acm课程练习2–1005

题目描述

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

大意

求长为l，宽为w的汽车能否通过前后道路宽度依次为x与y的90度直角弯道

思考

很明显，这是一道数学题，公式的推导过程很是麻烦，我也是参考了题解才推导出正确的公式，主要参考了这篇博客。

这是一个凸性函数，因此我用了三分搜素法来做

AC代码

#include <iostream>
#include <stdio.h>
#include <math.h>
using namespace std;
double pi = acos(-1.0);
double x,y,l,w,s,h;
double cal(double a)
{
    s = l*cos(a)+w*sin(a)-x;
    h = s*tan(a)+w*cos(a);
    return h;
}
int main()
{
    double left,right,mid,midmid;
    while(scanf("%lf%lf%lf%lf",&x,&y,&l,&w)!=EOF)
    {
        left = 0.0;
        right = pi/2;
        while(fabs(right-left)>1e-8)
        {
            mid = (left+right)/2;
            midmid = (mid+right)/2;
            if(cal(mid)>=cal(midmid))right = midmid;
            else left = mid;
        }
        if(cal(mid)<=y)printf("yes\n");
        else printf("no\n");
    }
    return 0;
}//三分法程序

做这道题好像做高中的数学题（不过好难）。。。。

来自为知笔记(Wiz)