请看我自己的答案，我想我做到了！

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你好

编程竞赛的一个示例问题是编写一个程序，以找出在给定数量的宝石下可能有多少个多米诺骨牌。

因此，对于两块石头（n = 2），只有一个多米诺骨牌：

XX

您可能会认为这是第二种解决方案：

X
X

但事实并非如此。如果可以旋转多义字，它们并不是唯一的。

因此，对于4个石头（n = 4），有7个解决方案：

X
X   XX   X    X     X   X
X   X    XX   X    XX   XX   XX
X   X    X    XX   X     X   XX

该应用程序必须能够找到解决方案 1 <= n <=10

PS：不允许在Wikipedia上使用多氨基酸列表；）

编辑：当然，问题是：如何在Java，C / C ++，C＃中做到这一点

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我用Java启动了这个项目。但是后来我不得不承认我不知道如何使用有效的算法来构建多米诺骨牌。

这是我到目前为止的内容：

import java.util.ArrayList;
import java.util.List;


public class Main
{

    private int countPolyminos(int n)
    {
        hashes.clear();
        count = 0;
        boolean[][] matrix = new boolean[n][n];
        createPolyominos(matrix, n);
        return count;
    }

    private List<Integer> hashes = new ArrayList<Integer>();
    private int count;

    private void createPolyominos(boolean[][] matrix, int n)
    {
        if (n == 0)
        {
            boolean[][] cropped = cropMatrix(matrix); 
            int hash = hashMatrixOrientationIndependent(matrix);
            if (!hashes.contains(hash))
            {
                count++;
                hashes.add(hash);
            }
            return;
        }
    // Here is the real trouble!!
    // Then here something like; createPolyominos(matrix, n-1);
    // But, we need to keep in mind that the polyominos can have ramifications
    }

    public boolean[][] copy(boolean[][] matrix)
    {
        boolean[][] b = new boolean[matrix.length][matrix[0].length];
        for (int i = 0; i < matrix.length; ++i)
        {
            System.arraycopy(matrix[i], 0, b, 0, matrix[i].length);
        }
        return b;
    }

    public boolean[][] cropMatrix(boolean[][] matrix)
    {
        int l = 0, t = 0, r = 0, b = 0;
        // Left
        left: for (int x = 0; x < matrix.length; ++x)
        {
            for (int y = 0; y < matrix[x].length; ++y)
            {
                if (matrix[x][y])
                {
                    break left;
                }
            }
            l++;
        }
        // Right
        right: for (int x = matrix.length - 1; x >= 0; --x)
        {
            for (int y = 0; y < matrix[x].length; ++y)
            {
                if (matrix[x][y])
                {
                    break right;
                }
            }
            r++;
        }
        // Top
        top: for (int y = 0; y < matrix[0].length; ++y)
        {
            for (int x = 0; x < matrix.length; ++x)
            {
                if (matrix[x][y])
                {
                    break top;
                }
            }
            t++;
        }
        // Bottom
        bottom: for (int y = matrix[0].length; y >= 0; --y)
        {
            for (int x = 0; x < matrix.length; ++x)
            {
                if (matrix[x][y])
                {
                    break bottom;
                }
            }
            b++;
        }

        // Perform the real crop
        boolean[][] cropped = new boolean[matrix.length - l - r][matrix[0].length - t - b];
        for (int x = l; x < matrix.length - r; ++x)
        {
            System.arraycopy(matrix[x - l], t, cropped, 0, matrix[x].length - t - b);
        }
        return cropped;
    }

    public int hashMatrix(boolean[][] matrix)
    {
        int hash = 0;
        for (int x = 0; x < matrix.length; ++x)
        {
            for (int y = 0; y < matrix[x].length; ++y)
            {
                hash += matrix[x][y] ? (((x + 7) << 4) * ((y + 3) << 6) * 31) : ((((x+5) << 9) * (((y + x) + 18) << 7) * 53));
            }
        }
        return hash;
    }

    public int hashMatrixOrientationIndependent(boolean[][] matrix)
    {
        int hash = 0;
        hash += hashMatrix(matrix);
        for (int i = 0; i < 3; ++i)
        {
            matrix = rotateMatrixLeft(matrix);
            hash += hashMatrix(matrix);
        }
        return hash;
    }

    public boolean[][] rotateMatrixRight(boolean[][] matrix)
    {
        /* W and H are already swapped */
        int w = matrix.length;
        int h = matrix[0].length;
        boolean[][] ret = new boolean[h][w];
        for (int i = 0; i < h; ++i)
        {
            for (int j = 0; j < w; ++j)
            {
                ret[i][j] = matrix[w - j - 1][i];
            }
        }
        return ret;
    }

    public boolean[][] rotateMatrixLeft(boolean[][] matrix)
    {
        /* W and H are already swapped */
        int w = matrix.length;
        int h = matrix[0].length;
        boolean[][] ret = new boolean[h][w];
        for (int i = 0; i < h; ++i)
        {
            for (int j = 0; j < w; ++j)
            {
                ret[i][j] = matrix[j][h - i - 1];
            }
        }
        return ret;
    }

}