Inplace rotate square matrix by 90 degrees
The problem is to rotate a given square matrix (2D array) by 90 degrees in place, i.e., without using any additional memory. The rotation should be done clockwise.
Example
Consider the following square matrix:
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36After rotating the matrix by 90 degrees clockwise, it becomes:
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31Idea to Solve the Problem
To rotate the matrix in place, we can divide the task into three steps:
-
First, we transpose the matrix. Transposing a matrix means swapping its elements across its main diagonal (i.e., swapping matrix[i][j] with matrix[j][i]).
-
Next, we reverse each row of the transposed matrix. Reversing a row means swapping its elements from both ends.
-
The resulting matrix after transposing and reversing each row will be the matrix rotated by 90 degrees clockwise.
Algorithm
- Create a function
rotate_90_degreeto perform the rotation. - Perform the transposition of the matrix by swapping elements matrix[i][j] with matrix[j][i] for all i and j where i < j.
- Reverse each row of the transposed matrix.
- The matrix is now rotated by 90 degrees clockwise.
Pseudocode
rotate_90_degree(matrix, size):
Transpose the matrix
Reverse each row of the matrixCode Solution
/*
C Program
Inplace rotate square matrix by 90 degrees
*/
#include <stdio.h>
#define SIZE 6
//Rotate the square matrix element in 90 degrees
void rotate_90_degree(int matrix[SIZE][SIZE])
{
//Define loop control variables
int i = 1;
int j = 0;
int temp = 0;
// Diagonal transform the elements of upper triangular matrix
// Example
/*
/ / /
/ / Upper Triangular
/
------------
1 2 3
4 5 Element Like this
6
-------------
1 4 6
2 5 After transform
3
-------------
*/
for (i = 1; i < SIZE; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[j][i - j];
matrix[j][i - j] = matrix[i - j][j];
matrix[i - j][j] = temp;
j++;
}
}
// Diagonal transform the elements of lower triangular matrix
// Example
/*
/
/ /
/ / / Lower Triangular
-------
1
2 3 Element Like this
4 5 6
-------------
4
2 5 After transform
1 3 6
-------------
*/
for (i = 1; i < SIZE - 1; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[i - j][(SIZE - 1) - j];
matrix[i - j][(SIZE - 1) - j] = matrix[(SIZE - 1) - j][i - j];
matrix[(SIZE - 1) - j][i - j] = temp;
j++;
}
}
// Invert column values
/*
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for (i = 0; i < SIZE; ++i)
{
for (j = 0; j < SIZE / 2; ++j)
{
temp = matrix[j][i];
matrix[j][i] = matrix[(SIZE - 1) - j][i];
matrix[(SIZE - 1) - j][i] = temp;
}
}
}
//Display matrix elements
void show_data(int matrix[SIZE][SIZE])
{
int i = 0;
int j = 0;
for (i = 0; i < SIZE; ++i)
{
for (j = 0; j < SIZE; ++j)
{
printf("%3d", matrix[i][j]);
}
printf("\n");
}
printf("\n");
}
int main()
{
int matrix[SIZE][SIZE] =
{
{
1 , 2 , 3 , 4 , 5 , 6
} ,
{
7 , 8 , 9 , 10 , 11 , 12
} ,
{
13 , 14 , 15 , 16 , 17 , 18
} ,
{
19 , 20 , 21 , 22 , 23 , 24
} ,
{
25 , 26 , 27 , 28 , 29 , 30
} ,
{
31 , 32 , 33 , 34 , 35 , 36
}
};
printf("\n Before rotate \n");
show_data(matrix);
rotate_90_degree(matrix);
printf("\n After rotate \n");
show_data(matrix);
return 0;
}Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
/*
Java Program
Inplace rotate square matrix by 90 degrees
*/
public class MyMatrix
{
//Rotate the square matrix element in 90 degrees
public void rotate_90_degree(int [][]matrix,int size)
{
//Define loop control variables
int i = 1;
int j = 0;
int temp = 0;
// Diagonal transform the elements of upper triangular matrix
// Example
/*
/ / /
/ / Upper Triangular
/
