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# Turn an image by 90 degree

• Difficulty Level : Easy
• Last Updated : 28 Mar, 2023

Given an image, how will you turn it by 90 degrees? A vague question. Minimize the browser and try your solution before going further. An image can be treated as 2D matrix which can be stored in a buffer. We are provided with matrix dimensions and it’s base address. How can we turn it? For example see the below picture,

```* * * ^ * * *
* * * | * * *
* * * | * * *
* * * | * * *```

After rotating right, it appears (observe arrow direction)

```* * * *
* * * *
* * * *
— — — >
* * * *
* * * *
* * * *```

The idea is simple. Transform each row of source matrix into required column of final image. We will use an auxiliary buffer to transform the image. From the above picture, we can observe that

```first row of source ------> last column of destination
second row of source ------> last but-one column of destination
so ... on
last row of source ------> first column of destination```

In pictorial form, we can represent the above transformations of an (m x n) matrix into (n x m) matrix, If you have not attempted, atleast try your pseudo code now. It will be easy to write our pseudo code. In C/C++ we will usually traverse matrix on row major order. Each row is transformed into different column of final image. We need to construct columns of final image. See the following algorithm (transformation)

```for (r = 0; r < m; r++)
{
for (c = 0; c < n; c++)
{
// Hint: Map each source element indices into
// indices of destination matrix element.
dest_buffer [ c ] [ m - r - 1 ] = source_buffer [ r ] [ c ];
}
}```

Note that there are various ways to implement the algorithm based on traversal of matrix, row major or column major order. We have two matrices and two ways (row and column major) to traverse each matrix. Hence, there can atleast be 4 different ways of transformation of source matrix into final matrix.

## C++

 `// C++ program to turn an``// image by 90 Degree``#include ``using` `namespace` `std;``void` `displayMatrix(unsigned ``int` `const` `*p,``                    ``unsigned ``int` `row,``                   ``unsigned ``int` `col);``                    ` `void` `rotate(unsigned ``int` `*pS,``            ``unsigned ``int` `*pD,``            ``unsigned ``int` `row,``            ``unsigned ``int` `col);``            ` `void` `displayMatrix(unsigned ``int` `const` `*p,``                   ``unsigned ``int` `r,``                   ``unsigned ``int` `c)``{``    ``unsigned ``int` `row, col;``    ``cout << ``"\n\n"``;` `    ``for` `(row = 0; row < r; row++)``    ``{``        ``for` `(col = 0; col < c; col++)``            ``cout << * (p + row * c + col) << ``"\t"``;``        ``cout << ``"\n"``;``    ``}` `    ``cout << ``"\n\n"``;``}` `void` `rotate(unsigned ``int` `*pS,``            ``unsigned ``int` `*pD,``            ``unsigned ``int` `row,``            ``unsigned ``int` `col)``{``    ``unsigned ``int` `r, c;``    ``for` `(r = 0; r < row; r++)``    ``{``        ``for` `(c = 0; c < col; c++)``        ``{``            ``*(pD + c * row + (row - r - 1)) =``                        ``*(pS + r * col + c);``        ``}``    ``}``}` `// Driver Code``int` `main()``{``    ` `    ``// declarations``    ``unsigned ``int` `image[] = {{1, 2, 3, 4},``                               ``{5, 6, 7, 8},``                               ``{9, 10, 11, 12}};``    ``unsigned ``int` `*pSource;``    ``unsigned ``int` `*pDestination;``    ``unsigned ``int` `m, n;` `    ``// setting initial values``    ``// and memory allocation``    ``m = 3, n = 4, pSource = (unsigned ``int` `*)image;``    ``pDestination = (unsigned ``int` `*)``malloc``                   ``(``sizeof``(``int``) * m * n);` `    ``// process each buffer``    ``displayMatrix(pSource, m, n);` `    ``rotate(pSource, pDestination, m, n);` `    ``displayMatrix(pDestination, n, m);` `    ``free``(pDestination);` `    ``return` `0;``}` `// This code is contributed by rathbhupendra`

