hdu 2438

Problem Description

Mr. West bought a new car! So he is travelling around the city.



One day he comes to a vertical corner. The street he is currently in has a width x, the street he wants to turn to has a width y. The car has a length l and a width d.



Can Mr. West go across the corner?







Input

Every line has four real numbers, x, y, l and w.

Proceed to the end of file.





Output

If he can go across the corner, print "yes". Print "no" otherwise.





Sample Input

10 6 13.5 4

10 6 14.5 4





Sample Output

yes

no

思路：看懂题意后就会知道，这个是让找最值得；首先就的有函数关系式； 根据p到许仙的距离和角a有关系是：

f(a)=L*cos(a)-((x-w*cos(a))/tan(a)-w*sin(a))=L*cos(a)+(w-x*cos(a))/sin(a);

之后进行三分查找就行了；如果函数的最大值大于y值，不能通过；否则，通过；

如下图：

代码：

#include <stdio.h>
#include <string>
#include<iostream>
#include <cstring>
#include <iomanip>
#include <cmath>
#define pi 3.1415926
#include <algorithm>
using namespace std;
double x,l,y,w,a,b,c;
double f(double t);
int main(){
	while(cin>>x>>y>>l>>w)
	{   a=0.0;
	    b=pi/2.0;
		double mid,mmid;
        while(b-a>1e-10){
           mid=(a+a+b)/3.0;
		   mmid=(mid+2*b)/3.0;
		   if(f(mid)>f(mmid))
		       b=mmid;
 	 	 else
		       a=mid;
        }
        if(f(a)>y)
            cout<<"no"<<endl;
        else cout<<"yes"<<endl;
	}
	return 0;
}
double f(double t){
	return l*cos(t)+(w-x*cos(t))/(sin(t));
}