【模拟+数学】2018 hdu多校第五场 1005 Everything Has Changed

Everything Has Changed

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others)
Total Submission(s): 3444    Accepted Submission(s): 909
Special Judge
 

Problem Description

Edward is a worker for Aluminum Cyclic Machinery. His work is operating mechanical arms to cut out designed models. Here is a brief introduction of his work.
Assume the operating plane as a two-dimensional coordinate system. At first, there is a disc with center coordinates (0,0) and radius R. Then, m mechanical arms will cut and erase everything within its area of influence simultaneously, the i-th area of which is a circle with center coordinates (xi,yi) and radius ri (i=1,2,⋯,m). In order to obtain considerable models, it is guaranteed that every two cutting areas have no intersection and no cutting area contains the whole disc.
Your task is to determine the perimeter of the remaining area of the disc excluding internal perimeter.
Here is an illustration of the sample, in which the red curve is counted but the green curve is not.

 

Input

The first line contains one integer T, indicating the number of test cases.
The following lines describe all the test cases. For each test case:
The first line contains two integers m and R.
The i-th line of the following m lines contains three integers xi,yi and ri, indicating a cutting area.
1≤T≤1000, 1≤m≤100, −1000≤xi,yi≤1000, 1≤R,ri≤1000 (i=1,2,⋯,m).

 

Output

For each test case, print the perimeter of the remaining area in one line. Your answer is considered correct if its absolute or relative error does not exceed 10−6.
Formally, let your answer be a and the jury's answer be b. Your answer is considered correct if |a−b|max(1,|b|)≤10−6.

Sample Input

1

4 10

6 3 5

10 -4 3

-2 -4 4

0 9 1

Sample Output

81.62198908430238475376

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注意全包含和不包含不算

只要内切和部分包含

特别注意如果贴上去的圆的半径大于原来圆的时候，反三角函数算的是较小角，要判一下

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<queue>
using namespace std;
const double pi=acos(-1.0);
double dis(double x1,double y1,double x2,double y2)
{
    return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
int main()
{
    int t,i,m,j;
    double R,xi,yi,ri,C,c,x,h,xh,q1,q2,aa,bb;
    while(~scanf("%d",&t))
    {
        while(t--)
        {
            scanf("%d%lf",&m,&R);
            C=2*pi*R;
            for(i=1;i<=m;i++)
            {
                scanf("%lf%lf%lf",&xi,&yi,&ri);
                xi=abs(xi);
                yi=abs(yi);
                ri=abs(ri);
                if(dis(0,0,xi,yi)+ri>=R&&dis(0,0,xi,yi)-ri<R)
                {
                    x=dis(0,0,xi,yi);
                    xh=(R*R-ri*ri+x*x)/(x*2.0);
                    h=sqrt(ri*ri-(xh-x)*(xh-x));
                    q1=asin(h/ri);
                    q2=asin(h/R);
                    if(xh>x) aa=2*pi*ri-2*q1*ri;
                    else aa=2*q1*ri;
                    if(xh<0) bb=2*pi*R-2*q2*R;
                    else bb=2*q2*R;
                    C=C-bb+aa;
                }
            }
            printf("%.14f\n",C);
        }
    }
}