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

#include <iostream>
#include <iomanip>

using namespace std;
const int SIZE=3;
void print(int a[][SIZE],int);
void rotate(int a[][SIZE],int);

void main()
{
    int a[SIZE][SIZE]={{11,22,33},{44,55,66},{77,88,99}};
    cout<<"the array befor rotate\n";

    print(a,SIZE);
    rotate( a,SIZE);
    cout<<"the array after rotate\n";
    print(a,SIZE);
    cout<<endl;

}

void print(int a[][SIZE],int SIZE)
{
    int i,j;
    for(i=0;i<SIZE;i++)
       for(j=0;j<SIZE;j++)
          cout<<a[i][j]<<setw(4);
}

void rotate(int a[][SIZE],int SIZE)
{
    int temp[3][3],i,j;
    for(i=0;i<SIZE;i++)
       for(j=0;j<SIZE/2.5;j++)
       {
           temp[i][j]= a[i][j];
           a[i][j]= a[j][SIZE-i-1] ;
           a[j][SIZE-i-1] =temp[i][j];

       }
}

其他回答

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).

你可以通过3个简单步骤做到这一点:

1)假设我们有一个矩阵

   1 2 3
   4 5 6
   7 8 9

2)求矩阵的转置

   1 4 7
   2 5 8
   3 6 9

3)交换行得到旋转矩阵

   3 6 9
   2 5 8
   1 4 7

Java源代码:

public class MyClass {

    public static void main(String args[]) {
        Demo obj = new Demo();
        /*initial matrix to rotate*/
        int[][] matrix = { { 1, 2, 3 }, { 4, 5, 6 }, { 7, 8, 9 } };
        int[][] transpose = new int[3][3]; // matrix to store transpose

        obj.display(matrix);              // initial matrix

        obj.rotate(matrix, transpose);    // call rotate method
        System.out.println();
        obj.display(transpose);           // display the rotated matix
    }
}

class Demo {   
    public void rotate(int[][] mat, int[][] tran) {

        /* First take the transpose of the matrix */
        for (int i = 0; i < mat.length; i++) {
            for (int j = 0; j < mat.length; j++) {
                tran[i][j] = mat[j][i]; 
            }
        }

        /*
         * Interchange the rows of the transpose matrix to get rotated
         * matrix
         */
        for (int i = 0, j = tran.length - 1; i != j; i++, j--) {
            for (int k = 0; k < tran.length; k++) {
                swap(i, k, j, k, tran);
            }
        }
    }

    public void swap(int a, int b, int c, int d, int[][] arr) {
        int temp = arr[a][b];
        arr[a][b] = arr[c][d];
        arr[c][d] = temp;    
    }

    /* Method to display the matrix */
    public void display(int[][] arr) {
        for (int i = 0; i < arr.length; i++) {
            for (int j = 0; j < arr.length; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }
    }
}

输出:

1 2 3 
4 5 6 
7 8 9 

3 6 9 
2 5 8 
1 4 7 

这是一个Javascript解决方案:

const transpose = m => m[0].map((x,i) => m.map(x => x[i]));

a: // original matrix
123
456
789

transpose(a).reverse(); // rotate 90 degrees counter clockwise 
369
258
147

transpose(a.slice().reverse()); // rotate 90 degrees clockwise 
741
852
963

transpose(transpose(a.slice().reverse()).slice().reverse())
// rotate 180 degrees 
987
654
321

这是将数组旋转90度的简单C代码。希望这能有所帮助。

#include <stdio.h>

void main(){
int arr[3][4] =     {85, 2, 85,  4,
                     85, 6,  7, 85,
                     9, 85, 11, 12};


int arr1[4][3];

int i = 0, j = 0;

for(i=0;i<4;i++){
int k = 2;//k = (number of columns in the new array arr1 - 1)
for(j=0;j<3;j++){
arr1[i][j]=arr[k][i];
k--;
}
}

int l, m;
for(l=0;l<4;l++){
for(m=0;m<3;m++){
printf("%d ", arr1[l][m]);
}
printf("\n");
}
}//end main

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;
}