HDU 4273 Rescue(三维凸包 + 重心)
2015-08-26 10:58
609 查看
Rescue
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 398 Accepted Submission(s): 296
Problem Description
I work at NASA outer space rescue team which needs much courage and patient. In daily life, I always receive a lot of mission, and I must complete it right now.
Today, team leader announced me that there is a huge spaceship dropping anchor in the out space, and we should reach there for rescue. As a working principle, at first, we should check whether there are persons living in the spaceship. So we carry a kind of
machine called life sensor which can sense the life phenomenon when the distance between the machine and the living is not farther than the sense radius.
I have read the designing paper of the spaceship in advance. It has a form of a convex polyhedron, and we can assume it is isodense. For best control, control center of the whole ship is located at the center of the mass. It is sure that if someone is still
alive, he will stay at the control center.
It's unfortunately that I find the door is stocked when I try to enter into the spaceship, so I can only sense the living out of the space ship. Now I have opened the machine and it's time to set the sense radius of it. I wonder the minimal radius of the machine
which can allowe me to check whether there are persons living in the spaceship.
Input
There are multiple test cases.
The first line contains an integer n indicating the number of vertices of the polyhedron. (4 <= n <= 100)
Each of the next n lines contains three integers xi, yi, zi, the coordinates of the polyhedron vertices (-10,000 <= xi, yi, zi <= 10,000).
It guaranteed that the given points are vertices of the convex polyhedron, and the polyhedron is non-degenerate.
Output
For each test case, output a float number indicating the minimal radius of the machine. Your answer should accurate up to 0.001.
Sample Input
4 0 0 0 1 0 0 0 1 0 0 0 1 8 0 0 0 0 0 2 0 2 0 0 2 2 2 0 0 2 0 2 2 2 0 2 2 2
Sample Output
0.144 1.000
Source
2012 ACM/ICPC Asia Regional Changchun Online
kuangbin大神的模板一遍过。。。膜拜一下
#include<stdio.h> #include<algorithm> #include<string.h> #include<math.h> #include<stdlib.h> #define eps 1e-8 #define N 110 using namespace std; struct point { double x,y,z; point() {} point(double xx,double yy,double zz): x(xx),y(yy),z(zz) {} point operator -(const point p) { return point(x-p.x, y-p.y, z-p.z); } point operator +(const point p) { return point(x+p.x, y+p.y, z+p.z); } point operator *(const point p) { return point(y*p.z-z*p.y, z*p.x-x*p.z, x*p.y-y*p.x); } point operator *(double p) { return point(x*p, y*p,z*p); } point operator /(double p) { return point(x/p, y/p,z/p); } double operator ^( point p) { return x*p.x+y*p.y+z*p.z; } }; struct node { struct face { int a,b,c; bool ok; }; int n; point tn ; int num; face F[8*N]; int g ; double vlen(point a) { return sqrt(a.x*a.x+a.y*a.y+a.z*a.z); } point cross(const point &a,const point &b,const point &c) { return point ( (b.y-a.y)*(c.z-a.z) - (b.z-a.z)*(c.y-a.y), (b.z-a.z)*(c.x-a.x) - (b.x-a.x)*(c.z-a.z), (b.x-a.x)*(c.y-a.y) - (b.y-a.y)*(c.x-a.x) ); } double area(point a,point b,point c) { return vlen((b*a)*(c-a)); } double volume(point a,point b,point c,point d) { return (b-a)*(c-a)^(d-a); } double dbcmp(point &p,face &f) { point m = tn[f.b] - tn[f.a]; point n = tn[f.c] - tn[f.a]; point t = p - tn[f.a]; return (m*n)^t; } void