Rotate a matrix by 90 degree in clockwise direction in C++

May 4, 2022

Rotate a matrix by 90 degree in clockwise direction in C++

Here, in this page we will discuss the program to rotate a matrix by 90 degree in clockwise direction in C++ Programming Language. We are given with matrix and we need to print the rotated matrix. We will discuss the approaches that solve this problem in constant space.

Example :

  • Input :  [{1, 2, 3}, {4, 5, 6}, {7, 8, 9}]
  • Output :  [{7, 4, 1} {8, 5, 2} {9, 6, 3}]

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Rotate a matrix by 90 degree in clockwise direction in C++

Method 1 :

  • First transpose the matrix.
  • For this run a loop from i=0 to n and another loop from j=i+1 to j<n and swap(mat[i][j], mat[j][i]).
  • After doing this, now iterate over rows and reverse each rows.
  • After this print the entire matrix (that gets rotated).

Time and Space Complexity :

  • Time-Complexity : O(n*n)
  • Space-Complexity : O(1)
Rotate the matrix in C++

Code to rotate a matrix by 90 degree in clockwise direction in C++

Run 
#include<bits/stdc++.h>
using namespace std;
int main(){

   int n=4;
   int mat[n][n]= { { 1, 2, 3, 4 },{ 5, 6, 7, 8 },{ 9, 10, 11, 12 },{ 13, 14, 15, 16 } };

   //Tranposing the matrix
   for(int i=0; i<n; i++){
     for(int j=i+1; j<n; j++)
         swap(mat[i][j], mat[j][i]);
    }

   //Reversing each row of the matrix
   for(int i=0; i<n; i++){
     for(int j=0; j<n/2; j++){
        swap(mat[i][j], mat[i][n-j-1]);
     }
   }

   //Print the matrix
   cout<<"Rotated Matrix :\n";
   for(int i=0; i<n; i++){
     for(int j=0; j<n; j++){
       cout<<mat[i][j]<<" ";
     }
     cout<<endl;
   }
}
Output
Rotated Matrix is :
13 9 5 1
14 10 6 2
15 11 7 3
16 12 8 4

Method 2 :

  • First rotate the matrix about its main diagonal.
  • For this run a loop from i=0 to n and another loop from j=0 to 1, and swap (mat[i][j], mat[j][i])
  • Now, rotate the matrix about middle column.
  • For this run a loop from i=0 to n, and another loop from j=0 to n/2 and swap (mat[i][j],, mat[i][n-j-1]).
  • After this print the entire matrix (that gets rotated).

Time and Space Complexity :

  • Time-Complexity : O(n*n)
  • Space-Complexity : O(1)

Code to rotate a matrix by 90 degree in clockwise direction in C++

Run 
#include<bits/stdc++.h>
using namespace std;

int main(){

   int n=4;
   int mat[n][n]= { { 1, 2, 3, 4 },{ 5, 6, 7, 8 },{ 9, 10, 11, 12 },{ 13, 14, 15, 16 } };

   //Rotate the matrix about the main diagonal
   for(int i=0; i<n; i++){
     for(int j=0; j<i; j++)
         swap(mat[i][j], mat[j][i]);
    }

   //Rotate the matrix about middle column
   for(int i=0; i<n; i++){
     for(int j=0; j<n/2; j++){
        swap(mat[i][j], mat[i][n-j-1]);
     }
   }

   //Print the matrix
   cout<<"Rotated Matrix :\n";
   for(int i=0; i<n; i++){
     for(int j=0; j<n; j++){
       cout<<mat[i][j]<<" ";
     }
     cout<<endl;
   }
}
Output
Rotated Matrix is :
13 9 5 1
14 10 6 2
15 11 7 3
16 12 8 4

Method 3 :

  • First rotate the matrix about its secondary diagonal.
  • For this run a loop from i=0 to n and another loop from j=0 to n-1, and swap (mat[i][j], mat[n-1-i][n-1-j])
  • Now, rotate the matrix about middle row.
  • For this run a loop from i=0 to n/2, and another loop from j=0 to n and swap (mat[i][j], mat[n-1-i][j]).
  • After this print the entire matrix (that gets rotated).

Time and Space Complexity :

  • Time-Complexity : O(n*n)
  • Space-Complexity : O(1)

Code to rotate a matrix by 90 degree in clockwise direction in C++

Run 
#include<bits/stdc++.h>
using namespace std;

int main(){

   int n=4;
   int mat[n][n]= { { 1, 2, 3, 4 },{ 5, 6, 7, 8 },{ 9, 10, 11, 12 },{ 13, 14, 15, 16 } };

   //Rotate the matrix about the secondary diagonal
   for(int i=0; i<n; i++){
     for(int j=0; j<n-i; j++)
         swap(mat[i][j], mat[n-1-i][n-1-j]);
    }

   //Rotate the matrix about middle row
   for(int i=0; i<n/2; i++){
     for(int j=0; j<n; j++){
        swap(mat[i][j], mat[n-1-i][j]);
     }
   }

   //Print the matrix
   cout<<"Rotated Matrix :\n";
   for(int i=0; i<n; i++){
     for(int j=0; j<n; j++){
       cout<<mat[i][j]<<" ";
     }
     cout<<endl;
   }
}
Output
Rotated Matrix is :
13 9 5 1
14 10 6 2
15 11 7 3
16 12 8 4
While loop in C