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  • POJ 2208--Pyramids(欧拉四面体体积计算)

    Pyramids
    Time Limit: 1000MS   Memory Limit: 65536K
    Total Submissions: 3451   Accepted: 1123   Special Judge

    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

    Source

    Northeastern Europe 2002, Northern Subregion

     

    Problem: 2208    
    Memory: 188K   Time: 47MS
    Language: C++   Result: Accepted
     1 #include<iostream>
     2 #include<algorithm>
     3 #include<cmath>
     4 #include<cstdio>
     5 using namespace std;
     6 //p,q,r为AD,BD,CD;n,l,m为AB,BC,AC;
     7 double V_tetrahedron(double l, double m, double n, double q, double p, double r) {
     8     //return sqrt((4 * 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;
     9     double x = q*q + r*r - l*l, y = r*r + p*p - m*m, z = p*p + q*q - n*n;
    10     return sqrt((4 * p*p*q*q*r*r - p*p*x*x - q*q*y*y - r*r*z*z + z*x*y)) / 12.0;
    11 }
    12 int main(){
    13     double l,m,n,q,p,r;
    14     cin>>n>>m>>p>>l>>q>>r;
    15     double ans=V_tetrahedron(l,m,n,q,p,r);
    16     printf("%.4lf
    ",ans);
    17     return 0;
    18 }
    View Code
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  • 原文地址:https://www.cnblogs.com/FlyerBird/p/9518178.html
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