Rotate matrix by 90 degrees

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Problem statement

You are given a square matrix of non-negative integers 'MATRIX'. Your task is to rotate that array by 90 degrees in an anti-clockwise direction using constant extra space.

For example:

For given 2D array :

    [    [ 1,  2,  3 ],
         [ 4,  5,  6 ],
         [ 7,  8,  9 ]  ]

After 90 degree rotation in anti clockwise direction, it will become:

    [   [ 3,  6,  9 ],
        [ 2,  5,  8 ],
        [ 1,  4,  7 ]   ]
Detailed explanation ( Input/output format, Notes, Images )
Input Format : 
The first line of input contains an integer 'T' representing the number of the test case. Then the test case follows.

The first line of each test case contains an integer 'N' representing the size of the square matrix 'ARR'.

Each of the next 'N' lines contains 'N' space-separated integers representing the elements of the matrix 'ARR'.

Output format :

For each test case, print N lines where N is the size of the matrix, containing N space-separated integer denoting the elements of the matrix after rotation.

The output of each test case will be printed in a separate line.
Note: 
You do not need to print anything; it has already been taken care of. Just implement the given function.
Constraints: 
1 ≤ T ≤ 50
1 ≤ N ≤ 100
1 ≤ MATRIX[i][j] ≤ 10 ^ 5

Time Limit: 1 sec.
Sample Input 1:
2
3
1  2  3
4  5  6
7  8  9
4
1  2  3  4 
5  6  7  8 
9 10 11 12 
13 14 15 16
Sample Output 1:
3  6  9 
2  5  8 
1  4  7
4  8 12 16 
3  7 11 15 
2  6 10 14 
1  5  9 13
Explanation of Input 1:
For, first test case, the given matrix has been rotated by 90 degrees in an anticlockwise direction as the first row is now the first column inverted and so on for second and third rows.

For, second test case, the given matrix has been rotated by 90 degrees in an anticlockwise direction as the first row is now first column inverted and so on for second, third and fourth rows.
Sample Input 2:
2
3
7  4  1 
8  5  2 
9  6  3
4
13  9  5  1 
14  10  6  2 
15 11 7 3 
16 12 8 4
Sample Output 2:
1  2  3
4  5  6
7  8  9
1  2  3  4 
5  6  7  8 
9 10 11 12 
13 14 15 16
Hint

Try to think about how you can perform rotation using some matrix property.

Approaches (2)
Transpose and Reverse

The idea is to find the transpose of the given matrix and then reverse the columns of the transposed matrix. For example:

For the given 2D matrix:
	[ [ 1,  2,  3 ],
	  [ 4,  5,  6 ],
	  [ 7,  8,  9 ] ]
After taking transpose, it will become:
	[ [ 1,  4,  7 ],
	  [ 2,  5,  8 ],
	  [ 3,  6,  9 ] ]
After reversing the columns, it will become 90-degree rotation in the anti-clockwise direction of the given matrix, it will become:
	[ [ 3,  6,  9 ],
	  [ 2,  5,  8 ],
	  [ 1,  4,  7 ] ]
  1. To solve the problem, there have to perform two tasks.
    1. Finding the transpose
    2. Reversing the columns
  2. For finding the transpose of the matrix we swap ARR[i][j] with ARR[j][i] for each 0 <= i < N and i <= j < N i.e. we swap elements across the principal diagonal of the matrix.
  3. Then we reverse the columns by swapping ARR[j][i] to ARR[k][i] for each  0 <= i < N representing the columns and 0 <= j, k < N where,
    1. j is incremented from 0 to the point where j>=k.
    2. k is decremented from N-1 to the point where k<=j.
Time Complexity

O(N ^ 2), where ‘N’ is the side of the matrix.

 

Since the matrix is traversed twice, once while taking transpose and then while reversing columns, so the overall time complexity will be O(N ^ 2).

Space Complexity

O(1) 

 

We are doing an in-place rotation, and no extra space is required, so the overall space complexity will be O(1).

Code Solution
(100% EXP penalty)
Rotate matrix by 90 degrees
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