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
short normal[4][4] = {{8,4,7,5},{3,4,5,7},{9,5,5,6},{3,3,3,3}};
short rotated[4][4];
for (int r = 0; r < 4; ++r)
{
for (int c = 0; c < 4; ++c)
{
rotated[r][c] = normal[c][3-r];
}
}
简单的c++方法,尽管在大数组中会有很大的内存开销。
其他回答
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;
}
}
}
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).
ruby方式:.transpose。地图&:反向
这里有大量的好代码,但我只是想以几何形式展示,这样你就能更好地理解代码逻辑。以下是我的处理方法。
首先,不要把这和换位相混淆,换位是很容易的。
基本的想法是把它当作层,我们一次旋转一个层。
假设我们有一辆4x4
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16
当我们顺时针旋转90度,我们得到
13 9 5 1
14 10 6 2
15 11 7 3
16 12 8 4
我们来分解它,首先旋转这四个角
1 4
13 16
然后我们旋转下面这个有点歪斜的菱形
2
8
9
15
然后是第二个斜菱形
3
5
12
14
这就搞定了外缘基本上我们一次做一个壳层直到
最后是中间的方块(如果是奇数则是最后一个不动的元素)
6 7
10 11
现在我们来算出每一层的指标,假设我们总是在最外层工作,我们正在做
[0,0] -> [0,n-1], [0,n-1] -> [n-1,n-1], [n-1,n-1] -> [n-1,0], and [n-1,0] -> [0,0]
[0,1] -> [1,n-1], [1,n-2] -> [n-1,n-2], [n-1,n-2] -> [n-2,0], and [n-2,0] -> [0,1]
[0,2] -> [2,n-2], [2,n-2] -> [n-1,n-3], [n-1,n-3] -> [n-3,0], and [n-3,0] -> [0,2]
等等等等 直到我们走到边缘的一半
所以总的来说模式是
[0,i] -> [i,n-i], [i,n-i] -> [n-1,n-(i+1)], [n-1,n-(i+1)] -> [n-(i+1),0], and [n-(i+1),0] to [0,i]
原地旋转不可能比O(n²)更快,原因是如果我们想旋转矩阵,我们必须至少一次触及所有n²元素,无论你实现什么算法。