L - Pyramids解题报告（熊禾强）

L - Pyramids

Time Limit:1000MS     Memory Limit:65536KB     64bit IO Format:%I64d & %I64u

Submit  Status  Practice  POJ 2208

Description

Recently in Farland, a country in Asia, a famous scientist Mr. Log Archeo has discovered ancient pyramids. But unlike those in Egypt and Central America, they have triangular (not rectangular) foundation. That is, they are tetrahedrons in mathematical sense. In order to find out some important facts about the early society of the country (it is widely believed that the pyramid sizes are in tight connection with Farland ancient calendar), Mr. Archeo needs to know the volume of the pyramids. Unluckily, he has reliable data about their edge lengths only. Please, help him!

Input

The file contains six positive integer numbers not exceeding 1000 separated by spaces, each number is one of the edge lengths of the pyramid ABCD. The order of the edges is the following: AB, AC, AD, BC, BD, CD.

Output

A real number -- the volume printed accurate to four digits after decimal point.

Sample Input

1000 1000 1000 3 4 5

Sample Output

1999.9938

题目大意：输入四面体的六条棱，求体积。

解题思路：欧拉公式：http://course.szu.edu.cn/weijifen/picture/MC50024.htm

V=sqrt((4*a*a*b*b*c*c-a*a*(b*b+c*c-m*m)*(b*b+c*c-m*m)-b*b*(c*c+a*a-n*n)*(c*c+a*a-n*n)-c*c*(a*a+b*b-l*l)*(a*a+b*b-l*l)+(a*a+b*b-l*l)*(b*b+c*c-m*m)*(c*c+a*a-n*n)))/12;

没公式做不出来，所以最好不要痴迷于此题

代码：

#include <stdio.h>   
#include <math.h>   
double a,b,c,d,e,f;  
double i1,i2,i3,i4;  
int main()
{  
 while(scanf("%lf %lf %lf %lf %lf %lf",&a,&b,&c,&d,&e,&f)!=EOF){  
  i1=acos((a*a+b*b-d*d)/2/a/b);  
  i2=acos((b*b+c*c-f*f)/2/c/b);  
  i3=acos((a*a+c*c-e*e)/2/a/c);  
  i4=1.0/2*(i1+i2+i3);  
 printf("%.4f\n",1.0/3*a*b*c*sqrt(sin(i4)*sin(i4-i1)*sin(i4-i2)*sin(i4-i3)));  
 }  
  return 0;  
}