HDU 5839 Special Tetrahedron

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<iostream>
using namespace std;
typedef long long LL;
const double pi=acos(-1.0);
void File()
{
    freopen("D:\\in.txt","r",stdin);
    freopen("D:\\out.txt","w",stdout);
}
template <class T>
inline void read(T &x)
{
    char c = getchar(); x = 0;while(!isdigit(c)) c = getchar();
    while(isdigit(c)) { x = x * 10 + c - ‘0‘; c = getchar();  }
}

const int maxn=300;
struct point
{
    int x,y,z;
}p[maxn];
int T,n,len[10];

bool isonLine(int i,int j,int k)
{
    int ax=p[j].x-p[i].x, ay=p[j].y-p[i].y, az=p[j].z-p[i].z;
    int bx=p[k].x-p[i].x, by=p[k].y-p[i].y, bz=p[k].z-p[i].z;
    int tx=(ay*bz-az*by), ty=(az*bx-ax*bz), tz=(ax*by-ay*bx);
    int ans=tx*tx+ty*ty+tz*tz;
    if(ans==0)return true;
    return false;
}
int dis(int i,int j)
{
    int x=p[j].x-p[i].x, y=p[j].y-p[i].y, z=p[j].z-p[i].z;
    return x*x+y*y+z*z;
}
bool isonFace(int i,int j,int k,int l)
{
     point s1,s2,s3;
     s1.x=p[j].x-p[i].x;s1.y=p[j].y-p[i].y;s1.z=p[j].z-p[i].z;
     s2.x=p[k].x-p[i].x;s2.y=p[k].y-p[i].y;s2.z=p[k].z-p[i].z;
     s3.x=p[l].x-p[i].x;s3.y=p[l].y-p[i].y;s3.z=p[l].z-p[i].z;
     int ans=s1.x*s2.y*s3.z+s1.y*s2.z*s3.x+s1.z*s2.x*s3.y-s1.z*s2.y*s3.x-s1.x*s2.z*s3.y-s1.y*s2.x*s3.z;
     if(ans == 0) return true;
     return false;
}

int main()
{
    scanf("%d",&T); int cas=1;
    while(T--)
    {
        scanf("%d",&n);

        for(int i=1;i<=n;i++) scanf("%d%d%d",&p[i].x,&p[i].y,&p[i].z);

        int ans=0;
        for(int i=1;i<=n;i++)
        {
            for(int j=i+1;j<=n;j++)
            {
                for(int k=j+1;k<=n;k++)
                {
                    if(isonLine(i,j,k)) continue;

                    len[1]=dis(i,j); len[2]=dis(i,k); len[3]=dis(j,k);

                    int f;
                    if(len[1]==len[2]&&len[1]==len[3]) f=len[1];
                    else if(len[1]==len[2]) f=len[1];
                    else if(len[1]==len[3]) f=len[1];
                    else if(len[2]==len[3]) f=len[2];
                    else continue;

                    for(int s=k+1;s<=n;s++)
                    {
                        if(isonFace(i,j,k,s)) continue;

                        len[4]=dis(i,s); len[5]=dis(j,s); len[6]=dis(k,s);
                        int sum=0; for(int d=1;d<=6;d++) if(len[d]==f) sum++;
                        if(sum<4) continue;
                        else if(sum>=5) ans++;
                        else
                        {
                            int id1,id2,flag=0;
                            for(int d=1;d<=6;d++)
                            {
                                if(len[d]==f) continue;
                                if(flag==0) id1=d,flag=1; else id2=d;
                            }
                            if( (id1==1&&id2==6) || (id1==2&&id2==5) || (id1==3&&id2==4) ) ans++;
                        }

                    }

                }
            }
        }
        printf("Case #%d: %d\n",cas++,ans);
    }
    return 0;
}