受Raymond Chen帖子的启发,假设你有一个4x4二维数组,写一个函数使它旋转90度。Raymond链接到伪代码中的解决方案,但我想看到一些真实的东西。
[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]
就变成:
[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]
更新:Nick的答案是最直接的,但是有没有比n²更好的方法呢?如果矩阵是10000x10000呢?
受Raymond Chen帖子的启发,假设你有一个4x4二维数组,写一个函数使它旋转90度。Raymond链接到伪代码中的解决方案,但我想看到一些真实的东西。
[1][2][3][4]
[5][6][7][8]
[9][0][1][2]
[3][4][5][6]
就变成:
[3][9][5][1]
[4][0][6][2]
[5][1][7][3]
[6][2][8][4]
更新:Nick的答案是最直接的,但是有没有比n²更好的方法呢?如果矩阵是10000x10000呢?
当前回答
PHP:
array_unshift($array, null);
$array = call_user_func_array("array_map", $array);
如果你需要旋转矩形二维阵列90度,在上面的代码之前或之后添加以下一行(取决于你需要的旋转方向):
$array = array_reverse($array);
其他回答
一些人已经举了一些例子,其中涉及到创建一个新数组。
还有一些需要考虑的事情:
(a)不实际移动数据,只需以不同的方式遍历“旋转”的数组。
(b)就地轮换可能有点棘手。您需要一点空白的地方(大概相当于一行或一列的大小)。有一篇古老的ACM论文是关于进行原地转置的(http://doi.acm.org/10.1145/355719.355729),但是他们的示例代码是令人讨厌的充满goto的FORTRAN。
附录:
http://doi.acm.org/10.1145/355611.355612是另一种更优越的就地转置算法。
下面是Java语言:
public static void rotateInPlace(int[][] m) {
for(int layer = 0; layer < m.length/2; layer++){
int first = layer;
int last = m.length - 1 - first;
for(int i = first; i < last; i ++){
int offset = i - first;
int top = m[first][i];
m[first][i] = m[last - offset][first];
m[last - offset][first] = m[last][last - offset];
m[last][last - offset] = m[i][last];
m[i][last] = top;
}
}
}
Nick的答案也适用于NxM阵列,只需要做一点修改(与NxN相反)。
string[,] orig = new string[n, m];
string[,] rot = new string[m, n];
...
for ( int i=0; i < n; i++ )
for ( int j=0; j < m; j++ )
rot[j, n - i - 1] = orig[i, j];
考虑这个问题的一种方法是将轴(0,0)的中心从左上角移动到右上角。你只是简单地从一个转置到另一个。
下面是PHP的递归方法:
$m = array();
$m[0] = array('a', 'b', 'c');
$m[1] = array('d', 'e', 'f');
$m[2] = array('g', 'h', 'i');
$newMatrix = array();
function rotateMatrix($m, $i = 0, &$newMatrix)
{
foreach ($m as $chunk) {
$newChunk[] = $chunk[$i];
}
$newMatrix[] = array_reverse($newChunk);
$i++;
if ($i < count($m)) {
rotateMatrix($m, $i, $newMatrix);
}
}
rotateMatrix($m, 0, $newMatrix);
echo '<pre>';
var_dump($newMatrix);
echo '<pre>';
基于大量的其他答案,我用c#想出了这个:
/// <param name="rotation">The number of rotations (if negative, the <see cref="Matrix{TValue}"/> is rotated counterclockwise;
/// otherwise, it's rotated clockwise). A single (positive) rotation is equivalent to 90° or -270°; a single (negative) rotation is
/// equivalent to -90° or 270°. Matrices may be rotated by 90°, 180°, or 270° only (or multiples thereof).</param>
/// <returns></returns>
public Matrix<TValue> Rotate(int rotation)
{
var result = default(Matrix<TValue>);
//This normalizes the requested rotation (for instance, if 10 is specified, the rotation is actually just +-2 or +-180°, but all
//correspond to the same rotation).
var d = rotation.ToDouble() / 4d;
d = d - (int)d;
var degree = (d - 1d) * 4d;
//This gets the type of rotation to make; there are a total of four unique rotations possible (0°, 90°, 180°, and 270°).
//Each correspond to 0, 1, 2, and 3, respectively (or 0, -1, -2, and -3, if in the other direction). Since
//1 is equivalent to -3 and so forth, we combine both cases into one.
switch (degree)
{
case -3:
case +1:
degree = 3;
break;
case -2:
case +2:
degree = 2;
break;
case -1:
case +3:
degree = 1;
break;
case -4:
case 0:
case +4:
degree = 0;
break;
}
switch (degree)
{
//The rotation is 0, +-180°
case 0:
case 2:
result = new TValue[Rows, Columns];
break;
//The rotation is +-90°
case 1:
case 3:
result = new TValue[Columns, Rows];
break;
}
for (uint i = 0; i < Columns; ++i)
{
for (uint j = 0; j < Rows; ++j)
{
switch (degree)
{
//If rotation is 0°
case 0:
result._values[j][i] = _values[j][i];
break;
//If rotation is -90°
case 1:
//Transpose, then reverse each column OR reverse each row, then transpose
result._values[i][j] = _values[j][Columns - i - 1];
break;
//If rotation is +-180°
case 2:
//Reverse each column, then reverse each row
result._values[(Rows - 1) - j][(Columns - 1) - i] = _values[j][i];
break;
//If rotation is +90°
case 3:
//Transpose, then reverse each row
result._values[i][j] = _values[Rows - j - 1][i];
break;
}
}
}
return result;
}
其中_values对应于由Matrix<TValue>定义的私有二维数组(形式为[][])。result = new TValue[Columns, Rows]可能通过隐式操作符重载并将二维数组转换为Matrix<TValue>。 Columns和Rows两个属性是公共属性,用于获取当前实例的列数和行数:
public uint Columns
=> (uint)_values[0].Length;
public uint Rows
=> (uint)_values.Length;
当然,假设您更喜欢使用无符号下标;-)
所有这些都允许您指定它应该旋转多少次,以及它应该向左旋转(如果小于零)还是向右旋转(如果大于零)。您可以改进此方法,以检查实际角度的旋转,但如果值不是90的倍数,则可能会抛出异常。有了这些输入,你可以相应地改变方法:
public Matrix<TValue> Rotate(int rotation)
{
var _rotation = (double)rotation / 90d;
if (_rotation - Math.Floor(_rotation) > 0)
{
throw new NotSupportedException("A matrix may only be rotated by multiples of 90.").
}
rotation = (int)_rotation;
...
}
Since a degree is more accurately expressed by double than int, but a matrix can only rotate in multiples of 90, it is far more intuitive to make the argument correspond to something else that can be accurately represented by the data structure used. int is perfect because it can tell you how many times to rotate it up to a certain unit (90) as well as the direction. double may very well be able to tell you that also, but it also includes values that aren't supported by this operation (which is inherently counter-intuitive).