------------
1 2 3
4 5 Element Like this
6
-------------
1 4 6
2 5 After transform
3
-------------
*/
for (i = 1; i < size; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[j][i - j];
matrix[j][i - j] = matrix[i - j][j];
matrix[i - j][j] = temp;
j++;
}
}
// Diagonal transform the elements of lower triangular matrix
// Example
/*
/
/ /
/ / / Lower Triangular
-------
1
2 3 Element Like this
4 5 6
-------------
4
2 5 After transform
1 3 6
-------------
*/
for (i = 1; i < size - 1; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[i - j][(size - 1) - j];
matrix[i - j][(size - 1) - j] = matrix[(size - 1) - j][i - j];
matrix[(size - 1) - j][i - j] = temp;
j++;
}
}
// Invert column values
/*
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for (i = 0; i < size; ++i)
{
for (j = 0; j < size / 2; ++j)
{
temp = matrix[j][i];
matrix[j][i] = matrix[(size - 1) - j][i];
matrix[(size - 1) - j][i] = temp;
}
}
}
//Display matrix elements
public void show_data(int[][] matrix,int size)
{
int i = 0;
int j = 0;
for (i = 0; i < size; ++i)
{
for (j = 0; j < size; ++j)
{
System.out.print(" " + matrix[i][j] );
}
System.out.print("\n");
}
System.out.print("\n");
}
public static void main(String[] args)
{
MyMatrix obj = new MyMatrix();
int[][] matrix = {
{
1 , 2 , 3 , 4 , 5 , 6
} , {
7 , 8 , 9 , 10 , 11 , 12
} , {
13 , 14 , 15 , 16 , 17 , 18
} , {
19 , 20 , 21 , 22 , 23 , 24
} , {
25 , 26 , 27 , 28 , 29 , 30
} , {
31 , 32 , 33 , 34 , 35 , 36
}
};
int size = matrix[0].length;
System.out.print("\n Before rotate \n");
obj.show_data(matrix,size);
obj.rotate_90_degree(matrix,size);
System.out.print("\n After rotate \n");
obj.show_data(matrix,size);
}
}Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
// Include header file
#include <iostream>
#define SIZE 6
using namespace std;
/*
C++ Program
Inplace rotate square matrix by 90 degrees
*/
class MyMatrix
{
public:
// Rotate the square matrix element in 90 degrees
void rotate_90_degree(int matrix[SIZE][SIZE])
{
// Define loop control variables
int i = 1;
int j = 0;
int temp = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
for (i = 1; i < SIZE; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[j][i - j];
matrix[j][i - j] = matrix[i - j][j];
matrix[i - j][j] = temp;
j++;
}
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
for (i = 1; i < SIZE - 1; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[i - j][(SIZE - 1) - j];
matrix[i - j][(SIZE - 1) - j] = matrix[(SIZE - 1) - j][i - j];
matrix[(SIZE - 1) - j][i - j] = temp;
j++;
}
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for (i = 0; i < SIZE; ++i)
{
for (j = 0; j < SIZE / 2; ++j)
{
temp = matrix[j][i];
matrix[j][i] = matrix[(SIZE - 1) - j][i];
matrix[(SIZE - 1) - j][i] = temp;
}
}
}
// Display matrix elements
void show_data(int matrix[SIZE][SIZE])
{
int i = 0;
int j = 0;
for (i = 0; i < SIZE; ++i)
{
for (j = 0; j < SIZE; ++j)
{
cout << " " << matrix[i][j];
}
cout << "\n";
}
cout << "\n";
}
};
int main()
{
MyMatrix obj = MyMatrix();
int matrix[SIZE][SIZE] = {
{
1 , 2 , 3 , 4 , 5 , 6
} , {
7 , 8 , 9 , 10 , 11 , 12
} , {
13 , 14 , 15 , 16 , 17 , 18
} , {
19 , 20 , 21 , 22 , 23 , 24
} , {
25 , 26 , 27 , 28 , 29 , 30
} , {
31 , 32 , 33 , 34 , 35 , 36
}
};
cout << "\n Before rotate \n";
obj.show_data(matrix);
obj.rotate_90_degree(matrix);
cout << "\n After rotate \n";
obj.show_data(matrix);
return 0;
}Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
// Include namespace system
using System;
/*
C# Program
Inplace rotate square matrix by 90 degrees
*/
public class MyMatrix
{
// Rotate the square matrix element in 90 degrees
