題目：Rotating Scoreboard

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題意：題目要求判斷多邊形內核是否存在，若存在就輸出YES，不存在就輸出NO，本題和POJ1474一樣。本題點的輸入順序是順時針方向。

/*Goujinping 2013.4.12 NEFUThe masterplate of Polygon kernel.Now the global variable Area stand for the area of Polygon kernelIn most case,the problem let us judge whether the Polygon kernel exist or not and calculate the area,perimeter,or other constants about the Polygon kernel.*/#include <math.h> #include <stdio.h> #include <iostream> #include <algorithm>using namespace std;const int N=11111; const double EPS = 1e-8;typedef double DIY;DIY Area,Length;struct Point {DIY x,y;Point() {}Point(DIY _x,DIY _y):x(_x),y(_y) {} } p[N];Point MakeVector(Point &P,Point &Q) {return Point(Q.x-P.x,Q.y-P.y); }DIY CrossProduct(Point P,Point Q) {return P.x*Q.y-P.y*Q.x; }DIY MultiCross(Point P,Point Q,Point R) {return CrossProduct(MakeVector(Q,P),MakeVector(Q,R)); }struct halfPlane {Point s,t;DIY angle;halfPlane() {}halfPlane(Point _s,Point _t):s(_s),t(_t) {}halfPlane(DIY sx,DIY sy,DIY tx,DIY ty):s(sx,sy),t(tx,ty) {}void GetAngle(){angle=atan2(t.y-s.y,t.x-s.x);} } hp[N],q[N];Point IntersectPoint(halfPlane P,halfPlane Q) {DIY a1=CrossProduct(MakeVector(P.s,Q.t),MakeVector(P.s,Q.s));DIY a2=CrossProduct(MakeVector(P.t,Q.s),MakeVector(P.t,Q.t));return Point((P.s.x*a2+P.t.x*a1)/(a2+a1),(P.s.y*a2+P.t.y*a1)/(a2+a1)); }bool cmp(halfPlane P,halfPlane Q) {if(fabs(P.angle-Q.angle)<EPS)return MultiCross(P.s,P.t,Q.s)>0;return P.angle<Q.angle; }bool IsParallel(halfPlane P,halfPlane Q) {return fabs(CrossProduct(MakeVector(P.s,P.t),MakeVector(Q.s,Q.t)))<EPS; }void HalfPlaneIntersect(int n,int &m) {sort(hp,hp+n,cmp);int i,l=0,r=1;for(m=i=1; i<n; ++i)if(hp[i].angle-hp[i-1].angle>EPS) hp[m++]=hp[i];n=m; m=0;q[0]=hp[0];q[1]=hp[1];for(i=2; i<n; i++){if(IsParallel(q[r],q[r-1])||IsParallel(q[l],q[l+1])) return;while(l<r&&MultiCross(hp[i].s,hp[i].t,IntersectPoint(q[r],q[r-1]))>0) --r;while(l<r&&MultiCross(hp[i].s,hp[i].t,IntersectPoint(q[l],q[l+1]))>0) ++l;q[++r]=hp[i];}while(l<r&&MultiCross(q[l].s,q[l].t,IntersectPoint(q[r],q[r-1]))>0) --r;while(l<r&&MultiCross(q[r].s,q[r].t,IntersectPoint(q[l],q[l+1]))>0) ++l;q[++r]=q[l];for(i=l; i<r; ++i)p[m++]=IntersectPoint(q[i],q[i+1]); }void Solve(Point *p,int n,int &m) {int i,j;p[n]=p[0];for(i=0;i<n;i++){hp[i]=halfPlane(p[(i+1)%n],p[i]);hp[i].GetAngle();}HalfPlaneIntersect(n,m); }int main() {int n,m,t;cin>>t;while(t--){cin>>n;for(int i=0; i<n; i++)cin>>p[i].x>>p[i].y;Solve(p,n,m);if(m<3) puts("NO");else puts("YES");}return 0; }

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