Pyramids

pyraids

时间限制:

1000ms

内存限制:

65536kB

描述

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!

输入

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.

输出

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

样例输入

1000 1000 1000 3 4 5

样例输出

1999.9938

数学题，精度问题，输入数字的类型设为double型，才可以。

//纯粹的数学问题，但是要注意精度问题
//若abcde均为整型，测试数据结果为1999.9938；
//为double类型时，测试数据结果为1999.9937,测试数据可能有点问题
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
int main()
{
    double a,b,c,d,e,f;
    double v,w;
    double x,y,z,q;
    //有多组测试数据
    //Mr. Archeo needs to know the volume of the pyramids. 
    //Unluckily, he has reliable data about their edge lengths only.

    while(scanf ("%lf %lf %lf %lf %lf %lf",&a,&b,&c,&d,&e,&f)!=EOF){
    x=(a*f)*(a*f)*(-a*a+b*b+c*c-f*f+e*e+d*d);
    y=(b*e)*(b*e)*(a*a-b*b+c*c+f*f-e*e+d*d);
    z=(c*d)*(c*d)*(a*a+b*b-c*c+f*f+e*e-d*d);
    q=(a*b*d)*(a*b*d)+(a*c*e)*(a*c*e)+(b*c*f)*(b*c*f)+(f*e*d)*(f*e*d);
    w=(x+y+z-q);
    v=sqrt(w)/12;
    printf ("%.4f\n",v);
    }
    return 0;
}