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
为新手程序员,在纯c++。(宝蓝的东西)
#include<iostream.h>
#include<conio.h>
int main()
{
clrscr();
int arr[10][10]; // 2d array that holds input elements
int result[10][10]; //holds result
int m,n; //rows and columns of arr[][]
int x,y; //rows and columns of result[][]
int i,j; //loop variables
int t; //temporary , holds data while conversion
cout<<"Enter no. of rows and columns of array: ";
cin>>m>>n;
cout<<"\nEnter elements of array: \n\n";
for(i = 0; i < m; i++)
{
for(j = 0; j<n ; j++)
{
cin>>arr[i][j]; // input array elements from user
}
}
//rotating matrix by +90 degrees
x = n ; //for non-square matrix
y = m ;
for(i = 0; i < x; i++)
{ t = m-1; // to create required array bounds
for(j = 0; j < y; j++)
{
result[i][j] = arr[t][i];
t--;
}
}
//print result
cout<<"\nRotated matrix is: \n\n";
for(i = 0; i < x; i++)
{
for(j = 0; j < y; j++)
{
cout<<result[i][j]<<" ";
}
cout<<"\n";
}
getch();
return 0;
}
其他回答
试试我图书馆的算盘——常见的:
@Test
public void test_42519() throws Exception {
final IntMatrix matrix = IntMatrix.range(0, 16).reshape(4);
N.println("======= original =======================");
matrix.println();
// print out:
// [0, 1, 2, 3]
// [4, 5, 6, 7]
// [8, 9, 10, 11]
// [12, 13, 14, 15]
N.println("======= rotate 90 ======================");
matrix.rotate90().println();
// print out:
// [12, 8, 4, 0]
// [13, 9, 5, 1]
// [14, 10, 6, 2]
// [15, 11, 7, 3]
N.println("======= rotate 180 =====================");
matrix.rotate180().println();
// print out:
// [15, 14, 13, 12]
// [11, 10, 9, 8]
// [7, 6, 5, 4]
// [3, 2, 1, 0]
N.println("======= rotate 270 ======================");
matrix.rotate270().println();
// print out:
// [3, 7, 11, 15]
// [2, 6, 10, 14]
// [1, 5, 9, 13]
// [0, 4, 8, 12]
N.println("======= transpose =======================");
matrix.transpose().println();
// print out:
// [0, 4, 8, 12]
// [1, 5, 9, 13]
// [2, 6, 10, 14]
// [3, 7, 11, 15]
final IntMatrix bigMatrix = IntMatrix.range(0, 10000_0000).reshape(10000);
// It take about 2 seconds to rotate 10000 X 10000 matrix.
Profiler.run(1, 2, 3, "sequential", () -> bigMatrix.rotate90()).printResult();
// Want faster? Go parallel. 1 second to rotate 10000 X 10000 matrix.
final int[][] a = bigMatrix.array();
final int[][] c = new int[a[0].length][a.length];
final int n = a.length;
final int threadNum = 4;
Profiler.run(1, 2, 3, "parallel", () -> {
IntStream.range(0, n).parallel(threadNum).forEach(i -> {
for (int j = 0; j < n; j++) {
c[i][j] = a[n - j - 1][i];
}
});
}).printResult();
}
正如我在上一篇文章中所说的,这里有一些c#代码,可以为任何大小的矩阵实现O(1)矩阵旋转。为了简洁性和可读性,没有错误检查或范围检查。代码:
static void Main (string [] args)
{
int [,]
// create an arbitrary matrix
m = {{0, 1}, {2, 3}, {4, 5}};
Matrix
// create wrappers for the data
m1 = new Matrix (m),
m2 = new Matrix (m),
m3 = new Matrix (m);
// rotate the matricies in various ways - all are O(1)
m1.RotateClockwise90 ();
m2.Rotate180 ();
m3.RotateAnitclockwise90 ();
// output the result of transforms
System.Diagnostics.Trace.WriteLine (m1.ToString ());
System.Diagnostics.Trace.WriteLine (m2.ToString ());
System.Diagnostics.Trace.WriteLine (m3.ToString ());
}
class Matrix
{
enum Rotation
{
None,
Clockwise90,
Clockwise180,
Clockwise270
}
public Matrix (int [,] matrix)
{
m_matrix = matrix;
m_rotation = Rotation.None;
}
// the transformation routines
public void RotateClockwise90 ()
{
m_rotation = (Rotation) (((int) m_rotation + 1) & 3);
}
public void Rotate180 ()
{
m_rotation = (Rotation) (((int) m_rotation + 2) & 3);
}
public void RotateAnitclockwise90 ()
{
m_rotation = (Rotation) (((int) m_rotation + 3) & 3);
}
// accessor property to make class look like a two dimensional array
public int this [int row, int column]
{
get
{
int
value = 0;
switch (m_rotation)
{
case Rotation.None:
value = m_matrix [row, column];
break;
case Rotation.Clockwise90:
value = m_matrix [m_matrix.GetUpperBound (0) - column, row];
break;
case Rotation.Clockwise180:
value = m_matrix [m_matrix.GetUpperBound (0) - row, m_matrix.GetUpperBound (1) - column];
break;
case Rotation.Clockwise270:
value = m_matrix [column, m_matrix.GetUpperBound (1) - row];
break;
}
return value;
}
set
{
switch (m_rotation)
{
case Rotation.None:
m_matrix [row, column] = value;
break;
case Rotation.Clockwise90:
m_matrix [m_matrix.GetUpperBound (0) - column, row] = value;
break;
case Rotation.Clockwise180:
m_matrix [m_matrix.GetUpperBound (0) - row, m_matrix.GetUpperBound (1) - column] = value;
break;
case Rotation.Clockwise270:
m_matrix [column, m_matrix.GetUpperBound (1) - row] = value;
break;
}
}
}
// creates a string with the matrix values
public override string ToString ()
{
int
num_rows = 0,
num_columns = 0;
switch (m_rotation)
{
case Rotation.None:
case Rotation.Clockwise180:
num_rows = m_matrix.GetUpperBound (0);
num_columns = m_matrix.GetUpperBound (1);
break;
case Rotation.Clockwise90:
case Rotation.Clockwise270:
num_rows = m_matrix.GetUpperBound (1);
num_columns = m_matrix.GetUpperBound (0);
break;
}
StringBuilder
output = new StringBuilder ();
output.Append ("{");
for (int row = 0 ; row <= num_rows ; ++row)
{
if (row != 0)
{
output.Append (", ");
}
output.Append ("{");
for (int column = 0 ; column <= num_columns ; ++column)
{
if (column != 0)
{
output.Append (", ");
}
output.Append (this [row, column].ToString ());
}
output.Append ("}");
}
output.Append ("}");
return output.ToString ();
}
int [,]
// the original matrix
m_matrix;
Rotation
// the current view of the matrix
m_rotation;
}
好的,我把手举起来,当旋转时,它实际上不会对原始数组做任何修改。但是,在面向对象系统中,只要对象看起来像是被旋转到类的客户端,这就无关紧要了。目前,Matrix类使用对原始数组数据的引用,因此改变m1的任何值也将改变m2和m3。对构造函数稍加更改,创建一个新数组并将值复制到该数组中,就可以将其整理出来。
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。
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。
ruby方式:.transpose。地图&:反向