angry_birds_again_and_again(2014年山东省第五届ACM大学生程序设计竞赛A题）

http://acm.sdut.edu.cn/sdutoj/problem.php?action=showproblem&problemid=2877

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.

```1
2 1 1.0```

`0.692`

来源

2014年山东省第五届ACM大学生程序设计竞赛

```#include <iostream>
#include <cmath>
#include <cstdio>
using namespace std;

int main()
{
int T;
double px,tx,t,ty,sum,a;
cin>>T;
while(T--)
{
cin>>px>>tx>>a;
t=(tan(a)*px)/(tx*tx-2.0*tx*px);
ty=t*tx*tx+tx*tan(a);
sum=(0.5*(px-tx)*ty)+(1/3.0*t*tx*tx*tx+0.5*tan(a)*tx*tx);
printf("%.3lf\n",sum);
}
return 0;
}```

```//题意：求由实线O-Tappingposition-Pig-O所围成图形的面积 s.

#include<stdio.h>
#include<math.h>
int main()
{
int n;
scanf("%d",&n);
while(n--)
{
int t,p;
double a,t1,t2;
scanf("%d%d%lf",&p,&t,&a);
t1=p*t*(3*p-2*t);
t2=6*(2*p-t);
printf("%.3lf\n",t1/t2*tan(a));
}
return 0;
}
/*由题意可设抛物线方程为f(x)=a*x^2+b*x ，Tap点的纵坐标为 y,

f‘(x)=2*a*x+b
s=s1+s2  ...... (1)
s2=1/2*(px-tx)*y  ...... (2)
s1=1/3*a*tx^3+1/2*b*tx^2  ...... (3)
f‘(0)=tan(a) => b=tan(a)  ...... (4)
f(tx)=y => a*tx^2+b*tx=y  ...... (5)
f‘(tx)=-y/(px-tx) => 2*a*tx+b=-y/(px-tx)  ...... (6)

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A  angry_birds_again_and_again http://www.sdutacm.org/sdutoj/problem.php?action=showproblem&problemid=2877 数学题,求抛物线和直线围成的面积,用积分来做. 设方程 y=ax^2+bx+c ,图中曲线经过原点,所以c=0. 对方程求导 y'=2ax+b ,  y'代表斜率,那么原点(0,0)这一点,代人y'=b,即该点的斜率,根据题意b=tan( α) 如图:在题目中x=tx这一点时,容易混,

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