The N-body problem—which simulates the evolution of a system of particles interacting through a gravitational field—holds significant computational challenges due to its inherent complexity. In this work, we implemented and compared two approaches to N-body simulations—a direct method and the Barnes-Hut algorithm. The direct method computes pairwise gravitational forces between all particles (bodies), resulting in an \(\mathcal {O}(N^2)\) time complexity, which ensures accuracy but poorly scales with large systems. Conversely, the Barnes-Hut algorithm leverages a hierarchical tree structure—quadtree for 2D and octree for 3D—to approximate distant forces, achieving a time complexity of \(\mathcal {O}(N\log N)\) and improving performance for large-scale simulations. Both methods were implemented using C++ programming language, combined with the OpenMP library for parallel processing and the SDL2 graphics library for visualization tools. Simulation results highlight the trade-offs between computational cost and precision, with the direct method excelling in small systems and the Barnes-Hut method outperforming it as N increases. This work details the algorithms, their implementations, and performance comparisons, offering insights into their practical applications and limitations.