## C

 `// C program to turn an``// image by 90 Degree``#include ``#include ` `void` `displayMatrix(unsigned ``int` `const` `*p,``                   ``unsigned ``int` `row,``                   ``unsigned ``int` `col);``                   ` `void` `rotate(unsigned ``int` `*pS,``            ``unsigned ``int` `*pD,``            ``unsigned ``int` `row,``            ``unsigned ``int` `col);``            ` `void` `displayMatrix(unsigned ``int` `const` `*p,``                   ``unsigned ``int` `r,``                   ``unsigned ``int` `c)``{``    ``unsigned ``int` `row, col;``    ``printf``(``"\n\n"``);` `    ``for` `(row = 0; row < r; row++)``    ``{``        ``for` `(col = 0; col < c; col++)``            ``printf``(``"%d\t"``, * (p + row * c + col));``        ``printf``(``"\n"``);``    ``}` `    ``printf``(``"\n\n"``);``}` `void` `rotate(unsigned ``int` `*pS,``            ``unsigned ``int` `*pD,``            ``unsigned ``int` `row,``            ``unsigned ``int` `col)``{``    ``unsigned ``int` `r, c;``    ``for` `(r = 0; r < row; r++)``    ``{``        ``for` `(c = 0; c < col; c++)``        ``{``            ``*(pD + c * row + (row - r - 1)) =``                            ``*(pS + r * col + c);``        ``}``    ``}``}` `// Driver Code``int` `main()``{``    ` `    ``// declarations``    ``unsigned ``int` `image[] = {{1,2,3,4},``                               ``{5,6,7,8},``                               ``{9,10,11,12}};``    ``unsigned ``int` `*pSource;``    ``unsigned ``int` `*pDestination;``    ``unsigned ``int` `m, n;` `    ``// setting initial values``    ``// and memory allocation``    ``m = 3, n = 4, pSource = (unsigned ``int` `*)image;``    ``pDestination =``        ``(unsigned ``int` `*)``malloc``        ``(``sizeof``(``int``) * m * n);` `    ``// process each buffer``    ``displayMatrix(pSource, m, n);` `    ``rotate(pSource, pDestination, m, n);` `    ``displayMatrix(pDestination, n, m);` `    ``free``(pDestination);` `    ``getchar``();``    ``return` `0;``}`

## Java

 `// Java program to turn an``// image by 90 Degree``import` `java.util.*;` `class` `GFG``{``  ``static` `void` `displayMatrix(``int``[] p, ``int` `r, ``int` `c)``  ``{``    ``int` `row, col;``    ``System.out.println(``"\n\n"``);` `    ``for` `(row = ``0``; row < r; row++) {``      ``for` `(col = ``0``; col < c; col++)``        ``System.out.print(p[row * c + col] + ``"\t"``);``      ``System.out.println();``    ``}` `    ``System.out.println(``"\n"``);``  ``}` `  ``static` `void` `rotate(``int``[] pS, ``int``[] pD, ``int` `row, ``int` `col)``  ``{``    ``int` `r, c;``    ``for` `(r = ``0``; r < row; r++) {``      ``for` `(c = ``0``; c < col; c++) {``        ``pD = pS[r * col + c];``      ``}``    ``}``  ``}` `  ``// Driver Code` `  ``public` `static` `void` `main(String[] args)``  ``{``    ``// declarations``    ``int``[] image = { ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10``, ``11``, ``12` `};` `    ``// setting initial values``    ``// and memory allocation``    ``int` `m = ``3``, n = ``4``;``    ``int``[] pSource = ``new` `int``[image.length];``    ``for` `(``int` `i = ``0``; i < image.length; i++)``      ``pSource[i] = image[i];` `    ``int``[] pDestination  = ``new` `int``[m * n];` `    ``// process each buffer``    ``displayMatrix(pSource, m, n);` `    ``rotate(pSource, pDestination, m, n);` `    ``displayMatrix(pDestination, n, m);``  ``}``}` `// This code is contributed by phasing17`