public void rotate_90_degree(int[,] matrix, int size)
{
// Define loop control variables
int i = 1;
int j = 0;
int temp = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
for (i = 1; i < size; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[j,i - j];
matrix[j,i - j] = matrix[i - j,j];
matrix[i - j,j] = temp;
j++;
}
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
for (i = 1; i < size - 1; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[i - j,(size - 1) - j];
matrix[i - j,(size - 1) - j] = matrix[(size - 1) - j,i - j];
matrix[(size - 1) - j,i - j] = temp;
j++;
}
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for (i = 0; i < size; ++i)
{
for (j = 0; j < size / 2; ++j)
{
temp = matrix[j,i];
matrix[j,i] = matrix[(size - 1) - j,i];
matrix[(size - 1) - j,i] = temp;
}
}
}
// Display matrix elements
public void show_data(int[,] matrix, int size)
{
int i = 0;
int j = 0;
for (i = 0; i < size; ++i)
{
for (j = 0; j < size; ++j)
{
Console.Write(" " + matrix[i,j]);
}
Console.Write("\n");
}
Console.Write("\n");
}
public static void Main(String[] args)
{
MyMatrix obj = new MyMatrix();
int[,] matrix = {
{
1 , 2 , 3 , 4 , 5 , 6
} , {
7 , 8 , 9 , 10 , 11 , 12
} , {
13 , 14 , 15 , 16 , 17 , 18
} , {
19 , 20 , 21 , 22 , 23 , 24
} , {
25 , 26 , 27 , 28 , 29 , 30
} , {
31 , 32 , 33 , 34 , 35 , 36
}
};
int size = matrix.GetLength(0);
Console.Write("\n Before rotate \n");
obj.show_data(matrix, size);
obj.rotate_90_degree(matrix, size);
Console.Write("\n After rotate \n");
obj.show_data(matrix, size);
}
}Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
<?php
/*
Php Program
Inplace rotate square matrix by 90 degrees
*/
class MyMatrix
{
// Rotate the square matrix element in 90 degrees
public function rotate_90_degree( & $matrix, $size)
{
// Define loop control variables
$i = 1;
$j = 0;
$temp = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
for ($i = 1; $i < $size; ++$i)
{
$j = 0;
while ($j < $i)
{
$temp = $matrix[$j][$i - $j];
$matrix[$j][$i - $j] = $matrix[$i - $j][$j];
$matrix[$i - $j][$j] = $temp;
$j++;
}
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
for ($i = 1; $i < $size - 1; ++$i)
{
$j = 0;
while ($j < $i)
{
$temp = $matrix[$i - $j][($size - 1) - $j];
$matrix[$i - $j][($size - 1) - $j] = $matrix[($size - 1) - $j][$i - $j];
$matrix[($size - 1) - $j][$i - $j] = $temp;
$j++;
}
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for ($i = 0; $i < $size; ++$i)
{
for ($j = 0; $j < intval($size / 2); ++$j)
{
$temp = $matrix[$j][$i];
$matrix[$j][$i] = $matrix[($size - 1) - $j][$i];
$matrix[($size - 1) - $j][$i] = $temp;
}
}
}
// Display matrix elements
public function show_data( & $matrix, $size)
{
$i = 0;
$j = 0;
for ($i = 0; $i < $size; ++$i)
{
for ($j = 0; $j < $size; ++$j)
{
echo " ". $matrix[$i][$j];
}
echo "\n";
}
echo "\n";
}
}
function main()
{
$obj = new MyMatrix();
$matrix = array(
array(1, 2, 3, 4, 5, 6),
array(7, 8, 9, 10, 11, 12),
array(13, 14, 15, 16, 17, 18),
array(19, 20, 21, 22, 23, 24),
array(25, 26, 27, 28, 29, 30),
array(31, 32, 33, 34, 35, 36));
$size = count($matrix[0]);
echo "\n Before rotate \n";
$obj->show_data($matrix, $size);
$obj->rotate_90_degree($matrix, $size);
echo "\n After rotate \n";
$obj->show_data($matrix, $size);
}
main();Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
/*
Node Js Program
Inplace rotate square matrix by 90 degrees
*/
class MyMatrix
{
// Rotate the square matrix element in 90 degrees
rotate_90_degree(matrix, size)
{
// Define loop control variables
var i = 1;
var j = 0;
var temp = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
