Pyramids
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 3448 Accepted: 1122 Special Judge
Description
Recently in Farland, a country in Asia, a famous scientist Mr. 结实的大炮 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
Source
Northeastern Europe 2002, Northern Subregion
利用欧拉四面体计算公式带入计算
和HDU 1411一样,只是是否是多组输入的问题。
/**Memory: 188K Time: 47MS*Language: C++ Result: Accepted*/#include<iostream>#include<algorithm>#include<cmath>#include<cstdio>using namespace std;//p,q,r为AD,BD,CD;n,l,m为AB,BC,AC;double V_tetrahedrondouble l, double m, double n, double q, double p, double r) { //return sqrt4 * p*p*q*q*r*r – p*p*q*q + r*r – l*l)*q*q + r*r – l*l) – q*q*r*r + p*p – m*m)*r*r + p*p – m*m) – r*r*p*p + q*q – n*n)*p*p + q*q – n*n) + p*p + q*q – n*n)*q*q + r*r – l*l)*r*r + p*p – m*m))) / 12.0; double x = q*q + r*r – l*l, y = r*r + p*p – m*m, z = p*p + q*q – n*n; return sqrt4 * p*p*q*q*r*r – p*p*x*x – q*q*y*y – r*r*z*z + z*x*y)) / 12.0;}int main){ double l,m,n,q,p,r; cin>>n>>m>>p>>l>>q>>r; double ans=V_tetrahedronl,m,n,q,p,r); printf”%.4lf\n”,ans); return 0;}