●POJ 1873 The Fortified Forest
题链:
http://poj.org/problem?id=1873
题解:
计算几何,凸包
枚举被砍的树的集合。求出剩下点的凸包。然后判断即可。
代码:
#include<cmath> #include<cstdio> #include<cstring> #include<iostream> #include<algorithm> using namespace std; const int MAXN=16,INF=0x3f3f3f3f; const double eps=1e-8; int sign(double x){ if(fabs(x)<=eps) return 0; return x<0?-1:1; } struct Point{ double x,y; Point(double _x=0,double _y=0):x(_x),y(_y){} void Read(){scanf("%lf%lf",&x,&y);} }D[MAXN],H[MAXN]; typedef Point Vector; bool operator < (Point A,Point B){return sign(A.x-B.x)<0||(sign(A.x-B.x)==0&&sign(A.y-B.y)<0);} bool operator == (Point A,Point B){return sign(A.x-B.x)==0&&sign(A.y-B.y)==0;} Vector operator - (Point A,Point B){return Vector(A.x-B.x,A.y-B.y);} double operator ^ (Vector A,Vector B){return A.x*B.y-A.y*B.x;} double operator * (Vector A,Vector B){return A.x*B.x+A.y*B.y;} int V[MAXN],N,ansS,ansV,ansN; double L[MAXN],resL; double GL(Vector A){//Get_Length return sqrt(A*A); } int Andrew(int S){ int hnt=0,k=0,tnt=0; static Point tmp[MAXN]; for(int i=1;i<=N;i++) if(!(S&(1<<(i-1)))) tmp[++tnt]=D[i]; sort(tmp+1,tmp+tnt+1); tnt=unique(tmp+1,tmp+tnt+1)-tmp-1; for(int i=1;i<=tnt;i++){ while(hnt>1&&sign((H[hnt]-H[hnt-1])^(tmp[i]-H[hnt-1]))<=0) hnt--; H[++hnt]=tmp[i]; } k=hnt; for(int i=tnt-1;i>=1;i--){ while(hnt>k&&sign((H[hnt]-H[hnt-1])^(tmp[i]-H[hnt-1]))<=0) hnt--; H[++hnt]=tmp[i]; } return hnt; } double GCPC(int hnt){//Get_Convex_Polygon_Circumference double C=0; for(int i=1;i<hnt;i++) C+=GL(H[i+1]-H[i]); return C; } int main(){ double C,nowL; int nowS,nowV,nowN,Case=0; while(scanf("%d",&N)&&N){ if(N==0) break; ansS=(1<<N)-1; ansV=INF; ansN=N; resL=0; for(int i=1;i<=N;i++) D[i].Read(),scanf("%d%lf",&V[i],&L[i]); for(int S=1;S<=(1<<N)-1;S++){ nowS=S; nowN=0; nowL=0; nowV=0; for(int i=1;i<=N;i++) if(S&(1<<(i-1))) nowN++,nowV+=V[i],nowL+=L[i]; C=GCPC(Andrew(S)); if(sign(nowL-C)<0) continue; if(nowV<ansV||(nowV==ansV&&nowN<ansN)) ansS=nowS,ansV=nowV,ansN=nowN,resL=nowL-C; } if (Case) puts(""); printf("Forest %d\n",++Case); printf("Cut these trees:"); for(int i=1;i<=N;i++) if(ansS&(1<<(i-1))) printf(" %d",i); printf("\nExtra wood: %.2lf\n",resL); } return 0; }
Do not go gentle into that good night.
Rage, rage against the dying of the light.
————Dylan Thomas