for (i = 1; i < size; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[j][i - j];
matrix[j][i - j] = matrix[i - j][j];
matrix[i - j][j] = temp;
j++;
}
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
for (i = 1; i < size - 1; ++i)
{
j = 0;
while (j < i)
{
temp = matrix[i - j][(size - 1) - j];
matrix[i - j][(size - 1) - j] = matrix[(size - 1) - j][i - j];
matrix[(size - 1) - j][i - j] = temp;
j++;
}
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
for (i = 0; i < size; ++i)
{
for (j = 0; j < parseInt(size / 2); ++j)
{
temp = matrix[j][i];
matrix[j][i] = matrix[(size - 1) - j][i];
matrix[(size - 1) - j][i] = temp;
}
}
}
// Display matrix elements
show_data(matrix, size)
{
var i = 0;
var j = 0;
for (i = 0; i < size; ++i)
{
for (j = 0; j < size; ++j)
{
process.stdout.write(" " + matrix[i][j]);
}
process.stdout.write("\n");
}
process.stdout.write("\n");
}
}
function main()
{
var obj = new MyMatrix();
var matrix = [
[1, 2, 3, 4, 5, 6] ,
[7, 8, 9, 10, 11, 12] ,
[13, 14, 15, 16, 17, 18] ,
[19, 20, 21, 22, 23, 24] ,
[25, 26, 27, 28, 29, 30] ,
[31, 32, 33, 34, 35, 36]
];
var size = matrix[0].length;
process.stdout.write("\n Before rotate \n");
obj.show_data(matrix, size);
obj.rotate_90_degree(matrix, size);
process.stdout.write("\n After rotate \n");
obj.show_data(matrix, size);
}
main();Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
# Python 3 Program
# Inplace rotate square matrix by 90 degrees
class MyMatrix :
# Rotate the square matrix element in 90 degrees
def rotate_90_degree(self, matrix, size) :
# Define loop control variables
i = 1
j = 0
temp = 0
#
# Diagonal transform the elements of upper triangular matrix
# Example
# ----------------------------
# / / /
# / / Upper Triangular
# /
# ----------------------------
# 1 2 3
# 4 5 Element Like this
# 6
# -----------------------------
# 1 4 6
# 2 5 After transform
# 3
# --------------------------------
#
i = 1
while (i < size) :
j = 0
while (j < i) :
temp = matrix[j][i - j]
matrix[j][i - j] = matrix[i - j][j]
matrix[i - j][j] = temp
j += 1
i += 1
#
# Diagonal transform the elements of lower triangular matrix
# Example
# ---------------------------
# /
# / /
# / / / Lower Triangular
# ---------------------------
# 1
# 2 3 Element Like this
# 4 5 6
#
# ------------------------------
# 4
# 2 5 After transform
# 1 3 6
# ------------------------------
#
i = 1
while (i < size - 1) :
j = 0
while (j < i) :
temp = matrix[i - j][(size - 1) - j]
matrix[i - j][(size - 1) - j] = matrix[(size - 1) - j][i - j]
matrix[(size - 1) - j][i - j] = temp
j += 1
i += 1
#
# Invert column values
# | | | |
# | | | | pattern
# | | | |
# | | | |
#
# -------
# 1 5 9 13
# 2 6 10 14 Element Like this
# 3 7 11 15
# 4 9 12 16
# -------------
# 4 9 12 16
# 3 7 11 15 After transform
# 2 6 10 14
# 1 5 9 13
# -------------
#
i = 0
while (i < size) :
j = 0
while (j < int(size / 2)) :
temp = matrix[j][i]
matrix[j][i] = matrix[(size - 1) - j][i]
matrix[(size - 1) - j][i] = temp
j += 1
i += 1
# Display matrix elements
def show_data(self, matrix, size) :
i = 0
j = 0
i = 0
while (i < size) :
j = 0
while (j < size) :
print(" ", matrix[i][j], end = "")
j += 1
print("\n", end = "")
i += 1
print("\n", end = "")
def main() :
obj = MyMatrix()
matrix = [
[1, 2, 3, 4, 5, 6] ,
[7, 8, 9, 10, 11, 12] ,
[13, 14, 15, 16, 17, 18] ,
[19, 20, 21, 22, 23, 24] ,
[25, 26, 27, 28, 29, 30] ,
[31, 32, 33, 34, 35, 36]
]
size = len(matrix[0])
print("\n Before rotate \n", end = "")
obj.show_data(matrix, size)
obj.rotate_90_degree(matrix, size)
print("\n After rotate \n", end = "")
obj.show_data(matrix, size)
if __name__ == "__main__": main()Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
