angry_birds_again_and_again SD5THACM



angry_birds_again_and_again

Time Limit: 2000MS Memory limit: 65536K

题目描述

The problems called "Angry Birds" and "Angry Birds Again and Again" has been solved by many teams in the series of contest in 2011 Multi-University Training Contest.

 

This time we focus on the yellow bird called Chuck. Chuck can pick up speed and distance when tapped.

 

You can assume that before tapped, Chuck flies along the parabola. When tapped, it changes to fly along the tangent line. The Chuck starts at the coordinates (0, 0). Now you are given the coordinates of the pig (Px, 0), the x-coordinate of the tapping position (Tx) and the initial flying angle of Chuck (α).

∠AOx = α

Please calculate the area surrounded by Chuck’s path and the ground.(The area surrounded by the solid line O-Tapping position-Pig-O)

输入

The first line contains only one integer T (T is about 1000) indicates the number of test cases. For each case there are two integers, px tx, and a float number α.（0 < Tx ≤ Px ≤ 1000, 0 < α <  ） .

输出

One line for each case specifying the distance rounded to three digits.

示例输入

1
2 1 1.0

示例输出

0.692

数学题：已知一个二次函数过零点的角度，已知另外一条切线，求x轴与直线和二次函数包围的取余面积

#include <iostream>
#include <cmath>
#include <cstdio>

using namespace std;

int T,n,px,tx;
double s1,s2,b,c;
float a;


int main()
{
    cin >> T;
    while(T--)
    {
        cin >> px >> tx >> a;
        c = tan(a);
        b = c * px / (tx * tx - 2 * px * tx);
        //cout << b << endl;
        s1 = b / 3.0 * (tx * tx * tx) + c / 2.0 * tx * tx;
        //cout << s1 << endl;
        s2 = 1 / 2.0 * (b * tx * tx + c * tx) * (px - tx);
        //cout << s2 << endl;
        printf("%.3lf\n",s1 +s2);
    }
    return 0;
}