Rotate by 90 degree

 Given a square matrix of size N x N. The task is to rotate it by 90 degrees in anti-clockwise direction without using any extra space. 


Example 1:

Input:
N = 3 
matrix[][] = {{1, 2, 3},
              {4, 5, 6}
              {7, 8, 9}}
Output: 
Rotated Matrix:
3 6 9
2 5 8
1 4 7

Example 2:

Input:
N = 2
matrix[][] = {{1, 2},
              {3, 4}}
Output: 
Rotated Matrix:
2 4
1 3


method 1:

c++ implementation:

void rotateby90(int n, int m[][n]) 
{
    int a[n][n];
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<n;j++)
        {
            a[i][j]=m[i][j];
        }
    }
    for(int i=0;i<n;i++)
    {
        for(int j=0;j<n;j++)
        {
             m[n-1-j][i]=a[i][j];
        }
    }
   
    
} 
Time Complexity: O(n*n) 

space Complexity: O(n*n) 



method 2:
first transpose the matrix
than reverse the rows of the matrix
  void rotateby90(int n, int m[][n]) 
  {     
        for (int i = 0; i < n; i++) 
            for (int j = i; j < n; j++) 
                swap(m[i][j], m[j][i]);               //transpose the matrix
     
       for (int i = 0; i < n/2; i++) 
            for (int j = 0; j < n; j++) 
             swap(m[i][j],m[n-i-1][j]);                 //reverse the rows
     
  }
Time Complexity: O(n*n) 

space Complexity: O(1) 
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