## Python3

 `# Python3 program to turn an``# image by 90 Degree``def` `displayMatrix(p, r, c):` `    ``print``(``"\n\n"``);``    ` `    ``for` `row ``in` `range``(r):``        ``for` `col ``in` `range``(c):``            ``print``(p[row ``*` `c ``+` `col], end ``=` `"\t"``);``        ``print``()``    ``print``(``"\n"``)` `def` `rotate(pS, pD, row, col):` `    ``for` `r ``in` `range``(row):``        ``for` `c ``in` `range``(col):``            ``pD ``=` `pS[r ``*` `col ``+` `c];``        ` `# Driver Code` `# declarations``image ``=` `[ ``1``, ``2``, ``3``, ``4``, ``5``, ``6``, ``7``, ``8``, ``9``, ``10``, ``11``, ``12` `];` `# setting initial values``# and memory allocation``m ``=` `3``n ``=` `4``;``pSource ``=` `image.copy()``pDestination  ``=` `[``None``] ``*` `(m ``*` `n);` `# process each buffer``displayMatrix(pSource, m, n);``rotate(pSource, pDestination, m, n);``displayMatrix(pDestination, n, m);` `# This code is contributed by phasing17`

## C#

 `// C# program to turn an``// image by 90 Degree``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{``  ``static` `void` `displayMatrix(``int``[] p, ``int` `r, ``int` `c)``  ``{``    ``int` `row, col;``    ``Console.WriteLine(``"\n\n"``);` `    ``for` `(row = 0; row < r; row++) {``      ``for` `(col = 0; col < c; col++)``        ``Console.Write(p[row * c + col] + ``"\t"``);``      ``Console.WriteLine();``    ``}` `    ``Console.WriteLine(``"\n"``);``  ``}` `  ``static` `void` `rotate(``int``[] pS, ``int``[] pD, ``int` `row, ``int` `col)``  ``{``    ``int` `r, c;``    ``for` `(r = 0; r < row; r++) {``      ``for` `(c = 0; c < col; c++) {``        ``pD = pS[r * col + c];``      ``}``    ``}``  ``}` `  ``// Driver Code` `  ``public` `static` `void` `Main(``string``[] args)``  ``{``    ``// declarations``    ``int``[] image = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 };` `    ``// setting initial values``    ``// and memory allocation``    ``int` `m = 3, n = 4;``    ``int``[] pSource = ``new` `int``[image.Length];``    ``for` `(``int` `i = 0; i < image.Length; i++)``      ``pSource[i] = image[i];` `    ``int``[] pDestination  = ``new` `int``[m * n];` `    ``// process each buffer``    ``displayMatrix(pSource, m, n);` `    ``rotate(pSource, pDestination, m, n);` `    ``displayMatrix(pDestination, n, m);``  ``}``}` `// This code is contributed by phasing17`

## Javascript

 `// JS program to turn an``// image by 90 Degree` `function` `displayMatrix(p, r, c)``{``    ``let row, col;``    ``console.log(``"\n\n"``);` `    ``for` `(row = 0; row < r; row++) {``        ``for` `(col = 0; col < c; col++)``            ``process.stdout.write(p[row * c + col] + ``"\t"``);``        ``console.log()``    ``}` `    ``console.log(``"\n"``)``}` `function` `rotate(pS, pD, row, col)``{``    ``let r, c;``    ``for` `(r = 0; r < row; r++) {``        ``for` `(c = 0; c < col; c++) {``            ``pD = pS[r * col + c];``        ``}``    ``}``}` `// Driver Code` `// declarations``let image = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 ];` `// setting initial values``// and memory allocation``let m = 3, n = 4;``let pSource = [... image]``let pDestination  = ``new` `Array(m * n);` `// process each buffer``displayMatrix(pSource, m, n);` `rotate(pSource, pDestination, m, n);` `displayMatrix(pDestination, n, m);` `// This code is contributed by phasing17`

