# Rotate a matrix by 90 degree without using any extra space | Set 2

Given a square matrix, turn it by 90 degrees in anti-clockwise direction without using any extra space.

Examples:

Input
1  2  3
4  5  6
7  8  9
Output:
3  6  9
2  5  8
1  4  7

Input:
1  2  3  4
5  6  7  8
9 10 11 12
13 14 15 16
Output:
4  8 12 16
3  7 11 15
2  6 10 14
1  5  9 13

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

An approach that requires extra space is already discussed in below set:
Inplace rotate square matrix by 90 degrees | Set 1

In this post another approach is discussed which is much simpler than the above approach.

There are two steps :

1. Find transpose of matrix.
2. Reverse columns of the transpose.

Illustration of above steps :

Let the given matrix be
1  2  3  4
5  6  7  8
9  10 11 12
13 14 15 16

First we find transpose.
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16

Then we reverse elements of every column.
4 8 12 16
3 7 11 15
2 6 10 14
1 5  9 13

Below is the implementation of above steps.

## C++

// C++ program for left rotation of matrix by 90
// degree wuthout using extra space
#include<bits/stdc++.h>
using namespace std;
#define R 4
#define C 4

// After transpose we swap elements of column
// one by one for finding left rotation of matrix
// by 90 degree
void reverseColumns(int arr[R][C])
{
for (int i=0; i<C; i++)
for (int j=0,  k=C-1; j<k; j++,k--)
swap(arr[j][i], arr[k][i]);
}

// Function for do transpose of matrix
void transpose(int arr[R][C])
{
for (int i=0; i<R; i++)
for (int j=i; j<C; j++)
swap(arr[i][j], arr[j][i]);
}

// Function for print matrix
void printMatrix(int arr[R][C])
{
for (int i=0; i<R; i++)
{
for (int j=0; j<C; j++)
cout << arr[i][j] << " ";
cout<<'\n';
}
}

// Function to anticlockwise rotate matrix
// by 90 degree
void rotate90(int arr[R][C])
{
transpose(arr);
reverseColumns(arr);
}

//Driven code
int main()
{
int arr[R][C]= { {1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}
};
rotate90(arr);
printMatrix(arr);
return 0;
}

## Java

// JAVA Code for left Rotation of a
// matrix by 90 degree without using
// any extra space
import java.util.*;

class GFG {

// After transpose we swap elements of
// column one by one for finding left
// rotation of matrix by 90 degree
static void reverseColumns(int arr[][])
{
for (int i = 0; i < arr[0].length; i++)
for (int j = 0,  k = arr[0].length - 1;
j < k; j++, k--)
{
int temp = arr[j][i];
arr[j][i] = arr[k][i];
arr[k][i] = temp;
}
}

// Function for do transpose of matrix
static void transpose(int arr[][])
{
for (int i = 0; i < arr.length; i++)
for (int j = i; j < arr[0].length; j++)
{
int temp = arr[j][i];
arr[j][i] = arr[i][j];
arr[i][j] = temp;
}
}

// Function for print matrix
static void printMatrix(int arr[][])
{
for (int i = 0; i < arr.length; i++)
{
for (int j = 0; j < arr[0].length; j++)
System.out.print(arr[i][j] + " ");
System.out.println("");

}
}

// Function to anticlockwise rotate
// matrix by 90 degree
static void rotate90(int arr[][])
{
transpose(arr);
reverseColumns(arr);
}

/* Driver program to test above function */
public static void main(String[] args)
{
int arr[][] = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};

rotate90(arr);
printMatrix(arr);

}
}

// This code is contributed by Arnav Kr. Mandal.

Output:

4 8 12 16
3 7 11 15
2 6 10 14
1 5 9 13

Time complexity :O(R*C)
Space complexity :O(1)

The above steps/program do left (or anticlockwise) rotation, how to right (or clockwise) rotate?
To right rotate, we do following steps.

1. Find transpose of matrix.
2. Reverse rows of the transpose.

Illustration of above steps :

Let the given matrix be
1  2  3  4
5  6  7  8
9  10 11 12
13 14 15 16

First we find transpose.
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16

Then we reverse elements of every row.
13  9 5 1
14 10 6 2
15 11 7 3
16 12 8 4

This article is contributed by DANISH_RAZA . If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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