#
# Ruby Program
# Inplace rotate square matrix by 90 degrees
class MyMatrix
# Rotate the square matrix element in 90 degrees
def rotate_90_degree(matrix, size)
# Define loop control variables
i = 1
j = 0
temp = 0
#
# Diagonal transform the elements of upper triangular matrix
# Example
# ----------------------------
# / / /
# / / Upper Triangular
# /
# ----------------------------
# 1 2 3
# 4 5 Element Like this
# 6
# -----------------------------
# 1 4 6
# 2 5 After transform
# 3
# --------------------------------
#
i = 1
while (i < size)
j = 0
while (j < i)
temp = matrix[j][i - j]
matrix[j][i - j] = matrix[i - j][j]
matrix[i - j][j] = temp
j += 1
end
i += 1
end
#
# // Diagonal transform the elements of lower triangular matrix
# // Example
# ---------------------------
# /
# / /
# / / / Lower Triangular
# ---------------------------
# 1
# 2 3 Element Like this
# 4 5 6
#
# ------------------------------
# 4
# 2 5 After transform
# 1 3 6
# ------------------------------
#
i = 1
while (i < size - 1)
j = 0
while (j < i)
temp = matrix[i - j][(size - 1) - j]
matrix[i - j][(size - 1) - j] = matrix[(size - 1) - j][i - j]
matrix[(size - 1) - j][i - j] = temp
j += 1
end
i += 1
end
#
# Invert column values
# | | | |
# | | | | pattern
# | | | |
# | | | |
#
# -------
# 1 5 9 13
# 2 6 10 14 Element Like this
# 3 7 11 15
# 4 9 12 16
# -------------
# 4 9 12 16
# 3 7 11 15 After transform
# 2 6 10 14
# 1 5 9 13
# -------------
#
i = 0
while (i < size)
j = 0
while (j < size / 2)
temp = matrix[j][i]
matrix[j][i] = matrix[(size - 1) - j][i]
matrix[(size - 1) - j][i] = temp
j += 1
end
i += 1
end
end
# Display matrix elements
def show_data(matrix, size)
i = 0
j = 0
i = 0
while (i < size)
j = 0
while (j < size)
print(" ", matrix[i][j])
j += 1
end
print("\n")
i += 1
end
print("\n")
end
end
def main()
obj = MyMatrix.new()
matrix = [
[1, 2, 3, 4, 5, 6] ,
[7, 8, 9, 10, 11, 12] ,
[13, 14, 15, 16, 17, 18] ,
[19, 20, 21, 22, 23, 24] ,
[25, 26, 27, 28, 29, 30] ,
[31, 32, 33, 34, 35, 36]
]
size = matrix[0].length
print("\n Before rotate \n")
obj.show_data(matrix, size)
obj.rotate_90_degree(matrix, size)
print("\n After rotate \n")
obj.show_data(matrix, size)
end
main()Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
/*
Scala Program
Inplace rotate square matrix by 90 degrees
*/
class MyMatrix
{
// Rotate the square matrix element in 90 degrees
def rotate_90_degree(matrix: Array[Array[Int]], size: Int): Unit = {
// Define loop control variables
var i: Int = 1;
var j: Int = 0;
var temp: Int = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
i = 1;
while (i < size)
{
j = 0;
while (j < i)
{
temp = matrix(j)(i - j);
matrix(j)(i - j) = matrix(i - j)(j);
matrix(i - j)(j) = temp;
j += 1;
}
i += 1;
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
i = 1;
while (i < size - 1)
{
j = 0;
while (j < i)
{
temp = matrix(i - j)((size - 1) - j);
matrix(i - j)((size - 1) - j) = matrix((size - 1) - j)(i - j);
matrix((size - 1) - j)(i - j) = temp;
j += 1;
}
i += 1;
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
i = 0;
while (i < size)
{
j = 0;
while (j < (size / 2).toInt)
{
temp = matrix(j)(i);
matrix(j)(i) = matrix((size - 1) - j)(i);
matrix((size - 1) - j)(i) = temp;
j += 1;
}
i += 1;
}
}
// Display matrix elements
def show_data(matrix: Array[Array[Int]], size: Int): Unit = {
var i: Int = 0;
var j: Int = 0;
i = 0;
while (i < size)
{
j = 0;
while (j < size)
{
print(" " + matrix(i)(j));
j += 1;
}
print("\n");
i += 1;
}
print("\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: MyMatrix = new MyMatrix();
var matrix: Array[Array[Int]] = Array(
