尝试在Java中解决魔方

Question

到目前为止，我已经开发了一个类，可以使用树状图表示魔方（最好的方法？）每种颜色都映射到键 0 - 53。 键始终保持不变，并由立方体的 2D 视图表示。我做了一个 rotate90 方法，该方法将采用一种颜色并将颜色面（中间立方体永远不会移动）顺时针旋转 90 度。所以我的问题是，我如何实现一个好的搜索（也许是 A*？）让这个多维数据集朝着正确的方向发展到它的 goalState（我也在代码中将其初始化为全局，以便我可以将其与当前状态进行比较）。任何正确方向的反馈或提示都会很棒。谢谢！

这是没有 rotate 90 方法的代码和一个只检查文件文本是否正常的 checkInput 方法。输入只是一个表示 2D 立方体的文本文件，如下所示。现在的解决方法只是我胡闹，并没有真正到达任何地方。

   GGW
   RRG
   RRG
OWWGGOYYR
OGOYYYRBR
YYYRBGRWW
   BOY
   BOB
   BOB
   OGO
   WWB
   WWB
package rubik;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.util.NavigableMap;
import java.util.TreeMap;
public class RubikCube {
final static String FILE_NAME = "rubikTest.txt";
public TreeMap<Integer, Character> goalState;

//swaps two colors given a cube
public static void swapColorValue(int color1, int color2, TreeMap<Integer, Character> rubik){
    char tempColor = rubik.get(color1);
    rubik.put(color1,rubik.get(color2));
    rubik.put(color2, tempColor);
}
//initialize the goal map
public void goalInit(TreeMap<Integer, Character> rubik){
    //initialize the goal state map each rubik.get(magicNumber) is the static center cubie
    TreeMap<Integer, Character> goalMap = new TreeMap<Integer,Character>();
    for(int i =0;i<=8;i++){
    goalMap.put(i,rubik.get(4));
    }
    //the left side
    goalMap.put(9, rubik.get(19));
    goalMap.put(10, rubik.get(19));
    goalMap.put(11, rubik.get(19));
    goalMap.put(18, rubik.get(19));
    goalMap.put(19, rubik.get(19));
    goalMap.put(20, rubik.get(19));
    goalMap.put(27, rubik.get(19));
    goalMap.put(28, rubik.get(19));
    goalMap.put(29, rubik.get(19));
    //the middle
    goalMap.put(12, rubik.get(22));
    goalMap.put(13, rubik.get(22));
    goalMap.put(14, rubik.get(22));
    goalMap.put(21, rubik.get(22));
    goalMap.put(22, rubik.get(22));
    goalMap.put(23, rubik.get(22));
    goalMap.put(30, rubik.get(22));
    goalMap.put(31, rubik.get(22));
    goalMap.put(32, rubik.get(22));
    //right side
    goalMap.put(15, rubik.get(25));
    goalMap.put(16, rubik.get(25));
    goalMap.put(17, rubik.get(25));
    goalMap.put(24, rubik.get(25));
    goalMap.put(25, rubik.get(25));
    goalMap.put(26, rubik.get(25));
    goalMap.put(33, rubik.get(25));
    goalMap.put(34, rubik.get(25));
    goalMap.put(35, rubik.get(25));
    //bottom
    for(int i = 36;i<=44;i++){
        goalMap.put(i, rubik.get(40));
    }
    //back
    for(int i = 45;i<=53;i++){
        goalMap.put(i, rubik.get(49));
    }
    //give it to the global variable
    goalState = (TreeMap<Integer, Character>) goalMap.clone();
}
//Maps a Integer key to a color given a file.
public static NavigableMap<Integer, Character> setup(String file) throws IOException{
    TreeMap<Integer, Character> rubik = new TreeMap<Integer, Character>();
    BufferedReader br = new BufferedReader(new FileReader(file));
    try {
        StringBuilder sb = new StringBuilder();
        String line = br.readLine();
        //add each line (without white spaces) to the stringbuilder
        while (line != null) {
            sb.append(line.trim());
            line = br.readLine();
        }
        //convert the stringbuilder(which has all the input from the file) to a char array
        char [] colors = sb.toString().toCharArray();
        //put the key,color into the Treemap.
        for(int i =0; i < colors.length;i++){
            rubik.put(i, colors[i]);
        }
    } finally {
        br.close();
    }
    //type Tree map
    return rubik;
    }
public int solve(TreeMap<Integer, Character> rubik){
    int j = 1;
    int check = 0;
    int redMatches=0;
    char [] colors = {'r','g','y','b','o','w'};
    for(int i = 0; i < 100;i++ ){
        if(j==6) j = 1;
        redMatches = 0;
        rotate90(colors[j],rubik);
        if(rubik.get(check)==goalState.get(check)){
            System.out.print("rubik match at: "+i+" with: "+rubik.get(i)+"match at goalState: "+i+" with: "+goalState.get(i));
            redMatches++;
        }
        j++;
    }

    return redMatches;
}
public static void main (String[] args){
    try {
        //check if file input is good
        //System.out.print(new RubikCube().checkInput(FILE_NAME));
        //Map the rubik cube(key,Color)
        RubikCube cubeInst = new RubikCube();
        //make sure to set up the mapping before calling rotate and goalInit    
        TreeMap<Integer, Character> cube = (TreeMap<Integer, Character>) (setup(FILE_NAME));
        cubeInst.goalInit(cube);
        //System.out.print(cubeInst.goalState);
        //rotate90('y',cube);
        //rotate90('y',cube);
        //System.out.print(cube);
        System.out.print(cubeInst.solve(cube));
    } catch (IOException e) {
        e.printStackTrace();
    }
}
}

Answer 1

我从来没有写过代码来解决魔方，但如果你使用像 A* 这样的启发式图遍历算法，我可以想到一些好的启发式方法来判断你离目标有多远：

1. 放错地方的小隔间数量。

2. 每个小隔间离目标状态有多远的总和，可能使用曼哈顿距离来判断它有多远。

问题是我不认为你可以为每个小隔间状态使用一种颜色。 您可能需要从某个任意角度将多维数据集表示为数据结构位置。 所以例如"左上角"是目标状态下的左上角部分（这也是左侧和背面的角隔间...... 然后你就会知道你的"左上角"小隔间是否不合适。