deal(int p,int a,int b) { int f = g[a][b]; face add; if(F[f].ok) { if(dbcmp(tn[p],F[f]) > eps) dfs(p,f); else { add.a=b; add.b=a; add.c=p; add.ok=true; g[p][b] = g[a][p] = g[b][a] =num; F[num++] = add; } } } void dfs(int p,int now) { F[now].ok = false; deal(p,F[now].b,F[now].a); deal(p,F[now].c,F[now].b); deal(p,F[now].a,F[now].c); } bool same(int s,int t) { point &a = tn[F[s].a]; point &b = tn[F[s].b]; point &c = tn[F[s].c]; return fabs( volume(a,b,c,tn[F[t].a])) < eps && fabs( volume(a,b,c,tn[F[t].b])) < eps && fabs( volume(a,b,c,tn[F[t].c])) < eps ; } void create() { int i,j,tmp; face add; num = 0; if(n<4) return ; bool flag =true; for(i=1; i<n; i++) { if(vlen(tn[0]-tn[i]) > eps) { swap(tn[1],tn[i]); flag = false; break; } } if(flag) return ; flag =true; for(i=2; i<n; i++) { if(vlen((tn[0]-tn[1])*(tn[1]-tn[i])) > eps ) { swap(tn[2],tn[i]); flag =false; break; } } if(flag) return ; flag =true; for(i =3; i<n; i++) { if(fabs((tn[0]-tn[1])*(tn[1]-tn[2])^(tn[0]-tn[i])) >eps ) { swap(tn[3],tn[i]); flag =false; break; } } if(flag) return ; for(i=0; i<4; i++) { add.a = (i+1)%4; add.b = (i+2)%4; add.c = (i+3)%4; add.ok = true; if(dbcmp(tn[i],add) > 0) { swap(add.b,add.c); } g[add.a][add.b] = g[add.b][add.c] = g[add.c][add.a] =num; F[num++]=add; } for(i =4; i<n; i++) { for(j =0; j<num; j++) { if(F[j].ok && dbcmp(tn[i],F[j])>eps) { dfs(i,j); break; } } } tmp =num; for(i=num=0; i<tmp; i++) { if(F[i].ok) F[num++] = F[i]; } } double area() { double res=0; if(n==3) { point p = cross(tn[0],tn[1],tn[2]); res = vlen(p)/2.0; return res; } for(int i=0; i<num; i++) { res += area(tn[F[i].a],tn[F[i].b],tn[F[i].c]); } return res/2.0; } double volume() { double res=0; point tmp(0,0,0); for(int i = 0; i<num; i++) res += volume(tmp,tn[F[i].a],tn[F[i].b],tn[F[i].c]); return fabs(res/6.0); } int triangle() { return num; } int polygon() { int i,j,res,flag; for(i=res=0; i<num; i++) { flag=1; for(j=0; j<i; j++) { if(same(i,j)) { flag=0; break; } } res+=flag; } return res; } point barycenter() { point ans(0,0,0),o(0,0,0); double all=0; for(int i=0; i<num; i++) { double vol = volume(o,tn[F[i].a],tn[F[i].b],tn[F[i].c]); ans = ans+(o+tn[F[i].a]+tn[F[i].b]+tn[F[i].c])/4.0*vol; all+=vol; } ans = ans/all; return ans; } double ptoface(point p,int i) { return fabs(volume(tn[F[i].a],tn[F[i].b],tn[F[i].c],p) / vlen( (tn[F[i].b]-tn[F[i].a])*(tn[F[i].c]-tn[F[i].a]) )); } }; node ans; int main() { while(~scanf("%d",&ans.n)) { for(int i=0; i<ans.n; i++) { scanf("%lf%lf%lf",&ans.tn[i].x,&ans.tn[i].y,&ans.tn[i].z); } ans.create(); point p=ans.barycenter(); double answer=1e20; for(int i=0; i<ans.num; i++) { answer=min(answer,ans.ptoface(p,i)); } printf("%.3lf\n",answer); } return 0; }
相关文章推荐
- UITextField 属性详解
- Storyboard (<UIStoryboard: 0x15e989a0>) doesn't contain a view controller with identifier "***C"
- 第3组UI(2)-AdapterView之GridView、AutoCompleteTextView、Spinner、Gallery和ExpandableListView
- iOS原生分享UIActivityViewController
- [LeetCode#187]Repeated DNA Sequences
- Leetcode: Implement Stack using Queues
- UITableViewCell分割线左边顶格
- 【生活小记】关闭miui系统插拔usb提示音
- STL源码剖析——deque的实现原理和使用方法详解
- 黑马程序员_常用API之BufferString、StringBuilder
- iOS GPUImage的简单说明
- UI18_单例
- poj 1019 Number Sequence
- UIButton 点击传递两个参数的实现
- AmazeUI基本样式
- Extjs4中up()和down()的用法以及组件查找_ComponentQuery类
- UIday01_zy: 用iPhone6模拟器设计一个6行5列的label,并把百家姓放进去
- 【转】Sprague-Grundy函数
- 改变UITextField placeHolder颜色、字体
- UIRefreshControl 问题