题目来源:[NWPU][2014][SRM][4] F题
http://vjudge.net/contest/view.action?cid=51335#problem/F
作者:npufz
题目:
F - Football Goal
Time Limit:500MS Memory Limit:65536KB 64bit IO Format:%I64d
& %I64u
Description
Unlike most students of the Mathematical Department, Sonya is fond of not only programming but also sports. One fine day she went to play football with her friends. Unfortunately, there was no football field anywhere around.
There only was a lonely birch tree in a corner of the yard. Sonya searched the closet at her home, found two sticks, and decided to construct a football goal using the sticks and the tree. Of course, the birch would be one of the side posts of the goal. It
only remained to make the other post and the crossbar.
Sonya wanted to score as many goals as possible, so she decided to construct a goal of maximum area. She knew that the standard football goal was rectangular, but, being creative, she assumed that her goal could have the form
of an arbitrary quadrangle.
You can assume that the birch tree is a segment of a straight line orthogonal to the ground.
Output
Output the maximum area of the goal that can be constructed with the use of the sticks and the birch tree. The answer must be accurate to at least six fractional digits.
代码:
#include <iostream>
#include <cmath>
#include <cstdio>
#include <cstdlib>
using namespace std;
int main()
{
double a,b;
cin>>a>>b;
printf("%.9lf\n",(a*a+b*b)/4.0+sqrt(2)*a*b/2.0);
return 0;
}
反思:一开始觉得两条边为一个圆的的弦时最大,就开始求角,由于过于着急就错了,后来冷静下来就推出了公式,就A了,但是没有给出证明,相信自己,沉着求解很关键
反思: