hduoj 3459 Rubik 2×2×2

http://acm.hdu.edu.cn/showproblem.php?pid=3459

 

Rubik 2×2×2

Time Limit: 10000/5000 MS (Java/Others)    Memory Limit: 327670/327670 K (Java/Others)

Total Submission(s): 654    Accepted Submission(s): 234

Special Judge

Problem Description

Sonny is probably the only computer science Ph.D. student who cannot solve a Rubik's cube. One day, he came across a neat little 2×2×2 Rubik's cube, and thought, "Finally, here's a cube that's easy enough for me to do!" Nope, wrong! He got pwned, hardcore. How embarrassing.To ensure that this does not happen again, he decides to write a computer program to solve the cube. Then he had this brilliant idea: Why not have the students at the programming contest do the work instead? So, given an initial con guration of the 2×2×2 Rubik's cube, your task for this problem is to write a program that solves it. The mini-cube has 6 faces, each with 4 painted tiles on it. The faces are labeled Front (F), Back (B),Up (U), Down (D), Left (L), and Right (R), according to the diagram below. Each of the tiles on the faces can be colored Red (R), Green (G), Blue (B), Yellow (Y), Orange (O), or White (W), and there are exactly 4 instances of each color. The cube is considered solved when the colors of all tiles on each distinct face of the cube match. You may use any combination of three distinct moves to transform the cube: a turn about the X-axis,a turn about the Y-axis, or a turn about the Z-axis. Each turn is exactly 90 degrees of all tiles on half the cube, in the directions illustrated below. Note that the back-down-left corner is fixed with respect to all valid transforms. Can you come up with a sequence of moves that will solve a given con guration of the Rubik's cube?

 

 

Input

You will be given maps of an "unwrapped" cubes showing colors on each of the faces, in the following format: The letters in the above diagram shows you where to fi nd the colors on each face (as shown in the first diagram) from the map only { it is not valid input! The front face is oriented as in the diagram, with the other faces on the map attached to it so that it wraps to cover the cube. The letters on the faces may be any of R, G, B, Y, O, or W to indicate the color. Dot (.) characters serve to pad the map to a 6 × 8 grid,and are of no other signi cance.The input consists of several con guration maps in the format described, separated by blank lines. You may assume that each con guration is both valid and solvable. The end of input is denoted by an "empty" con guration consisting solely of `.' characters; do not process this map.

 

 

Output

For each cube, output on a single line a sequence of moves that will solve the cube. Output `X' for a turn about the X-axis, `Y' for a turn about the Y-axis, and `Z' for a turn about the Z-axis. Any sequence of moves (that is reasonably finite) which solves the given confi guration will do. (After all, Sonny does need to execute your commands to verify that your program works!) A blank line will suffice for an input cube that is already solved.

 

 

Sample Input

..WO....

..WO....

BBOYGGWR

BBOYGGWR

..YR....

..YR....

 

..GY....

..BY....

ROYWRRBB

GWOWRBOW

..YG....

..OG....

 

........

........

........

........

........

........

 

 

 

Sample Output

X

YZXXXZYZXYXYZZYZZYZXYY

 

Source

2009 Stanford Local ACM Programming Contest

 

 

分析：

题目不难理解，就是求还原的最小步数。

从图中不难看出，无论魔方怎么旋转，与原点相接的那个小方块是不动的，那么我们可以由原点的小方块得出三个面的最终颜色，然后再通过这三个面去确定其他三个面的颜色

然后就是IDA的剪枝估测函数的h值，由于每次旋转能够改变8个小面，那么只要求出现在不在其位的面总数SUM，得出(sum+7)/8即可，加7是保证sum+7>=8得出步数。

 

 

AC代码：

 

