# Analysis of search and neural network based algorithms for different complexity variations of the game of dots and boxes

Title: Analysis of search and neural network-based algorithms for different complexity variations of the game of dots and boxes Goal: To analyze how the efficiency of existing game implementation algorithms changes depending on the complexity of the game based on the case study of the dots and boxes case study. Tasks (with short explanations): 1. Explaining the main concepts of computer implementations of games with full implementation. Besides other concepts you should elaborate on the notion of the complexity of the game depending on the size of the board. You should develop a mathematical model based on the existing theories for evaluating the complexity of the game. 2. Overview of the search based game implementation algorithms Here you have to shortly explain the idea of the search based implementations of the games and describe existing algorithms in the context of the game of dots and boxes. Since, this game is a bit specific (if you score a point, you make another move), you will have to slightly adapt the algorithms for your game. The result of this task would be a unified description of existing search based algorithms and a comparison of them to choose algorithms for the implementation. Also heuristic functions should be elaborated here. 3. Overview of neural network based game implementation algorithms The same as for task number 1, but about neural network based algorithms and their use in dots and boxes game. 4. Implementation of game environment (the mechanism of the game is the main thing, not UI) and implementation of the chosen algorithms The result of the task is implemented game environment with the possibility for the algorithms to play each other automatically as well as the implementations of the chosen algorithms. There should be several implementations of search based algorithms and at least one NN based. 5. Practical evaluation of the efficiency of the game implementation algorithms depending on the complexity of the game Designing and conducting the experiment with dots and boxes to empirically evaluate the chosen algorithms and to provide the guidelines for choosing an appropriate algorithm for an implementation of a game engine for a game with full information depending on the complexity of the game. The only remark: I believe that having only 3 different sizes is too few to give meaningful conclusions about this dependency of efficiency from the complexity of the game. Please calculate the approximate complexity of the state space depending on the size of the board to understand what can be one by brute force search. I suggest to calculate the growth of the complexity depending on the size to see what can actually be done.
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