UVALive 7509 三分

传送门

题意：有n个同宽的长方体，可以调换长方体的顺序，使得能用一个尽量小的半球包含所有的长方体

问最小半径

做法：对于他们同宽的这个条件，且这个宽度为1，那么在这宽度这一维里，球心可以在0,1中任意一个位置，如果球心在0,1/2，半径是增大，在1/2,半径是减小。（所以三分

球心在哪个位置）

对于另外两维，因为这些长方体一定是同宽，并且连成一条，还不理解的话可以看看下面的图片。那么我长的那一维的一半拿来做底，另外一维做高。球心一定是在长

的那一维的中心。

//china no.1#pragma comment(linker, "/STACK:1024000000,1024000000")#include <vector>#include <iostream>#include <string>#include <map>#include <stack>#include <cstring>#include <queue>#include <list>#include <stdio.h>#include <set>#include <algorithm>#include <cstdlib>#include <cmath>#include <iomanip>#include <cctype>#include <sstream>#include <functional>#include <stdlib.h>#include <time.h>#include <bitset>using namespace std;#define pi acos(-1)#define s_1(x) scanf("%d",&x)#define s_2(x,y) scanf("%d%d",&x,&y)#define s_3(x,y,z) scanf("%d%d%d",&x,&y,&z)#define s_4(x,y,z,X) scanf("%d%d%d%d",&x,&y,&z,&X)#define S_1(x) scan_d(x)#define S_2(x,y) scan_d(x),scan_d(y)#define S_3(x,y,z) scan_d(x),scan_d(y),scan_d(z)#define PI acos(-1)#define endl '\n'#define srand() srand(time(0));#define me(x,y) memset(x,y,sizeof(x));#define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++)#define close() ios::sync_with_stdio(0); cin.tie(0);#define FOR(x,n,i) for(int i=x;i<=n;i++)#define FOr(x,n,i) for(int i=x;i<n;i++)#define fOR(n,x,i) for(int i=n;i>=x;i--)#define fOr(n,x,i) for(int i=n;i>x;i--)#define W while#define sgn(x) ((x) < 0 ? -1 : (x) > 0)#define bug printf("***********\n");#define db double#define ll long long#define mp make_pair#define pb push_backtypedef long long LL;typedef pair <int, int> ii;const int INF=0x3f3f3f3f;const LL LINF=0x3f3f3f3f3f3f3f3fLL;const int dx[]={-1,0,1,0,1,-1,-1,1};const int dy[]={0,1,0,-1,-1,1,-1,1};const int maxn=1e5+10;const int maxx=4e5+10;const double EPS=1e-8;const double eps=1e-14;const int mod=1e9+7;template<class T>inline T min(T a,T b,T c) { return min(min(a,b),c);}template<class T>inline T max(T a,T b,T c) { return max(max(a,b),c);}template<class T>inline T min(T a,T b,T c,T d) { return min(min(a,b),min(c,d));}template<class T>inline T max(T a,T b,T c,T d) { return max(max(a,b),max(c,d));}template <class T>inline bool scan_d(T &ret){char c;int sgn;if (c = getchar(), c == EOF){return 0;}while (c != '-' && (c < '0' || c > '9')){c = getchar();}sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');while (c = getchar(), c >= '0' && c <= '9'){ret = ret * 10 + (c - '0');}ret *= sgn;return 1;}inline bool scan_lf(double &num){char in;double Dec=0.1;bool IsN=false,IsD=false;in=getchar();if(in==EOF) return false;while(in!='-'&&in!='.'&&(in<'0'||in>'9'))in=getchar();if(in=='-'){IsN=true;num=0;}else if(in=='.'){IsD=true;num=0;}else num=in-'0';if(!IsD){while(in=getchar(),in>='0'&&in<='9'){num*=10;num+=in-'0';}}if(in!='.'){if(IsN) num=-num;return true;}else{while(in=getchar(),in>='0'&&in<='9'){num+=Dec*(in-'0');Dec*=0.1;}}if(IsN) num=-num;return true;}void Out(LL a){if(a < 0) { putchar('-'); a = -a; }if(a >= 10) Out(a / 10);putchar(a % 10 + '0');}void print(LL a){ Out(a),puts("");}//freopen( "in.txt" , "r" , stdin );//freopen( "data.txt" , "w" , stdout );//cerr << "run time is " << clock() << endl;int n;db w[maxn];db calc(db x){    db x1=x,x2=1-x;    if(x1>x2) swap(x1,x2);    db ans=w[n]+x2*x2;    for(int i=1;i<n;i++)    {        if(i&1)        {            x1++;ans=max(ans,w[n-i]+x1*x1);        }        else        {            x2++;ans=max(ans,w[n-i]+x2*x2);        }    }    return sqrt(ans);}void solve(){    s_1(n);    for(int i=1;i<=n;i++)    {        db a,b;        scan_lf(a);        scan_lf(b);        if(a>b) swap(a,b);        w[i]=a*a+(b/2.0)*(b/2.0);    }    sort(w+1,w+n+1);    db l=0,r=1;    W(l<r)    {        db mid=(l+r)/2.0;        db mmid=(mid+r)/2.0;        if(calc(mmid)<calc(mid))            l=mid+eps;        else r=mmid-eps;    }    printf("%.10f\n",calc(l));}int main(){    //freopen( "in.txt" , "r" , stdin );    //freopen( "data.txt" , "w" , stdout );    int t=1;    //init();    s_1(t);    for(int cas=1;cas<=t;cas++)    {        printf("Case #%d: ",cas);        solve();    }}