Everything Has Changed（求圆周长）

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 $(0,0)(0,0) and\; radius RR.\; Then, mm mechanical\; arms\; will\; cut\; and\; erase\; everything\; within\; its\; area\; of\; influence\; simultaneously,\; the ii-th\; area\; of\; which\; is\; a\; circle\; with\; center\; coordinates (xi,yi)(xi,yi) and\; radius riri (i=1,2,\cdots ,m)(i=1,2,\cdots ,m).\; In\; order\; to\; obtain\; considerable\; models,\; it\; is\; guaranteed\; that\; every\; two\; cutting\; areas\; have\; no\; intersection\; and\; no\; cutting\; area\; contains\; the\; whole\; disc. Your\; task\; is\; to\; determine\; the\; perimeter\; of\; the\; remaining\; area\; of\; the\; disc\; excluding\; internal\; perimeter. Here\; is\; an\; illustration\; of\; the\; sample,\; in\; which\; the\; red\; curve\; is\; counted\; but\; the\; green\; curve\; is\; not.$

 

Input

The first line contains one integer $\mathrm{TT,\; indicating\; the\; number\; of\; test\; cases. The\; following\; lines\; describe\; all\; the\; test\; cases.\; For\; each\; test\; case: The\; first\; line\; contains\; two\; integers mm and RR. The ii-th\; line\; of\; the\; following mm lines\; contains\; three\; integers xi,yixi,yi and riri,\; indicating\; a\; cutting\; area. 1\le T\le 10001\le T\le 1000, 1\le m\le 1001\le m\le 100, -1000\le xi,yi\le 1000-1000\le xi,yi\le 1000, 1\le R,ri\le 10001\le R,ri\le 1000 (i=1,2,\cdots ,m)(i=1,2,\cdots ,m).}$

 

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 ${\mathrm{10-610-6. Formally,\; let\; your\; answer\; be aa and\; the\; jury\text{'}s\; answer\; be bb.\; Your\; answer\; is\; considered\; correct\; if |a-b|max(1,|b|)\le 10-6|a-b|max(1,|b|)\le 10-6.}}^{}$

 

Sample Input

1 4 10 6 3 5 10 -4 3 -2 -4 4 0 9 1

 

Sample Output

81.62198908430238475376

 

题意：求红色边边的周长，绿色不算。

1/相交的时候 减去与相交的大圆的边长，加上相交的小圆的在大圆内的边长

2/内切的时候 只需要加上小圆的面积

仔细读题啊////翻译成面积没脸了

 

#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#define PI acos(-1)
using namespace std;
int main(){
    int t,m,R;
    cin>>t;
    while(t--){
        cin>>m>>R;
        double x,y,r,l,h,ans=0;
        ans = 2.0*PI*R;
        for(int i=0;i<m;i++)
        {
            cin>>x>>y>>r;
            l = sqrt(x*x+y*y);
            if(l == R-r)//内切
            {
                ans+=2.0*PI*r;
            }
            else if(l == R+r || l < R-r)//外切或内含
            {
                ans+=0;
            }
            else if(l > R-r && l < R+r)//相交
            {
                if(l >= R){//小圆圆心在大圆外
                    h = (R*R+l*l-r*r)/(2.0*l);
                    ans-=2.0*R*acos(h/R);
                    ans+=2.0*r*acos((l-h)/r);
                }
                else{//小圆圆心在大圆外
                    h = (R*R-r*r-l*l)/(2.0*l);
                    ans-=2.0*R*acos((h+l)/R);
                    ans+=2*PI*r-2.0*r*acos(h/r);
                }
            }
        }
        printf("%.20lf\n",ans);
    }
    return 0;
}

 

转载于:https://www.cnblogs.com/LLLAIH/p/10800510.html