Cubesort

Cube sort is a comparison sorting algorithm that sorts an array by first computing the cube of each element, then sorting based on the cubed values.

Java example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
void cubeSort(int[] arr) {
  int n = arr.length;
    
  // Compute cubed values
  int[] cubed = new int[n];
  for (int i = 0; i < n; i++) {
    cubed[i] = arr[i] * arr[i] * arr[i]; 
  }
  
  // Sort based on cubed values
  Arrays.sort(cubed); 
  
  // Modify original array based on sort order
  for (int i = 0; i < n; i++) {
    arr[i] = cubed[i]; 
  }
}

C++ example:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
void cubeSort(vector<int>& arr) {
  int n = arr.size();

  vector<int> cubed(n);
  for (int i = 0; i < n; i++) {
    cubed[i] = arr[i] * arr[i] * arr[i];
  }

  sort(cubed.begin(), cubed.end());

  for (int i = 0; i < n; i++) {
    arr[i] = cubed[i];
  } 
}

Python example:

1
2
3
4
5
6
7
8
9
def cube_sort(arr):
  n = len(arr)
  
  cubed = [num**3 for num in arr]
  
  cubed.sort()

  for i in range(n): 
    arr[i] = cubed[i]

Cube sort demonstrates a different sorting strategy by transforming elements before comparing. It has average case complexity of O(n log n).

Cubesort is a parallel sorting algorithm that builds a self-balancing multi-dimensional array. As a parallel sorting algorithm, it divides the data into smaller parts and sorts them simultaneously. Cubesort’s structure allows for a highly parallel and distributed implementation, making it well-suited for hardware acceleration or use in distributed computing systems.

Despite its intriguing concept, cubesort isn’t widely used in practice, partly due to its complexity and the ease with which other, simpler algorithms can be parallelized.

Example Code

Here are skeleton examples for implementing Cubesort. Note that these are basic templates; the full implementation would be quite complex.

Java

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
public class CubeSort {
    // Cubesort main function
    public static void cubeSort(int[] arr) {
        // Implementation here
    }

    // Subfunction to sort individual cubes
    private static void sortCube(int[] cube) {
        // Implementation here
    }
    
    public static void main(String[] args) {
        int[] arr = { /* some integers */ };
        cubeSort(arr);
    }
}

C++

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
#include <iostream>
#include <vector>
using namespace std;

// Cubesort main function
void cubeSort(vector<int>& arr) {
    // Implementation here
}

// Subfunction to sort individual cubes
void sortCube(vector<int>& cube) {
    // Implementation here
}

int main() {
    vector<int> arr = { /* some integers */ };
    cubeSort(arr);
    return 0;
}

Python

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
def cube_sort(arr):
    # Implementation here
    pass

def sort_cube(cube):
    # Implementation here
    pass

if __name__ == "__main__":
    arr = [ /* some integers */ ]
    cube_sort(arr)

These are bare-bone structures, and the actual implementation would require more detail, especially for handling the parallel aspects and the multi-dimensional array.