How to rotate a N x N matrix by 90 degrees?

How to rotate a N x N matrix by 90 degrees. I want it to be inplace?

Answers


for(int i=0; i<n/2; i++)
   for(int j=0; j<(n+1)/2; j++)
       cyclic_roll(m[i][j], m[n-1-j][i], m[n-1-i][n-1-j], m[j][n-1-i]);


void cyclic_roll(int &a, int &b, int &c, int &d)
{
   int temp = a;
   a = b;
   b = c;
   c = d;
   d = temp;
}

Note I haven't tested this, just compoosed now on the spot. Please test before doing anything with it.


here is my solution: (rotate pi/2 clockwise)

  1. do the transpose of the array, (like matrix transpose)

  2. reverse the elements for each row

    cons int row = 10;
    cons int col = 10;
    //transpose
    for(int r = 0; r < row; r++) {
      for(int c = r; c < col; c++) {  
        swap(Array[r][c], Array[c][r]);
      }
    }
    //reverse elements on row order
    for(int r = 0; r < row; r++) {
        for(int c =0; c < col/2; c++) {
          swap(Array[r][c], Array[r][col-c-1])
        }
    }
    

if rotate pi/2 in counter-clockwise

  1. transpose the array

  2. reverse the elements on column order

never test the code! any suggestion would be appreciated!


A complete C program which illustrates my approach. Essentially it's recursive algo. At each recursion you rotate the outer layer. Stop when your matrix is 1x1 or 0x0.

#include <stdio.h>

int matrix[4][4] = {
     {11, 12, 13, 14},
     {21, 22, 23, 24},
     {31, 32, 33, 34},
     {41, 42, 43, 44} 
};

void print_matrix(int n)
{
   for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
         printf(" %d ", matrix[i][j]);
      }
      printf("\n");
   }
}

int *get(int offset, int x, int y)
{
   return &matrix[offset + x][offset + y];
}

void transpose(int offset, int n)
{
   if (n > 1) {
      for (int i = 0; i < n - 1; i++) {
         int *val1 = get(offset, 0, i);
         int *val2 = get(offset, i, n - 1);
         int *val3 = get(offset, n - 1, n - 1 - i);
         int *val4 = get(offset, n - 1 - i, 0);

         int temp = *val1;
         *val1 = *val4;
         *val4 = *val3;
         *val3 = *val2;
         *val2 = temp;
      }

      transpose(offset + 1, n - 2);
   }
}

main(int argc, char *argv[])
{
   print_matrix(4);
   transpose(0, 4);
   print_matrix(4);
   return 0;
}

//Java version, fully tested

public class Rotate90degree {


        public static void reverseElementsRowWise(int[][] matrix) {
            int n = matrix.length;
            for(int i = 0; i < n; ++i) {
                for(int j = 0; j < n / 2; ++j) {
                    int temp = matrix[i][n - j - 1];
                    matrix[i][n - j - 1] = matrix[i][j];
                    matrix[i][j] = temp;
                }
            }
        }

        public static void transpose(int[][] matrix) {
            int n = matrix.length;
            for(int i = 0; i < n; ++i) {
                for(int j = i + 1; j < n; ++j) {
                    int temp = matrix[i][j];
                    matrix[i][j] = matrix[j][i];
                    matrix[j][i] = temp;
                }
            }
        }

        public static void rotate90(int[][] matrix) {
            transpose(matrix);
            reverseElementsRowWise(matrix);
        }

        public static void print(int[][] matrix) {
            int n = matrix.length;
            for(int i = 0; i < n; ++i) {
                for(int j = 0; j < n; ++j) {
                    System.out.print(matrix[i][j]);
                    System.out.print(' ');
                }
                System.out.println();
            }
        }

        public static void main(String[] args) {
            int[][] matrix = {
                    {1, 2, 3, 4},
                    {5, 6, 7, 8},
                    {9, 10, 11, 12},
                    {13, 14, 15, 16}};
            System.out.println("before");
            print(matrix);
            rotate90(matrix);
            System.out.println("after");
            print(matrix);
        }
}

You could create a second array and then copy the first one into the second one by reading row-major in the first one and writing column-major to the second one.

So you would copy:

1  2  3
4  5  6
7  8  9

and you would read the first row then write it back up starting like:

3
2
1

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