  1 #include <stdio.h>
  2 #include <string.h>
  3 #include <algorithm>
  4 using namespace std;
  5 
  6 struct node
  7 {
  8     int x,y;
  9 } cube[10][10],side[10][10];
 10 
 11 char color[10],rubik[10][10];
 12 int ans[1000];
 13 int flag,step;
 14 
 15 void init()//cube代表每个小立方体的3个面对应字符数字的哪个位置，side则是6个面，每个面的四个元素分别是什么
 16 {
 17     cube[0][0].x=3,cube[0][0].y=2;
 18     cube[0][1].x=3,cube[0][1].y=1;
 19     cube[0][2].x=4,cube[0][2].y=2;
 20     cube[1][0].x=3,cube[1][0].y=3;
 21     cube[1][1].x=3,cube[1][1].y=4;
 22     cube[1][2].x=4,cube[1][2].y=3;
 23     cube[2][0].x=2,cube[2][0].y=2;
 24     cube[2][1].x=2,cube[2][1].y=1;
 25     cube[2][2].x=1,cube[2][2].y=2;
 26     cube[3][0].x=2,cube[3][0].y=3;
 27     cube[3][1].x=1,cube[3][1].y=3;
 28     cube[3][2].x=2,cube[3][2].y=4;
 29     cube[4][0].x=3,cube[4][0].y=0;
 30     cube[4][1].x=5,cube[4][1].y=2;
 31     cube[4][2].x=3,cube[4][2].y=7;
 32     cube[5][0].x=5,cube[5][0].y=3;
 33     cube[5][1].x=3,cube[5][1].y=5;
 34     cube[5][2].x=3,cube[5][2].y=6;
 35     cube[6][0].x=0,cube[6][0].y=2;
 36     cube[6][1].x=2,cube[6][1].y=7;
 37     cube[6][2].x=2,cube[6][2].y=0;
 38     cube[7][0].x=0,cube[7][0].y=3;
 39     cube[7][1].x=2,cube[7][1].y=5;
 40     cube[7][2].x=2,cube[7][2].y=6;
 41     side[0][0].x=0,side[0][0].y=2;
 42     side[0][1].x=0,side[0][1].y=3;
 43     side[0][2].x=1,side[0][2].y=2;
 44     side[0][3].x=1,side[0][3].y=3;
 45     side[1][0].x=2,side[1][0].y=0;
 46     side[1][1].x=2,side[1][1].y=1;
 47     side[1][2].x=3,side[1][2].y=0;
 48     side[1][3].x=3,side[1][3].y=1;
 49     side[2][0].x=2,side[2][0].y=2;
 50     side[2][1].x=2,side[2][1].y=3;
 51     side[2][2].x=3,side[2][2].y=2;
 52     side[2][3].x=3,side[2][3].y=3;
 53     side[3][0].x=2,side[3][0].y=4;
 54     side[3][1].x=2,side[3][1].y=5;
 55     side[3][2].x=3,side[3][2].y=4;
 56     side[3][3].x=3,side[3][3].y=5;
 57     side[4][0].x=2,side[4][0].y=6;
 58     side[4][1].x=2,side[4][1].y=7;
 59     side[4][2].x=3,side[4][2].y=6;
 60     side[4][3].x=3,side[4][3].y=7;
 61     side[5][0].x=4,side[5][0].y=2;
 62     side[5][1].x=4,side[5][1].y=3;
 63     side[5][2].x=5,side[5][2].y=2;
 64     side[5][3].x=5,side[5][3].y=3;
 65 }
 66 
 67 char get_color(int A,int B,int C)   //通过小格子的颜色获得每个面的颜色
 68 {
 69     for(int i=0; i<8; i++)
 70     {
 71         if(rubik[cube[i][0].x][cube[i][0].y]==color[A]&&rubik[cube[i][1].x][cube[i][1].y]==color[B]&&rubik[cube[i][2].x][cube[i][2].y]!=color[C])
 72             return rubik[cube[i][2].x][cube[i][2].y];
 73         if(rubik[cube[i][1].x][cube[i][1].y]==color[A]&&rubik[cube[i][0].x][cube[i][0].y]==color[B]&&rubik[cube[i][2].x][cube[i][2].y]!=color[C])
 74             return rubik[cube[i][2].x][cube[i][2].y];
 75         if(rubik[cube[i][0].x][cube[i][0].y]==color[A]&&rubik[cube[i][2].x][cube[i][2].y]==color[B]&&rubik[cube[i][1].x][cube[i][1].y]!=color[C])
 76             return rubik[cube[i][1].x][cube[i][1].y];
 77         if(rubik[cube[i][2].x][cube[i][2].y]==color[A]&&rubik[cube[i][0].x][cube[i][0].y]==color[B]&&rubik[cube[i][1].x][cube[i][1].y]!=color[C])
 78             return rubik[cube[i][1].x][cube[i][1].y];
 79         if(rubik[cube[i][1].x][cube[i][1].y]==color[A]&&rubik[cube[i][2].x][cube[i][2].y]==color[B]&&rubik[cube[i][0].x][cube[i][0].y]!=color[C])
 80             return rubik[cube[i][0].x][cube[i][0].y];
