HDOJ Intersection 5120【环相交面积】
2015-08-01 10:05
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Intersection
Time Limit: 4000/4000 MS (Java/Others) Memory Limit: 512000/512000 K (Java/Others)Total Submission(s): 949 Accepted Submission(s): 360
Problem Description
Matt is a big fan of logo design. Recently he falls in love with logo made up by rings. The following figures are some famous examples you may know.
A ring is a 2-D figure bounded by two circles sharing the common center. The radius for these circles are denoted by r and R (r < R). For more details, refer to the gray part in the illustration below.
Matt just designed a new logo consisting of two rings with the same size in the 2-D plane. For his interests, Matt would like to know the area of the intersection of these two rings.
Input
The first line contains only one integer T (T ≤ 105), which indicates the number of test cases. For each test case, the first line contains two integers r, R (0 ≤ r < R ≤ 10).
Each of the following two lines contains two integers xi, yi (0 ≤ xi, yi ≤ 20) indicating the coordinates of the center of each ring.
Output
For each test case, output a single line “Case #x: y”, where x is the case number (starting from 1) and y is the area of intersection rounded to 6 decimal places.
Sample Input
2 2 3 0 0 0 0 2 3 0 0 5 0
Sample Output
Case #1: 15.707963 Case #2: 2.250778
Source
2014ACM/ICPC亚洲区北京站-重现赛(感谢北师和上交)
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几何题,注意精度 PI 用 acos(-1.0)表示 否则会wa。
求黑色面积 可以用大圆相交面积-两个大小圆相交面积+小圆相交面积
#include <stdio.h> #include <math.h> #include <vector> #include <queue> #include <string> #include <string.h> #include <stdlib.h> #include <iostream> #include <algorithm> #define PI acos(-1.0) using namespace std; struct point{ double x,y; }; const double eps=1e-20; double dist(point C1,point C2) { return sqrt((C1.x-C2.x)*(C1.x-C2.x)+(C1.y-C2.y)*(C1.y-C2.y)); } double aear(point c1,double r1,point c2,double r2) { double d=dist(c1,c2); if(r1+r2-d<eps) return 0; if(d<fabs(r1-r2)+eps) { double r=min(r1,r2); return PI*r*r; } double x=(d*d+r1*r1-r2*r2)/(2*d); double t1=acos(x/r1); double t2=acos((d-x)/r2); return r1*r1*t1+r2*r2*t2-d*r1*sin(t1); } int main() { int t; scanf("%d",&t); int xp=1; while(t--) { double r,R; scanf("%lf%lf",&r,&R); point C1,C2; scanf("%lf%lf%lf%lf",&C1.x,&C1.y,&C2.x,&C2.y); double ringr_R=aear(C1,r,C2,R); double ringr_r=aear(C1,r,C2,r); double ringR_r=aear(C1,R,C2,r); double ringR_R=aear(C1,R,C2,R); printf("Case #%d: %.6lf\n",xp++,ringR_R-ringR_r-ringr_R+ringr_r); } return 0; }
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