[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\n", ++ cas, area > 0? "Yes" : "No"); } return 0; }
