HDU-4717 The Moving Points 三分

　　题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4717

　　每两个点之间的距离变化是一个单峰函数，因为每次求的值最大值，多个单峰函数的最值函数还是单峰的。。

  1 //STATUS:C++_AC_515MS_256KB

  2 #include <functional>

  3 #include <algorithm>

  4 #include <iostream>

  5 //#include <ext/rope>

  6 #include <fstream>

  7 #include <sstream>

  8 #include <iomanip>

  9 #include <numeric>

 10 #include <cstring>

 11 #include <cassert>

 12 #include <cstdio>

 13 #include <string>

 14 #include <vector>

 15 #include <bitset>

 16 #include <queue>

 17 #include <stack>

 18 #include <cmath>

 19 #include <ctime>

 20 #include <list>

 21 #include <set>

 22 #include <map>

 23 using namespace std;

 24 //#pragma comment(linker,"/STACK:102400000,102400000")

 25 //using namespace __gnu_cxx;

 26 //define

 27 #define pii pair<int,int>

 28 #define mem(a,b) memset(a,b,sizeof(a))

 29 #define lson l,mid,rt<<1

 30 #define rson mid+1,r,rt<<1|1

 31 #define PI acos(-1.0)

 32 //typedef

 33 typedef __int64 LL;

 34 typedef unsigned __int64 ULL;

 35 //const

 36 const int N=310;

 37 const int INF=0x3f3f3f3f;

 38 const int MOD=1000000007,STA=8000010;

 39 const LL LNF=1LL<<60;

 40 const double EPS=1e-5;

 41 const double OO=1e60;

 42 const int dx[4]={-1,0,1,0};

 43 const int dy[4]={0,1,0,-1};

 44 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};

 45 //Daily Use ...

 46 inline int sign(double x){return (x>EPS)-(x<-EPS);}

 47 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}

 48 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}

 49 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}

 50 template<class T> inline T Min(T a,T b){return a<b?a:b;}

 51 template<class T> inline T Max(T a,T b){return a>b?a:b;}

 52 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}

 53 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}

 54 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}

 55 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}

 56 //End

 57 

 58 struct Node{

 59     double x,y,dx,dy;

 60     Node(){}

 61     Node(int _x,int _y,int _dx,int _dy){x=_x,y=_y,dx=_dx,dy=_dy;}

 62 }nod[N];

 63 int T,n;

 64 

 65 double dist(const Node& a,const Node& b,double t)

 66 {

 67     Node p,q;

 68     p.x=a.x+a.dx*t,p.y=a.y+a.dy*t;

 69     q.x=b.x+b.dx*t,q.y=b.y+b.dy*t;

 70     return (p.x-q.x)*(p.x-q.x)+(p.y-q.y)*(p.y-q.y);

 71 }

 72 

 73 double maxdist(double t)

 74 {

 75     int i,j;

 76     double hig=0;

 77     for(i=0;i<n;i++){

 78         for(j=i+1;j<n;j++){

 79             hig=Max(hig,dist(nod[i],nod[j],t));

 80         }

 81     }

 82     return hig;

 83 }

 84 

 85 double trisection(double l,double r)

 86 {

 87     double mid,midmid,t1,t2;

 88     while(r-l>EPS){

 89         mid=(l+r)/2;

 90         midmid=(mid+r)/2;

 91         t1=maxdist(mid);

 92         t2=maxdist(midmid);

 93         if(t1<=t2)r=midmid;

 94         else l=mid;

 95     }

 96     return mid;

 97 }

 98 

 99 int main(){

100  //   freopen("in.txt","r",stdin);

101     int ca=1,i,j;

102     double x,y,dx,dy,anst;

103     scanf("%d",&T);

104     while(T--)

105     {

106         scanf("%d",&n);

107         for(i=0;i<n;i++){

108             scanf("%lf%lf%lf%lf",&x,&y,&dx,&dy);

109             nod[i]=Node(x,y,dx,dy);

110         }

111 

112         anst=trisection(0,1e6);

113 

114         printf("Case #%d: %.2lf %.2lf\n",ca++,anst,sqrt(maxdist(anst)));

115     }

116     return 0;

117 }