In this task, you need to write a command-line MPI application that can perform the N-body simulation in parallel on a distributed-memory system.

For this work, you will get a sample Unity project that you can use as a reference to understand the algorithms and the simulation itself. The solution in Unity is single-threaded and thus slow for high numbers of planets.

Your program should generate a similar sample set of planetary bodies as it is generated in the GenerateDebugData method in the PlayerController.cs file.

The PlanetController class should be turned into a simple array or struct to store position, mass, velocity, and other required state variables for each planet.

The program should only calculate the acceleration and output it to a file for a certain simulation time period (allow to specify it as command-line parameters).

The output should start with two numbers. On the first line output the number of bodies in the system. On the next line, output the Delta Time of the simulation. After that, write all the acceleration vector components for x and y separated by a whitespace. Each acceleration vector should be specified on a separate line.

Write a program that performs the brute-force O(N^2) simulation outlined in the method SimulateWithBruteforce in GravitationalSimulator.cs. You can get the maximum grade just by doing this option.

For extra points, try to parallelize the Barnes-Hut approach outlined in the method SimulateWithBarnesHut in GravitationalSimulator.cs. You can only do this option to get the full grade and extra points.