 81         if(rubik[cube[i][2].x][cube[i][2].y]==color[A]&&rubik[cube[i][1].x][cube[i][1].y]==color[B]&&rubik[cube[i][0].x][cube[i][0].y]!=color[C])
 82             return rubik[cube[i][0].x][cube[i][0].y];
 83     }
 84 }
 85 
 86 void turn_x(char maze[10][10])    //x轴
 87 {
 88     char tmp;
 89     tmp=maze[2][4];
 90     maze[2][4]=maze[2][5];
 91     maze[2][5]=maze[3][5];
 92     maze[3][5]=maze[3][4];
 93     maze[3][4]=tmp;
 94     tmp=maze[1][3];
 95     maze[1][3]=maze[2][6];
 96     maze[2][6]=maze[5][3];
 97     maze[5][3]=maze[3][3];
 98     maze[3][3]=tmp;
 99     tmp=maze[0][3];
100     maze[0][3]=maze[3][6];
101     maze[3][6]=maze[4][3];
102     maze[4][3]=maze[2][3];
103     maze[2][3]=tmp;
104 }
105 void turn_y(char maze[10][10])    //y轴
106 {
107     char tmp;
108     tmp=maze[2][0];
109     maze[2][0]=maze[2][6];
110     maze[2][6]=maze[2][4];
111     maze[2][4]=maze[2][2];
112     maze[2][2]=tmp;
113     tmp=maze[2][1];
114     maze[2][1]=maze[2][7];
115     maze[2][7]=maze[2][5];
116     maze[2][5]=maze[2][3];
117     maze[2][3]=tmp;
118     tmp=maze[0][2];
119     maze[0][2]=maze[0][3];
120     maze[0][3]=maze[1][3];
121     maze[1][3]=maze[1][2];
122     maze[1][2]=tmp;
123 }
124 void turn_z(char maze[10][10])    //z轴
125 {
126     char tmp;
127     tmp=maze[2][1];
128     maze[2][1]=maze[1][3];
129     maze[1][3]=maze[3][4];
130     maze[3][4]=maze[4][2];
131     maze[4][2]=tmp;
132     tmp=maze[3][1];
133     maze[3][1]=maze[1][2];
134     maze[1][2]=maze[2][4];
135     maze[2][4]=maze[4][3];
136     maze[4][3]=tmp;
137     tmp=maze[2][2];
138     maze[2][2]=maze[2][3];
139     maze[2][3]=maze[3][3];
140     maze[3][3]=maze[3][2];
141     maze[3][2]=tmp;
142 }
143 
144 int get_h(char mid[10][10])
145 {
146     int i,j,sum = 0;
147     for(i = 0; i<6; i++)
148     {
149         for(j = 0; j<4; j++)
150         {
151             if(mid[side[i][j].x][side[i][j].y]!=color[i])
152                 sum++;
153         }
154     }
155     return (sum+7)/8;
156 }
157 
158 int IDA(char mid[10][10],int cnt)
159 {
160     if(cnt+get_h(mid)>step)
161         return 0;
162     if(cnt == step)
163         return 1;
164     for(int i = 0; i<3; i++)
165     {
166         char tem[10][10];
167         for(int x = 0; x<6; x++)
168             for(int y = 0; y<8; y++)
169                 tem[x][y]=mid[x][y];
170         if(i == 0)
171             turn_x(tem);
172         else if(i == 1)
173             turn_y(tem);
174         else
175             turn_z(tem);
176         ans[cnt] = i;
177         if(IDA(tem,cnt+1))
178             return 1;
179     }
180     return 0;
181 }
182 int main()
183 {
184     int i;
185     init();
186     while(~scanf("%s",rubik[0]))
187     {
188         for(i = 1; i<6; i++)
189             scanf("%s",rubik[i]);
190         if(!strcmp(rubik[0],"........"))
191             break;
192         color[1]=rubik[3][0];
193         color[5]=rubik[5][2];
194         color[4]=rubik[3][7];
195         color[0]=get_color(1,4,5);
196         color[2]=get_color(1,5,4);
197         color[3]=get_color(4,5,1);
198         step = 0;
199         while(1)
200         {
201             if(IDA(rubik,0)) break;
202             step++;
203         }
204         for(i = 0; i<step; i++)
205             printf("%c",ans[i]+'X');
206         printf("\n");
207     }
208 
209     return 0;
210 }

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