Turn the corner HDU - 2438 三分 枚举角度 几何

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

Hint

题意

题解：

利用角度关系构造函数 求出车在转弯时所占据的长度 这个长度最大值如果大于y说明过不去 可以找到这个长度的函数表达式

f (t) = l*cos(t)+(w-x*cos(t))/sin(t);

AC代码

#include <cstdio>
#include <iostream>
#include <queue>
#include <map>
#include <vector>
#include <cmath>
#include <set>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
const double eps = 1e-8;
double x,y,l,w;
double check(double t){
double ans = l*cos(t)+(w-x*cos(t))/sin(t);
return ans;
}
int main(){

while (scanf("%lf%lf%lf%lf",&x,&y,&l,&w)!=EOF){
double l = 0,r = acos(-1.0)/2;
while (r-l>eps){
double ll = (2*l+r)/3;
double rr = (2*r+l)/3;
double ans1 = check(ll);
double ans2 = check(rr);
if (ans1<ans2) l = ll;
else r = rr;
}
if (check(l)>y) printf("no\n");
else printf("yes\n");
}

return 0;
}