }
    return 0;
}