问题描述
如何旋转矩阵
|3 4 5 6 8|
|5 4 3 2 6|
|3 3 7 8 9|
到
|8 6 9|
|6 2 8|
|5 3 7|
|4 4 3|
|3 5 3|
因为我见过的所有算法都是针对 N*N 矩阵的.
Because all algorithms I've seen was for N*N matrix.
推荐答案
如果你的矩阵是用数组 matrix[i, j]
表示的,其中 i
是行和 j
是列,然后实现以下方法:
If your matrix is represented by an array matrix[i, j]
, where the i
are the rows and the j
are the columns, then implement the following method:
static int[,] RotateMatrixCounterClockwise(int[,] oldMatrix)
{
int[,] newMatrix = new int[oldMatrix.GetLength(1), oldMatrix.GetLength(0)];
int newColumn, newRow = 0;
for (int oldColumn = oldMatrix.GetLength(1) - 1; oldColumn >= 0; oldColumn--)
{
newColumn = 0;
for (int oldRow = 0; oldRow < oldMatrix.GetLength(0); oldRow++)
{
newMatrix[newRow, newColumn] = oldMatrix[oldRow, oldColumn];
newColumn++;
}
newRow++;
}
return newMatrix;
}
这适用于所有大小的矩阵.
This works for matrices of all sizes.
编辑:如果这个操作代价太大,那么可以尝试改变读取矩阵的方式,而不是改变矩阵本身.例如,如果我按如下方式显示矩阵:
Edit: If this operation is too expensive, then one could try changing the way one reads the matrix instead of changing the matrix itself. For example, if I am displaying the matrix as follows:
for (int row = 0; row < matrix.GetLength(0); row++)
{
for (int col = 0; col < matrix.GetLength(1); col++)
{
Console.Write(matrix[row, col] + " ");
}
Console.WriteLine();
}
然后我可以通过改变读取矩阵的方式来表示逆时针旋转 90 度:
then I could represent a 90-degree counterclockwise rotation by changing the way I read the matrix:
for (int col = matrix.GetLength(1) - 1; col >= 0; col--)
{
for (int row = 0; row < matrix.GetLength(0); row++)
{
Console.Write(matrix[row, col] + " ");
}
Console.WriteLine();
}
这种访问模式也可以抽象为一个类.
This access pattern could be abstracted in a class, too.
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