1-7-matrix-rotation Algorithm
The 1-7-matrix-rotation Algorithm is a technique used for rotating a given NxN matrix by 90 degrees in a clockwise direction. This algorithm is particularly useful in image processing and computer graphics, where images or objects need to be manipulated by rotating them. It is a popular interview question for software engineering and data structure interviews, as it tests the candidate's problem-solving and programming skills.
The algorithm works by dividing the matrix into four equal partitions or layers and iteratively rotating the elements in each layer. The rotation process involves swapping the elements from the four corners of each layer, starting from the outermost layer and moving inwards. The process is repeated for the remaining layers until the entire matrix is rotated. This algorithm has a time complexity of O(N^2), as each element in the matrix is visited once, and a space complexity of O(1), as the rotation is done in-place without using any additional data structures.
#include<iostream>
void helper_transpose(int **matrix, int N)
{
for( int i = 0; i < N; ++i ) {
for( int j = i+1; j < N; ++j ) {
if ( i != j ) {
std::swap(matrix[i][j], matrix[j][i]);
}
}
}
}
void helper_reverse( int * row, int N ) {
for ( int i = 0; i < N/2; ++i ) {
std::swap(row[i], row[N-i-1]);
}
}
void rotate1(int ** matrix, int N) {
//transpose matrix
helper_transpose(matrix, N);
// reverse each row
for ( int i = 0; i < N; ++i ) {
helper_reverse(matrix[i], N);
}
}
void rotate2( int ** matrix, int N ) {
for( int i = 0; i < N/2; ++i ) {
for( int j = i; j < N-i-1; ++j ) {
int temp = matrix[i][j];
matrix[i][j] = matrix[j][N-i-1];
matrix[j][N-i-1] = matrix[N-i-1][N-j-1];
matrix[N-i-1][N-j-1]= matrix[N-j-1][i];
matrix[N-j-1][i] = temp;
}
}
}
void printMatrix( int ** matrix, int N) {
for ( int i = 0; i < N; ++i ) {
for( int j = 0; j < N; ++j ) {
std::cout << matrix[i][j] << " ";
}
std::cout << std::endl;
}
}
int main() {
int N;
std::cout << "Enter N for NxN matrix:";
std::cin >> N;
int ** matrix = new int*[N];
for ( int i = 0; i < N; ++i ) {
matrix[i] = new int[N];
}
for ( int i = 0; i < N; ++i) {
for ( int j = 0; j < N; ++j ) {
std::cin >> matrix[i][j];
}
}
std::cout << "Rotated matrix by 90 (clockwise):\n";
rotate1(matrix, N);
printMatrix(matrix, N);
std::cout << "Rotated matrix again by 90(anticlockwise):\n";
rotate2(matrix, N);
printMatrix(matrix, N);
return 0;
}
