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

C代码的矩阵旋转90度顺时针在任何M*N矩阵的地方

void rotateInPlace(int * arr[size][size], int row, int column){
    int i, j;
    int temp = row>column?row:column;
    int flipTill = row < column ? row : column;
    for(i=0;i<flipTill;i++){
        for(j=0;j<i;j++){
            swapArrayElements(arr, i, j);
        }
    }

    temp = j+1;

    for(i = row>column?i:0; i<row; i++){
            for(j=row<column?temp:0; j<column; j++){
                swapArrayElements(arr, i, j);
            }
    }

    for(i=0;i<column;i++){
        for(j=0;j<row/2;j++){
            temp = arr[i][j];
            arr[i][j] = arr[i][row-j-1];
            arr[i][row-j-1] = temp;
        }
    }
}

其他回答

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>';

这是c#的

int[,] array = new int[4,4] {
    { 1,2,3,4 },
    { 5,6,7,8 },
    { 9,0,1,2 },
    { 3,4,5,6 }
};

int[,] rotated = RotateMatrix(array, 4);

static int[,] RotateMatrix(int[,] matrix, int n) {
    int[,] ret = new int[n, n];

    for (int i = 0; i < n; ++i) {
        for (int j = 0; j < n; ++j) {
            ret[i, j] = matrix[n - j - 1, i];
        }
    }

    return ret;
}

下面是我的Ruby版本(注意,值显示的不一样,但它仍然按照描述旋转)。

def rotate(matrix)
  result = []
  4.times { |x|
    result[x] = []
    4.times { |y|
      result[x][y] = matrix[y][3 - x]
    }
  }

  result
end

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

def print_matrix(matrix)
  4.times { |y|
    4.times { |x|
      print "#{matrix[x][y]} "
    }
    puts ""
  }
end

print_matrix(matrix)
puts ""
print_matrix(rotate(matrix))

输出:

1 5 9 3 
2 6 0 4 
3 7 1 5 
4 8 2 6 

4 3 2 1 
8 7 6 5 
2 1 0 9 
6 5 4 3

PHP解决方案为顺时针和逆时针

$aMatrix = array(
    array( 1, 2, 3 ),
    array( 4, 5, 6 ),
    array( 7, 8, 9 )
    );

function CounterClockwise( $aMatrix )
{
    $iCount  = count( $aMatrix );
    $aReturn = array();
    for( $y = 0; $y < $iCount; ++$y )
    {
        for( $x = 0; $x < $iCount; ++$x )
        {
            $aReturn[ $iCount - $x - 1 ][ $y ] = $aMatrix[ $y ][ $x ];
        }
    }
    return $aReturn;
}

function Clockwise( $aMatrix )
{
    $iCount  = count( $aMatrix );
    $aReturn = array();
    for( $y = 0; $y < $iCount; ++$y )
    {
        for( $x = 0; $x < $iCount; ++$x )
        {
            $aReturn[ $x ][ $iCount - $y - 1 ] = $aMatrix[ $y ][ $x ];
        }
    }
    return $aReturn;
}

function printMatrix( $aMatrix )
{
    $iCount = count( $aMatrix );
    for( $x = 0; $x < $iCount; ++$x )
    {
        for( $y = 0; $y < $iCount; ++$y )
        {
            echo $aMatrix[ $x ][ $y ];
            echo " ";
        }
        echo "\n";
    }
}
printMatrix( $aMatrix );
echo "\n";
$aNewMatrix = CounterClockwise( $aMatrix );
printMatrix( $aNewMatrix );
echo "\n";
$aNewMatrix = Clockwise( $aMatrix );
printMatrix( $aNewMatrix );

下面是一个c#静态泛型方法,它可以为您完成这项工作。变量的名称很好,所以您可以很容易地理解算法的思想。

private static T[,] Rotate180 <T> (T[,] matrix)
{
    var height = matrix.GetLength (0);
    var width = matrix.GetLength (1);
    var answer = new T[height, width];

    for (int y = 0; y < height / 2; y++)
    {
        int topY = y;
        int bottomY = height - 1 - y;
        for (int topX = 0; topX < width; topX++)
        {
            var bottomX = width - topX - 1;
            answer[topY, topX] = matrix[bottomY, bottomX];
            answer[bottomY, bottomX] = matrix[topY, topX];
        }
    }

    if (height % 2 == 0)
        return answer;

    var centerY = height / 2;
    for (int leftX = 0; leftX < Mathf.CeilToInt(width / 2f); leftX++)
    {
        var rightX = width - 1 - leftX;
        answer[centerY, leftX] = matrix[centerY, rightX];
        answer[centerY, rightX] = matrix[centerY, leftX];
    }

    return answer;
}