Output :

```1    2    3    4
5    6    7    8
9    10    11    12

9    5    1
10    6    2
11    7    3
12    8    4    ```

Time Complexity: O(N*M), as we are using nested loops for traversing the matrix.

Auxiliary Space: O(N*M), as we are using extra space for matrix.

Another Approach:

• The input image is defined as a 2D list of pixels. In this example, the input image has 3 rows and 4 columns.
• The transposed_image matrix is created by swapping the rows and columns of the input image. This is achieved using a nested list comprehension that iterates over the rows and columns of the input image and creates a new matrix where the rows and columns are swapped.
• The rotated_image matrix is created by reversing the order of rows in the transposed_image matrix. This step effectively rotates the image by 90 degrees counterclockwise.
• Finally, the rotated image is printed by iterating over its rows and printing them.

## Python3

 `# define input image as a 2D list of pixels``image ``=` `[[``1``, ``2``, ``3``, ``4``],``         ``[``5``, ``6``, ``7``, ``8``],``         ``[``9``, ``10``, ``11``, ``12``]]` `# transpose image matrix``transposed_image ``=` `[[image[j][i] ``for` `j ``in` `range``(``len``(image))] ``for` `i ``in` `range``(``len``(image[``0``]))]` `# reverse the order of rows to rotate the image by 90 degrees counterclockwise``rotated_image ``=` `[``list``(``reversed``(row)) ``for` `row ``in` `transposed_image]` `# print rotated image``for` `row ``in` `rotated_image:``    ``print``(row)`

## Javascript

 `// define input image as a 2D array of pixels``const image = [[1, 2, 3, 4],``[5, 6, 7, 8],``[9, 10, 11, 12]];` `// transpose image matrix``const transposedImage = image.map((_, i) => image.map(row => row[i]));` `// reverse the order of rows to rotate the image by 90 degrees counterclockwise``const rotatedImage = transposedImage.map(row => row.reverse());` `// print rotated image``for` `(let row of rotatedImage) {``console.log(row);``}`

## C#

 `using` `System;` `class` `Program {``    ``static` `void` `Main(``string``[] args)``    ``{``        ``// Define input image as a 2D array of pixels``        ``int``[, ] image = ``new` `int``[, ] { { 1, 2, 3, 4 },``                                      ``{ 5, 6, 7, 8 },``                                      ``{ 9, 10, 11, 12 } };` `        ``// Transpose image matrix``        ``int``[, ] transposed_image``            ``= ``new` `int``[image.GetLength(1),``                      ``image.GetLength(0)];``        ``for` `(``int` `i = 0; i < image.GetLength(0); i++) {``            ``for` `(``int` `j = 0; j < image.GetLength(1); j++) {``                ``transposed_image[j, i] = image[i, j];``            ``}``        ``}` `        ``// Reverse the order of columns to rotate the image``        ``// by 90 degrees counterclockwise``        ``int``[, ] rotated_image``            ``= ``new` `int``[transposed_image.GetLength(0),``                      ``transposed_image.GetLength(1)];``        ``for` `(``int` `i = 0; i < transposed_image.GetLength(0);``             ``i++) {``            ``for` `(``int` `j = 0;``                 ``j < transposed_image.GetLength(1); j++) {``                ``rotated_image[i, j] = transposed_image``                    ``[i,``                     ``transposed_image.GetLength(1) - 1 - j];``            ``}``        ``}` `        ``// Print rotated image``        ``for` `(``int` `i = 0; i < rotated_image.GetLength(0);``             ``i++) {``            ``Console.Write(``"["``);``            ``for` `(``int` `j = 0; j < rotated_image.GetLength(1);``                 ``j++) {``                ``Console.Write(rotated_image[i, j] + ``", "``);``            ``}``            ``Console.WriteLine(``"]"``);``        ``}``    ``}``}`

Output

```[9, 5, 1]
[10, 6, 2]
[11, 7, 3]
[12, 8, 4]```

Time Complexity: O(N*M)
Auxiliary Space: O(N*M)

Inplace rotate square matrix by 90 degrees Compiled by Venki. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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