ural 1075. Thread in a Space

1075. Thread in a Space

Time limit: 1.0 second
Memory limit: 64 MB
There are three points in a 3-dimensional space: A, B and C. All the coordinates of the points are integer numbers with absolute values not greater than 1000. A solid ball with a center in the pointC is firmly fixed. A radius of the ball is R, a positive integer number. Distances from the point Cto the points A and B are strictly greater than R.
It is necessary to stretch a thread of minimal length between points A and B. Surely, the thread should be outside of the ball.
You are to find out a length of the thread.

Input

The first three lines contain coordinates of the points A, B and C respectively. The fourth one contains a radius R of the ball.

Output

should contain a minimal length of the thread to within 2 symbols after a decimal point. You should output answer with two or more digits.

Sample

inputoutput
0 0 12
12 0 0
10 0 10
10

19.71
Problem Author: Alexander Mironenko 
Problem Source: Ural State Univerisity Personal Contest Online February'2001 Students Session
Difficulty: 1029
 
题意：给出空间中三个整点。在一点的中央，固定了一个小球。小球的半径为R。其余两点在球外。 用最小长度的绳子连接剩下两点。求绳子的长度。
分析：因为只有三个点，所以可以放在平面上考虑。
如果连线不经过圆，显然可以直接求距离。
如果经过，那么有简单的平面几何知识即可。
而且处理时不需理会什么空间，直接用角度算即可。
  1 /**
  2 Create By yzx - stupidboy
  3 */
  4 #include <cstdio>
  5 #include <cstring>
  6 #include <cstdlib>
  7 #include <cmath>
  8 #include <deque>
  9 #include <vector>
 10 #include <queue>
 11 #include <iostream>
 12 #include <algorithm>
 13 #include <map>
 14 #include <set>
 15 #include <ctime>
 16 #include <iomanip>
 17 using namespace std;
 18 typedef long long LL;
 19 typedef double DB;
 20 #define MIT (2147483647)
 21 #define INF (1000000001)
 22 #define MLL (1000000000000000001LL)
 23 #define sz(x) ((int) (x).size())
 24 #define clr(x, y) memset(x, y, sizeof(x))
 25 #define puf push_front
 26 #define pub push_back
 27 #define pof pop_front
 28 #define pob pop_back
 29 #define ft first
 30 #define sd second
 31 #define mk make_pair
 32 
 33 inline int Getint()
 34 {
 35     int Ret = 0;
 36     char Ch = ' ';
 37     bool Flag = 0;
 38     while(!(Ch >= '0' && Ch <= '9'))
 39     {
 40         if(Ch == '-') Flag ^= 1;
 41         Ch = getchar();
 42     }
 43     while(Ch >= '0' && Ch <= '9')
 44     {
 45         Ret = Ret * 10 + Ch - '0';
 46         Ch = getchar();
 47     }
 48     return Flag ? -Ret : Ret;
 49 }
 50 
 51 const DB EPS = 1e-7;
 52 struct Point
 53 {
 54     DB x, y, z;
 55     inline void Read()
 56     {
 57         cin >> x >> y >> z;
 58     }
 59 } a, b, c;
 60 DB r;
 61 
 62 inline void Input()
 63 {
 64     a.Read();
 65     b.Read();
 66     c.Read();
 67     cin >> r;
 68 }
 69 
 70 inline DB Sqr(DB x)
 71 {
 72     return x * x;
 73 }
 74 
 75 inline DB Dist(Point a, Point b)
 76 {
 77     return sqrt(Sqr(a.x - b.x) + Sqr(a.y - b.y) + Sqr(a.z - b.z));
 78 }
 79 
 80 inline void Solve()
 81 {
 82     DB ans = 0.0;
 83 
 84     DB  ab = Dist(a, b),
 85         ac = Dist(a, c),
 86         bc = Dist(b, c);
 87 
 88     DB angle =
 89         acos((Sqr(ac) + Sqr(bc) - Sqr(ab)) / (2.0 * ac * bc)) -
 90         acos(r / ac) - acos(r/ bc);
 91     if(angle <= EPS)
 92     {
 93         printf("%.2lf\n", ab);
 94         return;
 95     }
 96 
 97     ans += sqrt(Sqr(ac) - Sqr(r));
 98     ans += sqrt(Sqr(bc) - Sqr(r));
 99     ans += angle * r;
100 
101     printf("%.2lf\n", ans);
102 }
103 
104 int main()
105 {
106     freopen("g.in", "r", stdin);
107     Input();
108     Solve();
109     return 0;
110 }
View Code

 

posted @ 2015-12-25 20:05  yanzx6  阅读(309)  评论(0)    收藏  举报