Array(1, 2, 3, 4, 5, 6),
Array(7, 8, 9, 10, 11, 12),
Array(13, 14, 15, 16, 17, 18),
Array(19, 20, 21, 22, 23, 24),
Array(25, 26, 27, 28, 29, 30),
Array(31, 32, 33, 34, 35, 36)
);
var size: Int = matrix(0).length;
print("\n Before rotate \n");
obj.show_data(matrix, size);
obj.rotate_90_degree(matrix, size);
print("\n After rotate \n");
obj.show_data(matrix, size);
}
}Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
/*
Swift 4 Program
Inplace rotate square matrix by 90 degrees
*/
class MyMatrix
{
// Rotate the square matrix element in 90 degrees
func rotate_90_degree(_ matrix: inout[[Int]], _ size: Int)
{
// Define loop control variables
var i: Int = 1;
var j: Int = 0;
var temp: Int = 0;
/*
Diagonal transform the elements of upper triangular matrix
Example
----------------------------
/ / /
/ / Upper Triangular
/
----------------------------
1 2 3
4 5 Element Like this
6
-----------------------------
1 4 6
2 5 After transform
3
--------------------------------
*/
i = 1;
while (i < size)
{
j = 0;
while (j < i)
{
temp = matrix[j][i - j];
matrix[j][i - j] = matrix[i - j][j];
matrix[i - j][j] = temp;
j += 1;
}
i += 1;
}
/*
// Diagonal transform the elements of lower triangular matrix
// Example
---------------------------
/
/ /
/ / / Lower Triangular
---------------------------
1
2 3 Element Like this
4 5 6
------------------------------
4
2 5 After transform
1 3 6
------------------------------
*/
i = 1;
while (i < size - 1)
{
j = 0;
while (j < i)
{
temp = matrix[i - j][(size - 1) - j];
matrix[i - j][(size - 1) - j] = matrix[(size - 1) - j][i - j];
matrix[(size - 1) - j][i - j] = temp;
j += 1;
}
i += 1;
}
/*
Invert column values
| | | |
| | | | pattern
| | | |
| | | |
-------
1 5 9 13
2 6 10 14 Element Like this
3 7 11 15
4 9 12 16
-------------
4 9 12 16
3 7 11 15 After transform
2 6 10 14
1 5 9 13
-------------
*/
i = 0;
while (i < size)
{
j = 0;
while (j < size / 2)
{
temp = matrix[j][i];
matrix[j][i] = matrix[(size - 1) - j][i];
matrix[(size - 1) - j][i] = temp;
j += 1;
}
i += 1;
}
}
// Display matrix elements
func show_data(_ matrix: [[Int]], _ size: Int)
{
var i: Int = 0;
var j: Int = 0;
i = 0;
while (i < size)
{
j = 0;
while (j < size)
{
print(" ", matrix[i][j], terminator: "");
j += 1;
}
print("\n", terminator: "");
i += 1;
}
print("\n", terminator: "");
}
}
func main()
{
let obj: MyMatrix = MyMatrix();
var matrix: [[Int]] = [
[1, 2, 3, 4, 5, 6] ,
[7, 8, 9, 10, 11, 12] ,
[13, 14, 15, 16, 17, 18] ,
[19, 20, 21, 22, 23, 24] ,
[25, 26, 27, 28, 29, 30] ,
[31, 32, 33, 34, 35, 36]
];
let size: Int = matrix[0].count;
print("\n Before rotate \n", terminator: "");
obj.show_data(matrix, size);
obj.rotate_90_degree(&matrix, size);
print("\n After rotate \n", terminator: "");
obj.show_data(matrix, size);
}
main();Output
Before rotate
1 2 3 4 5 6
7 8 9 10 11 12
13 14 15 16 17 18
19 20 21 22 23 24
25 26 27 28 29 30
31 32 33 34 35 36
After rotate
6 12 18 24 30 36
5 11 17 23 29 35
4 10 16 22 28 34
3 9 15 21 27 33
2 8 14 20 26 32
1 7 13 19 25 31
Output Explanation
The given Java code implements the above algorithm to rotate the matrix by 90 degrees clockwise in place. It prints the original matrix, performs the rotation, and then prints the rotated matrix.
Time Complexity
The time complexity of the provided solution is O(N^2), where N is the size of the square matrix. The function performs two operations: transposing the matrix and reversing each row. Both operations require iterating through the elements of the matrix at least once. Therefore, the overall time complexity is O(N^2).
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