There are many games that exist and are played by many people. Sudoku is one of them. This game is played by all ages. This is a comprehensive Sudoku application built in Java that not only allows a user to play the game in a full GUI but also serves as a powerful tool to analyse the performance of different solving algorithms. Sudoku here is solved using two different algorithms. The time complexity and space complexity is being compared for different levels of games. The two algorithms are the traditional Backtracking approach and Dancing Links (DLX), a technique created by Donald Knuth. Results show that Backtracking is easy, simple but slow and becomes more slower for complex levels. On the other hand, DLX is much faster and more reliable for tough puzzles, thanks to the way it organizes and checks possible moves. This comparison shows the balance between choosing a simple method that works for smaller problems and a more advanced one that performs better on harder challenges.