Codeforces Round #265 (Div. 2) D. Restore Cube 立方体判断_html/css_WEB-ITnose

http://codeforces.com/contest/465/problem/D

给定8个点坐标，对于每个点来说，可以随意交换x，y，z坐标的数值。问说8个点是否可以组成立方体。

暴力枚举即可，注意检查立方体姿势不对会T

如果8个点形成一个立方体是这样的：找到所有点对之间的最小距离，应等于边的长度L。每个顶点应该正好有三个点距离它为L，而且构成的三个边应两两垂直。如果这些条件都满足在每一点上，那么一定只能是立方体。检查复杂度约O(8^2)。

#include <cstdio>#include <cstdlib>#include <cmath>#include <cstring>#include <string>#include <queue>#include <vector>#include<set>#include <iostream>#include <algorithm>using namespace std;#define RD(x) scanf("%d",&x)#define RD2(x,y) scanf("%d%d",&x,&y)#define clr0(x) memset(x,0,sizeof(x))typedef long long LL;typedef pair<int int> pii;const double eps = 1e-9;const double pi = acos(-1.0);LL dianji(LL x1,LL y1,LL z1,LL x2,LL y2,LL z2){    return x1*x2+y1*y2+z1*z2;}LL dist2(LL x1,LL y1,LL z1,LL x2,LL y2,LL z2){    return (x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)+(z1-z2)*(z1-z2);}LL v[8][3],minl[8],l;int cntmin[8],to[8][8];int index[8];bool chuizhi(LL x1,LL y1,LL z1,LL x2,LL y2,LL z2){    return dianji(x1,y1,z1,x2,y2,z2) == 0;}bool chuizhi(int i,int a,int b){    return chuizhi(v[a][0] - v[i][0],v[a][1] - v[i][1],v[a][2] - v[i][2],v[b][0] - v[i][0],v[b][1] - v[i][1],v[b][2] - v[i][2]);}bool chuizhi(int i,int a,int b,int c){    return chuizhi(i,a,b)&&chuizhi(i,b,c)&&chuizhi(i,a,c);}bool check(){    clr0(index),clr0(minl),clr0(cntmin);    for(int i = 0;i  l)                minl[i] = l,to[i][cntmin[i] = 0] = j;            else if(minl[i] == l)                to[i][++cntmin[i]] = j;            if(!minl[j] || minl[j] > l)                minl[j] = l,to[j][cntmin[j] = 0] = j;            else if(minl[j] == l)                to[j][++cntmin[j]] = i;        }        if(cntmin[i]!=2 || !minl)            return false;        if(!chuizhi(i,to[i][0],to[i][1],to[i][2]))            return false;    }    return true;}bool find(int x){    if(x == 8){        return check();    }    do{        if(find(x+1))            return true;    }while(next_permutation(v[x],v[x]+3));    return false;}int main() {    for(int i = 0;i   <br>  <br>  <p></p> </int></algorithm></iostream></set></vector></queue></string></cstring></cmath></cstdlib></cstdio>