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)); }
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