POJ1022 Packing Unit 4D Cubes

题目来源：http://poj.org/problem?id=1022

题目大意：

　　有一些4维的单位体积的立方体盒子，每个立方体有8个面。要用一个大的4为盒子将它们包起来，求最小的大盒子体积。

输入：第一行为测试用例数。每个用例的第一行为单位立方体数目n。接下来的n行每行为一个立方体的信息。每行第一个数字为还立方体的编号，接下来的8个整数分别为对应面相邻的立方体的编号。该面没有邻居则为0.（给出的都是单一刚体。）

输出：最小的能把这个由小4D立方体拼起来的形状的盒子的体积。

---

Sample Input

1
9
1 2 3 4 5 6 7 8 9
2 0 1 0 0 0 0 0 0
3 1 0 0 0 0 0 0 0
4 0 0 0 1 0 0 0 0
5 0 0 1 0 0 0 0 0
6 0 0 0 0 0 1 0 0
7 0 0 0 0 1 0 0 0
8 0 0 0 0 0 0 0 1
9 0 0 0 0 0 0 1 0

Sample Output

81

---

本题题干描述得很复杂，想象起来也有一些抽象，其实很简单，跟3D的情况联系起来想就可以了。3D求包围盒的方法推广至4D即可。

 //////////////////////////////////////////////////////////////////////////
 //        POJ1022 Packing Unit 4D Cubes
 //        Memory: 300K        Time: 16MS
 //        Language: C++        Result: Accepted
 //////////////////////////////////////////////////////////////////////////

 #include <iostream>
 #include <vector>
 #include <map>

 using namespace std;

 class Cube {
 public:
     int x1p, x1n, x2p, x2n, x3p, x3n, x4p, x4n;
 };
 class Pos {
 public:
     int id;
     int x1, x2, x3, x4;
 };

 int main() {
     int ncase;
     cin >> ncase;
     for (int caseNo = ; caseNo <= ncase; ++caseNo) {
         int n;
         map<int, Cube> cubes;
         cin >> n;
         for (int i = ; i <= n; ++i) {
             int id;
             cin >> id;
             Cube cube;
             cin >> cube.x1p >> cube.x1n >> cube.x2p >> cube.x2n
                 >> cube.x3p >> cube.x3n >> cube.x4p >> cube.x4n;
             cubes[id] = cube;
         }
         bool ok = true;
         vector<Pos> solid;
         Pos firstPos;
         firstPos.id = (*cubes.begin()).first;
         firstPos.x1 = firstPos.x2 = firstPos.x3 = firstPos.x4 = ;
         solid.push_back(firstPos);
         for (map<int, Cube>::iterator itc = cubes.begin(); itc != cubes.end(); ++itc) {
             Cube cube1;
             int id = (*itc).first;
             int x1p = (*itc).second.x1p;
             //x1p
             if (x1p != ) {
                 if (cubes[x1p].x1n != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x1p;
                         pos.x1 = (*its).x1 + ;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x1p) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }

             //x1n
             int x1n = (*itc).second.x1n;
             if (x1n != ) {
                 if (cubes[x1n].x1p != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x1n;
                         pos.x1 = (*its).x1 - ;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x1n) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }

             //x2p
             int x2p = (*itc).second.x2p;
             if (x2p != ) {
                 if (cubes[x2p].x2n != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x2p;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2 + ;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x2p) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }
             //x2n
             int x2n = (*itc).second.x2n;
             if (x2n != ) {
                 if (cubes[x2n].x2p != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x2n;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2 - ;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x2n) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }

             //x3p
             int x3p = (*itc).second.x3p;
             if (x3p != ) {
                 if (cubes[x3p].x3n != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x3p;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3 + ;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x3p) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }
             //x3n
             int x3n = (*itc).second.x3n;;
             if (x3n != ) {
                 if (cubes[x3n].x3p != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x3n;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3 - ;
                         pos.x4 = (*its).x4;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x3n) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }
             //x4p
             int x4p = (*itc).second.x4p;
             if (x4p != ) {
                 if (cubes[x4p].x4n != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x4p;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4 + ;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x4p) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }
             //x4n
             int x4n = (*itc).second.x4n;
             if (x4n != ) {
                 if (cubes[x4n].x4p != id) {
                     ok = false;
                     break;
                 }
                 bool f = true;
                 Pos pos;
                 for (vector<Pos>::iterator its = solid.begin(); its != solid.end(); ++its) {
                     if (f == false) break;
                     if ((*its).id == id) {
                         pos.id = x4n;
                         pos.x1 = (*its).x1;
                         pos.x2 = (*its).x2;
                         pos.x3 = (*its).x3;
                         pos.x4 = (*its).x4 - ;
                         for (vector<Pos>::iterator itr = solid.begin(); itr != solid.end(); ++itr) {
                             if ((*itr).id == x4n) {
                                 f = false;
                                 break;
                             }
                         }
                     }
                 }
                 if (f == true) {
                     solid.push_back(pos);
                 }
             }
         }
         if (solid.size() != n) {
             ok = false;
         }
         if (ok == false) {
             cout << "Inconsistent" << endl;
             continue;
         }
         int x1min = ;
         int x1max = -;
         int x2min = ;
         int x2max = -;
         int x3min = ;
         int x3max = -;
         int x4min = ;
         int x4max = -;
         for (vector<Pos>::iterator it = solid.begin(); it != solid.end(); ++it) {
             if (x1min >(*it).x1) x1min  = (*it).x1;
             if (x1max < (*it).x1) x1max = (*it).x1;
             if (x2min >(*it).x2) x2min  = (*it).x2;
             if (x2max < (*it).x2) x2max = (*it).x2;
             if (x3min >(*it).x3) x3min  = (*it).x3;
             if (x3max < (*it).x3) x3max = (*it).x3;
             if (x4min >(*it).x4) x4min  = (*it).x4;
             if (x4max < (*it).x4) x4max = (*it).x4;
         }
         int vol = (x1max - x1min + ) * (x2max - x2min + ) * (x3max - x3min + ) * (x4max - x4min + );
         cout << vol << endl;
     }
     system("pause");
     return ;
 }