如何打印方阵的右半球

Question

我正在尝试打印矩阵的右半球。如果我们在矩阵中绘制主对角线和次对角线，我们会看到我们得到了 4 个相等的部分，右边的部分被称为（在我的算法教科书中）方阵的右半球。

例如，在下面的5 x 5 矩阵中，右半球由以下元素组成：-1, -3, -2, 0。

我尝试解决此问题的方法是开始并组合第二对角线的一半，然后在左对角线元素的右侧打印每个元素。到达次对角线的中间后，我在主对角线的下部重复此过程。

类似的东西（至少，这是我在脑海中的看法）：

这是一些打印5 x 5 矩阵右半球的工作代码。它可以工作，但是很难看，并且对于具有偶数行和列的矩阵（例如 4 x 4 矩阵）不能正常工作。

#include <iostream>

#define N 5
#define M 5

void printHemisphere(int matrix[N][M], int n, int m)
{
    int i = 1;
    for(int j = n - 1; j > n / 2; i++, j--)
    {
        for (int k = j + 1; k < m; ++k)
        {
            std::cout << matrix[i][k] << " ";
        }
        std::cout << std::endl;
    }

    for(int j = n / 2; j < n; i++, j++)
    {
        for (int k = j + 1; k < m; ++k)
        {
            std::cout << matrix[i][k] << " ";
        }
        std::cout << std::endl;
    }

}

int main(int argc, char const *argv[])
{
     int matrix5[N][M] = 
     {
        {1, 2, 3, 4, 5},
        {6, 7, 8, 9, 10},
        {11, 12, 13, 14, 15},
        {16, 17, 18, 19, 20},
        {21, 22, 23, 24, 25}
     };


    printHemisphere(matrix5, N, M);

    return 0;
}

你会如何解决这个问题？

Answer 1

我认为这应该适用于方阵：

void printHemisphere(int matrix[N][M], int n, int m)
{
    int mid = n / 2;
    for(int i = 1; i < mid; i++)
    {
        for (int j = n - i; j < m; ++j)
        {
            std::cout << matrix[i][j] << " ";
        }
        std::cout << std::endl;
    }

    for(int i = mid; i < n - 1; i++)
    {
        for (int j = i + 1; j < m; ++j)
        {
            std::cout << matrix[i][j] << " ";
        }
        std::cout << std::endl;
    }
}

外部循环跳过第一行和最后一行，因为它们不能有输出。

Answer 2

这是一种只使用双 for 循环的方法：

void printHemisphere(int matrix[N][M], int n, int m)
{
    for(int i = 1; i < n - 1 ; i++)
    {
        for (j = max(i, n - i) ; j < m ; j++)
        {
            std::cout << matrix[i][k] << " ";
        }
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

Answer 3

在伪代码中...：

for row in 1 -> height - 2 // Indices between 0 -> height - 1
   distance = min(row, height - 1 - row)
   for cell in (width - distance) -> width - 1
      print matrix[row][cell]

Answer 4

这是我的看法。我来晚了，因为您已经接受了解决方案；不过，我想向您展示一些东西。例如，如果您将这些矩阵视为一维数组，您可以只用一个函数测试所有大小的矩阵，因为大小不必“内置”到函数定义中的数据类型中。并且我已经评论了很多，希望尽可能的说清楚。

#include <iostream>
#include <algorithm>


// I store matrices as a monodimensional array, so that it is easier to deal
// with matrices of different sizes in the same program, because you can do
// everything with one function. Moreover, I use only one argument here, to make
// it clear that we are dealing with square matrices.
void printHemisphere(int* matrix, int last_row)
{
    int last_column = last_row; // It's a square matrix, so they are the same.
                                // Still, distinguishing between last_column
                                // and last_row can make the algorithm clearer,
                                // so I have kept both

    // In general I prefer to use "row" and "column" as variable names, instead
    // of "i" and "j"

    // Our rows go from 0 to last_row-1, but since the first and last one can
    // certainly not be used, we can skip them: we start at row = 1, and we stop
    // at last_row - 2 (that is, the last one for which row < last_row - 1)
    for(int row = 1; row < last_row - 1 ; row++)
    {
        // We want to start from the cell to the right of the rightmost diagonal.
        // The main diagonal has column = row;
        // The secondary diagonal has column = last_row - 1 - row
        // The rightmost one is the maximum of these 2.
        // Then, we want to take the cell to the right of the diagonal, so we
        // have to add 1 more.
        // All in all we have:
        for (int column = std::max(row, last_row - 1 - row) + 1;
             column < last_column;
             column++)
        {
            // since this is a 1-D array we have to access it this way
            std::cout << matrix[row*last_row+column] << " ";
        }
        std::cout << std::endl;
    }
    std::cout << std::endl;
}

int main(int argc, char const *argv[])
{
    // Since I am working with monodimensional arrays, I don't store them as
    // int matrix3[3][3], but rather as int matrix3[9], which I have expressed as
    // int matrix3[3*3] for clarity.
    //For each one I have indicated the expected output.

    // Expected output:
    // 6
    int matrix3[3*3] = 
    {
        1, 2, 3,
        4, 5, 6,
        7, 8, 9
    };

    // Expected output:
    // 8
    // 12
    int matrix4[4*4] = 
    {
        1, 2, 3, 4,
        5, 6, 7, 8,
        9, 10, 11, 12,
        13, 14, 15, 16
    };

    // Expected output:
    //    10
    // 14 15
    //    20
    int matrix5[5*5] = {
         1,  2,  3,  4,  5,
         6,  7,  8,  9, 10,
        11, 12, 13, 14, 15,
        16, 17, 18, 19, 20,
        21, 22, 23, 24, 25
    };

    // Expected output:
    //    12
    // 17 18
    // 23 24
    //    30 
    int matrix6[6*6] = {
         1,  2,  3,  4,  5,  6,
         7,  8,  9, 10, 11, 12,
        13, 14, 15, 16, 17, 18,
        19, 20, 21, 22, 23, 24,
        25, 26, 27, 28, 29, 30,
        31, 32, 33, 34, 35, 36
    };

    // Expected output:
    //       14
    //    20 21
    // 26 27 28
    //    34 35
    //       42
    int matrix7[7*7] = {
         1,  2,  3,  4,  5,  6,  7,
         8,  9, 10, 11, 12, 13, 14,
        15, 16, 17, 18, 19, 20, 21,
        22, 23, 24, 25, 26, 27, 28,
        29, 30, 31, 32, 33, 34, 35,
        36, 37, 38, 39, 40, 41, 42,
        43, 44, 45, 46, 47, 48, 49
    };


    printHemisphere(matrix3, 3);
    printHemisphere(matrix4, 4);
    printHemisphere(matrix5, 5);
    printHemisphere(matrix6, 6);
    printHemisphere(matrix7, 7);

    return 0;
}

我已经在 ideone 上验证了它，它可以工作。我唯一想补充的是：为确保代码正常工作，请确保使用奇数大小和偶数大小的矩阵对其进行测试。