Question

Implement optimized C/C++ code using code optimization techniques

Consider an image to be represented as a two-dimensional matrix M, where Mi,j denotes the value of M[i][j] th pixel of M. Pixel values are triples of red, green, and blue (RGB) values. We will only consider square images. Let N denote the number of rows (or columns) of an image (NxN square image). Rows and columns are numbered, in C-style, from 0 to N-1. Given this representation, the rotate operation can be implemented as the combination of the following two matrix operations:

 Transpose: For each (i,j) pair, Mi,j and Mj,i are interchanged.

 Exchange rows: Row i is exchanged with row N-1-i 1)

First task is to rotate a given image counterclockwise in 90 degree. Use the model image given in the assignment folder for rotation. To do that, first transpose the image then exchange the rows. These operations are illustrated in the following figure. Notice how red pixel moved during matrix transpose and exchange rows matrix operations.

Rotate by 90 (counter-clockwise) (0,0) (0,0) Transpose Exchange Rows Figure 1. Rotation of an image by 90 degree clockwise

Answer 1

Please refer to code screenshots

code screenshot

1 #include <iostream> #define N 4 4 using namespace std; 8 6 // function to transpose of A[][] 7- void transpose(int A[][N]) { int B[N][N]; // grid to store matrix for (int i = 0; i < N; i++){ for (int j = 0; j < N; j++){ B[i][j] = A[j][i]; // getting transpose for(int i = 0; i < N; i++){ for(int j = 0; j < N; j++){ A[i][j] = B[i][j]; // updating grid A 19 20 } 21 22 // function to exchange rows 23 - void exchangeRows(int A[][N]){ for(int i = 0; i < N / 2; i++){ for(int j = 0; j < N; j++){ int p = N - 1 - i; // row to exchange with // exchanging rows using swapping of elements int temp = A[i][j]; A[i][j] = A[p][j]; A[p][j] = temp;

34 35int main() { 36 // matrix for testing functions int A[N][N] = { {10, 10, 10, 10}, {20, 20, 20, 20}, 30, 30, 30, 30}, {40, 40, 40, 40} }; transpose(A); // calling function to get transpose of matrix exchangeRows(A); // calling function to get exhange of rows of matrix cout<<"Matrix after rotation\n"; // displaying matrix after rotation for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++){ cout<<A[i][j]«<' '; cout<< '\n'; return 0;

Output

Matrix after rotation 10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40 ... Program finished with exit code o Press ENTER to exit console.

Code to copy

#include <iostream>
#define N 4

using namespace std;

// function to transpose of A[][]
void transpose(int A[][N]) {
   int B[N][N]; // grid to store matrix
   for (int i = 0; i < N; i++){
       for (int j = 0; j < N; j++){
           B[i][j] = A[j][i]; // getting transpose
       }
   }
          
   for(int i = 0; i < N; i++){
   for(int j = 0; j < N; j++){
   A[i][j] = B[i][j]; // updating grid A
   }
   }
}

// function to exchange rows
void exchangeRows(int A[][N]){
for(int i = 0; i < N / 2; i++){
for(int j = 0; j < N; j++){
int p = N - 1 - i; // row to exchange with
// exchanging rows using swapping of elements
int temp = A[i][j];
A[i][j] = A[p][j];
A[p][j] = temp;
}
}
}

int main() {
// matrix for testing functions
   int A[N][N] = {
   {10, 10, 10, 10},
                   {20, 20, 20, 20},
                   {30, 30, 30, 30},
                   {40, 40, 40, 40}
   };

   transpose(A); // calling function to get transpose of matrix
   exchangeRows(A); // calling function to get exhange of rows of matrix

cout<<"Matrix after rotation\n";
  
// displaying matrix after rotation
   for (int i = 0; i < N; i++) {
       for (int j = 0; j < N; j++){
       cout<<A[i][j]<<' ';
       }
       cout<<'\n';
   }

   return 0;
}