In this article, we will learn to rotate images by 90 degrees using C++. Top recruiters have asked about this problem many times during tech interviews. Not only this, but this particular problem also has considerable significance in our daily lives.

Almost every smartphone has this feature to allow users to rotate images. This feature is of great importance for photo editors and graphic designers. Today we will see how this feature works on the code side of things. What is the algorithm behind it? So without any delay, let’s go through the problem statement.

## Problem Statement

*Given a two-dimensional matrix of RGB values, rotate the matrix by 90 degrees in the anticlockwise direction.*

All the images are simply two-dimensional matrices of RGB(Red, Green, and Blue) values. Rotation of an image implies that we have to rotate the RGB values stored in the image bitmap.

**Note:** In this article, we will only consider square matrices.

For example,

```
Input:
1 2 3 4
5 6 7 8
9 10 1112
13 14 15 16
Output:
4 8 12 16
3 7 11 15
2 6 10 14
1 5 9 13
```

## Concept of Rotating Images using C++

There are multiple ways to solve this problem. For ease of understanding, we will only cover the simplest method. We are going to approach this problem without using any extra space. One way can be to map each element with its new position. But this can be quite complex to code. We will follow the steps given below to write the code.

```
Input:
1 2 3 4
5 6 7 8
9 10 1112
13 14 15 16
Output:
4 8 12 16
3 7 11 15
2 6 10 14
1 5 9 13
Did you notice any relation between the input and the output?
If you did, you've nailed it. There's no need to worry if you haven't.
Step 1: Reverse the input matrix(row-wise)
1 2 3 4 --> 4 3 2 1
5 6 7 8 --> 8 7 6 5
9 10 1112 --> 12 11 10 9
13 14 15 16 --> 16 15 14 13
Now, if you notice carefully, you will find that the output matrix is just a transpose of this matrix.
Step 2: Take the transpose
4 3 2 1 --> 4 8 12 16
8 7 6 5 --> 3 7 11 15
12 11 10 9 --> 2 6 10 14
16 15 14 13 --> 1 5 9 13
```

Now, it’s time to write the code.

## Algorithm for Rotating Images using C++

```
void rotate_matrix(vector <vector <int>> &v)
{
int n = v.size();
// first reverse the vector row-wise
// we can either use the pre-defined
// stl reverse function or we can use
// for loops
for(int row = 0; row < n; row++)
{
int start_col = 0;
int end_col = n - 1;
while(start_col < end_col)
{
swap(v[row][start_col], v[row][end_col]);
start_col++;
end_col--;
}
}
// now transpose the vector
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
if(i < j)
swap(v[i][j], v[j][i]);
return;
}
```

## Implementing Image Rotation Using C++

```
#include <iostream>
#include <vector>
using namespace std;
void rotate_matrix(vector <vector <int>> &v)
{
int n = v.size();
// first reverse the vector row-wise
// we can either use the pre-defined
// stl reverse function or we can use
// for loops
for(int row = 0; row < n; row++)
{
int start_col = 0;
int end_col = n - 1;
while(start_col < end_col)
{
swap(v[row][start_col], v[row][end_col]);
start_col++;
end_col--;
}
}
// now transpose the vector
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
if(i < j)
swap(v[i][j], v[j][i]);
return;
}
void print_matrix(vector <vector <int>> v)
{
cout << "The rotated matrix is:" << endl;
for(int i = 0; i < v.size(); i++)
{
for(int j = 0; j < v.size(); j++)
cout << v[i][j] << " ";
cout << endl;
}
cout << endl;
}
int main()
{
cout << "Enter the size of the vector" << endl;
int n;
cin >> n;
vector <vector <int>> v(n, vector <int> (n, 0));
for(int i = 0; i < n; i++)
{
for(int j = 0; j < n; j++)
{
int ele;
cin >> ele;
v[i][j] = ele;
}
}
rotate_matrix(v);
print_matrix(v);
return 0;
}
```

## Output

## Conclusion

In this article, we learned to rotate an image by 90 degrees in the anti-clockwise direction using C++. The concept is simple and just comprises two steps. In the end, we wrote the algorithm, and a driver program using C++. The output shows the example matrix being rotated three times. The final rotation angle of the output matrix is 270 degrees. That’s all for today, thanks for reading.

## Further Readings

To learn more about vectors algorithms, you can also go through the following articles.

https://www.journaldev.com/60624/staircase-search-on-sorted-2d-matrices-cpp

https://www.journaldev.com/60799/spirally-read-2d-matrices-cpp