福建省赛-- Common Tangents(数学几何)
2015-12-27 18:41
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Problem B Common Tangents
Two different circles can have at most four common tangents.
The picture below is an illustration of two circles with four common tangents.
Now given the center and radius of two circles, your job is to find how many common tangents between them.
The first line contains an integer T, meaning the number of the cases (1 <= T <= 50.).
For each test case, there is one line contains six integers x1 (−100 ≤ x1 ≤ 100), y1 (−100 ≤ y1 ≤ 100), r1 (0 < r1 ≤ 200), x2 (−100 ≤ x2 ≤ 100), y2 (−100 ≤ y2 ≤ 100), r2 (0 < r2 ≤ 200). Here (x1, y1) and (x2, y2) are the coordinates of the center of the
first circle and second circle respectively, r1 is the radius of the first circle and r2 is the radius of the second circle.
For each test case, output the corresponding answer in one line.
If there is infinite number of tangents between the two circles then output -1.
3
10 10 5 20 20 5
10 10 10 20 20 10
10 10 5 20 10 5
4
2
3
判断两个圆有几条切线!有一点需要注意,两个圆重合的时候输出-1,重合时有无数条切线,水题一枚
Accept: 191 Submit: 608
Time Limit: 1000 mSec Memory Limit : 32768 KB
Problem Description
Two different circles can have at most four common tangents.The picture below is an illustration of two circles with four common tangents.
Now given the center and radius of two circles, your job is to find how many common tangents between them.
Input
The first line contains an integer T, meaning the number of the cases (1 <= T <= 50.).For each test case, there is one line contains six integers x1 (−100 ≤ x1 ≤ 100), y1 (−100 ≤ y1 ≤ 100), r1 (0 < r1 ≤ 200), x2 (−100 ≤ x2 ≤ 100), y2 (−100 ≤ y2 ≤ 100), r2 (0 < r2 ≤ 200). Here (x1, y1) and (x2, y2) are the coordinates of the center of the
first circle and second circle respectively, r1 is the radius of the first circle and r2 is the radius of the second circle.
Output
For each test case, output the corresponding answer in one line.If there is infinite number of tangents between the two circles then output -1.
Sample Input
310 10 5 20 20 5
10 10 10 20 20 10
10 10 5 20 10 5
Sample Output
42
3
判断两个圆有几条切线!有一点需要注意,两个圆重合的时候输出-1,重合时有无数条切线,水题一枚
#include<stdio.h> #include<math.h> #include<algorithm> using namespace std; int main() { int t; scanf("%d",&t); while(t--) { int x1,x2,y1,y2,r1,r2; double s1; scanf("%d%d%d%d%d%d",&x1,&y1,&r1,&x2,&y2,&r2); if(x1==x2&&y1==y2&&r1==r2) printf("-1\n"); else { s1=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)); if(r1+r2<s1) printf("4\n"); else if(r1+r2==s1) printf("3\n"); else if(r1+r2>s1) { if(s1+min(r1,r2)==max(r1,r2)) printf("1\n"); else if(s1+min(r1,r2)<max(r1,r2)) printf("0\n"); else printf("2\n"); } } } return 0; }
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