$10)$ a$)$ Consider a game tree with a branching factor of $10$ and a depth of $6.$ The evaluation function for thisgame returns a value between $-100$ and $100,$ representing the utility of a state. The game tree is fully expanded, meaning that all possible moves at each level have been explored.

Now, imagine that you are using the alpha beta pruning algorithm to search this game tree. At a certain point during the search, you have an alpha value of $80$ and a beta value of $90.$

Given this scenario, can you determine the exact number of nodes that would be pruned using alpha$-$beta pruning? Justify your answer.

Provide an example of a situation in which alpha$-$beta pruning would not be effective in reducing the number of nodes expanded. Explain why this situation occurs and discuss any potential implications for the search process.

b$)$ Consider a highly competitive game, such as Chess or Go$,$ where the Alpha Beta Pruning algorithm plays a critical role in optimizing the search process.

I Explain the concept of "cutoffs" in the Alpha Beta Pruning algorithm and how they affect the efficiency and accuracy of the algorithm. Provide a detailed example game scenario where a cutoff occurs, and discuss the implications of cutoffs on the quality of the Al's decision$-$making process.

Explore the impact of move ordering on the performance of the Alpha$-$Beta Pruning algoritm. Discuss different heuristics or strategies for ordering moves and their influence the pruning process. Provide an example scenario where move ordering significantly improves the efficiency of the algorithm.