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

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();
}

其他回答

当前所有的解决方案都有O(n^2)开销作为临时空间(这不包括那些肮脏的OOP骗子!)这里有一个内存占用为O(1)的解决方案,将矩阵原地右转90度。该死的延展性,这玩意儿跑得很快!

#include <algorithm>
#include <cstddef>

// Rotates an NxN matrix of type T 90 degrees to the right.
template <typename T, size_t N>
void rotate_matrix(T (&matrix)[N][N])
{
    for(size_t i = 0; i < N; ++i)
        for(size_t j = 0; j <= (N-i); ++j)
            std::swap(matrix[i][j], matrix[j][i]);
}

免责声明:我实际上并没有测试这个。让我们玩打虫游戏吧!

我的c#示例代码的伟大算法发送@dimple:

/* Author: Dudi,
 * http://www.tutorialspoint.com/compile_csharp_online.php?PID=0Bw_CjBb95KQMYm5qU3VjVGNuZFU */

using System.IO;
using System;

class Program
{
    static void Main()
    {
        Console.WriteLine("Rotating this matrix by 90+ degree:");

        int[,] values=new int[3,3]{{1,2,3}, {4,5,6}, {7,8,9}};
        //int[,] values=new int[4,4]{{101,102,103, 104}, {105,106, 107,108}, {109, 110, 111, 112}, {113, 114, 115, 116}};

        print2dArray(ref values);
        transpose2dArray(ref values);
        //print2dArray(ref values);
        reverse2dArray(ref values);
        Console.WriteLine("Output:");
        print2dArray(ref values);
    }

    static void print2dArray(ref int[,] matrix){
        int  nLen = matrix.GetLength(0);
        int  mLen = matrix.GetLength(1);    
        for(int n=0; n<nLen; n++){
            for(int m=0; m<mLen; m++){
                Console.Write(matrix[n,m] +"\t");
            }
            Console.WriteLine();        
        }
        Console.WriteLine();
    }

    static void transpose2dArray(ref int[,] matrix){
        int  nLen = matrix.GetLength(0);
        int  mLen = matrix.GetLength(1);    
        for(int n=0; n<nLen; n++){
            for(int m=0; m<mLen; m++){
                if(n>m){
                    int tmp = matrix[n,m];
                    matrix[n,m] = matrix[m,n];
                    matrix[m,n] = tmp;
                }
            }
        }
    }

    static void reverse2dArray(ref int[,] matrix){
        int  nLen = matrix.GetLength(0);
        int  mLen = matrix.GetLength(1);
        for(int n=0; n<nLen; n++){
            for(int m=0; m<mLen/2; m++){                
                int tmp = matrix[n,m];
                matrix[n,m] = matrix[n, mLen-1-m];
                matrix[n,mLen-1-m] = tmp;
            }
        }
    }
}

/*
Rotating this matrix by 90+ degree:                                                                                                                                             
1       2       3                                                                                                                                                               
4       5       6                                                                                                                                                               
7       8       9                                                                                                                                                               

Output:                                                                                                                                                                         
7       4       1                                                                                                                                                               
8       5       2                                                                                                                                                               
9       6       3  
*/

在JavaScript中实现dimple的+90伪代码(例如转置然后反转每一行):

function rotate90(a){
  // transpose from http://www.codesuck.com/2012/02/transpose-javascript-array-in-one-line.html
  a = Object.keys(a[0]).map(function (c) { return a.map(function (r) { return r[c]; }); });
  // row reverse
  for (i in a){
    a[i] = a[i].reverse();
  }
  return a;
}

PHP:

<?php    
$a = array(array(1,2,3,4),array(5,6,7,8),array(9,0,1,2),array(3,4,5,6));
$b = array(); //result

while(count($a)>0)
{
    $b[count($a[0])-1][] = array_shift($a[0]);
    if (count($a[0])==0)
    {
         array_shift($a);
    }
}

从PHP5.6开始,数组转位可以通过一个狡猾的array_map()调用来执行。换句话说,列被转换为行。

代码:(演示)

$array = [
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 0, 1, 2],
    [3, 4, 5, 6]
];
$transposed = array_map(null, ...$array);

美元转置:

[
    [1, 5, 9, 3],
    [2, 6, 0, 4],
    [3, 7, 1, 5],
    [4, 8, 2, 6]
]

从线性的角度来看,考虑以下矩阵:

    1 2 3        0 0 1
A = 4 5 6    B = 0 1 0
    7 8 9        1 0 0

现在求A

     1 4 7
A' = 2 5 8
     3 6 9

考虑A'对B的作用,或B对A'的作用。 分别为:

      7 4 1          3 6 9
A'B = 8 5 2    BA' = 2 5 8
      9 6 3          1 4 7

这对任何nxn矩阵都是可展开的。 在代码中快速应用这个概念:

void swapInSpace(int** mat, int r1, int c1, int r2, int c2)
{
    mat[r1][c1] ^= mat[r2][c2];
    mat[r2][c2] ^= mat[r1][c1];
    mat[r1][c1] ^= mat[r2][c2];
}

void transpose(int** mat, int size)
{
    for (int i = 0; i < size; i++)
    {
        for (int j = (i + 1); j < size; j++)
        {
            swapInSpace(mat, i, j, j, i);
        }
    }
}

void rotate(int** mat, int size)
{
    //Get transpose
    transpose(mat, size);

    //Swap columns
    for (int i = 0; i < size / 2; i++)
    {
        for (int j = 0; j < size; j++)
        {
            swapInSpace(mat, i, j, size - (i + 1), j);
        }
    }
}