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 }
